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2
Task/Non-transitive-dice/00-META.yaml
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2
Task/Non-transitive-dice/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Non-transitive_dice
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86
Task/Non-transitive-dice/00-TASK.txt
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86
Task/Non-transitive-dice/00-TASK.txt
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Let our dice select numbers on their faces with equal probability, i.e. fair dice.
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Dice may have more or less than six faces. (The possibility of there being a
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3D physical shape that has that many "faces" that allow them to be fair dice,
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is ignored for this task - a die with 3 or 33 defined sides is defined by the
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number of faces and the numbers on each face).
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Throwing dice will randomly select a face on each die with equal probability.
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To show which die of dice thrown multiple times is more likely to win over the
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others:
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# calculate all possible combinations of different faces from each die
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# Count how many times each die wins a combination
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# Each ''combination'' is equally likely so the die with more winning face combinations is statistically more likely to win against the other dice.
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<br>
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'''If two dice X and Y are thrown against each other then X likely to: win, lose, or break-even against Y can be shown as: <code>X > Y, X < Y, or X = Y</code> respectively.
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'''
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;Example 1:
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If X is the three sided die with 1, 3, 6 on its faces and Y has 2, 3, 4 on its
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faces then the equal possibility outcomes from throwing both, and the winners
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is:
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X Y Winner
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= = ======
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1 2 Y
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1 3 Y
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1 4 Y
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3 2 X
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3 3 -
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3 4 Y
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6 2 X
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6 3 X
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6 4 X
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TOTAL WINS: X=4, Y=4
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Both die will have the same statistical probability of winning, i.e.their comparison can be written as <code>X = Y</code>
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;Transitivity:
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In mathematics transitivity are rules like:
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if a op b and b op c then a op c
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If, for example, the op, (for operator), is the familiar less than, <, and it's applied to integers
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we get the familiar <code>if a < b and b < c then a < c</code>
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;Non-transitive dice
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These are an ordered list of dice where the '>' operation between successive
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dice pairs applies but a comparison between the first and last of the list
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yields the opposite result, '<'.<br>
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''(Similarly '<' successive list comparisons with a final '>' between first and last is also non-transitive).''
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<br><br>
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Three dice S, T, U with appropriate face values could satisfy
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S < T, T < U and yet S > U
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To be non-transitive.
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;Notes:
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* The order of numbers on the faces of a die is not relevant. For example, three faced die described with face numbers of 1, 2, 3 or 2, 1, 3 or any other permutation are equivalent. For the purposes of the task '''show only the permutation in lowest-first sorted order i.e. 1, 2, 3''' (and remove any of its perms).
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* A die can have more than one instance of the same number on its faces, e.g. <code>2, 3, 3, 4</code>
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* '''Rotations''': Any rotation of non-transitive dice from an answer is also an answer. You may ''optionally'' compute and show only one of each such rotation sets, ideally the first when sorted in a natural way. If this option is used then prominently state in the output that rotations of results are also solutions.
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<br><br>
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;Task:
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;====
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Find all the ordered lists of ''three'' non-transitive dice S, T, U of the form
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S < T, T < U and yet S > U; where the dice are selected from all ''four-faced die''
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, (unique w.r.t the notes), possible by having selections from the integers
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''one to four'' on any dies face.
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Solution can be found by generating all possble individual die then testing all
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possible permutations, (permutations are ordered), of three dice for
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non-transitivity.
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;Optional stretch goal:
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Find lists of '''four''' non-transitive dice selected from the same possible dice from the non-stretch goal.
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<br><br>
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Show the results here, on this page.
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<br>
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;References:
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* [https://youtu.be/zzKGnuvX6IQ The Most Powerful Dice] - Numberphile Video.
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* [https://en.wikipedia.org/wiki/Nontransitive_dice Nontransitive dice] - Wikipedia.
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<br>
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93
Task/Non-transitive-dice/ALGOL-68/non-transitive-dice.alg
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93
Task/Non-transitive-dice/ALGOL-68/non-transitive-dice.alg
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# iterates through all possible dice #
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PROC iterate = (PROC(INT, []INT)VOID f)VOID:
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BEGIN
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INT n := 1;
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[4]INT sides;
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FOR i FROM 1 TO 4 DO FOR j FROM i TO 4 DO
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FOR k FROM j TO 4 DO FOR l FROM k TO 4 DO
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sides := (i, j, k, l);
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f(n, sides);
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n +:= 1
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OD OD OD OD
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END;
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# compares 2 dice, returns (-1, 0, 1) for a (<, =, >) b #
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PROC compare = ([]INT a, []INT b)INT:
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BEGIN
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INT result := 0;
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FOR i TO UPB a DO
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FOR j TO UPB b DO
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result +:= SIGN(a[i] - b[j])
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OD
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OD;
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SIGN result
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END;
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# compact representation of die #
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PROC str = ([]INT die)STRING:
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BEGIN
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STRING result := " " * UPB die;
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FOR i TO UPB die DO
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result[i] := REPR (die[i] + ABS "0")
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OD;
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result
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END;
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# first count all possible dice #
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INT ndice := 0;
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iterate((INT n, []INT sides)VOID: ndice +:= 1);
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# store them by index #
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[ndice][4]INT dice;
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iterate((INT n, []INT sides)VOID: dice[n] := sides);
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# fill the results of an all-play-all tournament #
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[ndice,ndice]INT results;
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FOR i TO ndice DO
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FOR j FROM i TO ndice DO
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results[i,j] := compare(dice[i], dice[j]);
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results[j,i] := results[i,j] * -1
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OD
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OD;
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# helper function to print the intransitive sequence #
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PROC print seq = ([]INT idxs)VOID:
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BEGIN
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FOR i TO UPB idxs DO
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IF i > 1 THEN print((" < ")) FI;
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print((str(dice[idxs[i]])))
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OD;
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print((newline))
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END;
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# find all (s,t,u) where s < t < u < s #
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print(("3 dice:", newline));
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FOR s TO ndice DO
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FOR t TO ndice DO
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IF results[s,t] = -1 THEN
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FOR u TO ndice DO
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IF results[t,u] = -1 AND results[u,s] = -1 THEN
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print seq((s, t, u, s))
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FI
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OD
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FI
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OD
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OD;
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# find all (s,t,u,v) where s < t < u < v < s #
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print(("4 dice:", newline));
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FOR s TO ndice DO
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FOR t TO ndice DO
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IF results[s,t] = -1 THEN
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FOR u TO ndice DO
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IF results[t,u] = -1 THEN
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FOR v TO ndice DO
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IF results[u,v] = -1 AND results[v,s] = -1 THEN
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print seq((s, t, u, v, s))
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FI
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OD
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FI
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OD
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FI
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OD
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OD
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@ -0,0 +1,7 @@
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// Non-transitive dice. Nigel Galloway: August 9th., 2020
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let die=[for n0 in [1..4] do for n1 in [n0..4] do for n2 in [n1..4] do for n3 in [n2..4]->[n0;n1;n2;n3]]
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let N=seq{for n in die->(n,[for g in die do if (seq{for n in n do for g in g->compare n g}|>Seq.sum<0) then yield g])}|>Map.ofSeq
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let n3=seq{for d1 in die do for d2 in N.[d1] do for d3 in N.[d2] do if List.contains d1 N.[d3] then yield (d1,d2,d3)}
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let n4=seq{for d1 in die do for d2 in N.[d1] do for d3 in N.[d2] do for d4 in N.[d3] do if List.contains d1 N.[d4] then yield (d1,d2,d3,d4)}
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n3|>Seq.iter(fun(d1,d2,d3)->printfn "%A<%A; %A<%A; %A>%A\n" d1 d2 d2 d3 d1 d3)
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n4|>Seq.iter(fun(d1,d2,d3,d4)->printfn "%A<%A; %A<%A; %A<%A; %A>%A" d1 d2 d2 d3 d3 d4 d1 d4)
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// Non-transitive diceNigel Galloway: August 9th., 2020
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let die=[for n0 in [1..6] do for n1 in [n0..6] do for n2 in [n1..6] do for n3 in [n2..6] do for n4 in [n3..6] do for n5 in [n4..6]->[n0;n1;n2;n3;n4;n5]]
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let N=seq{for n in die->(n,[for g in die do if (seq{for n in n do for g in g->compare n g}|>Seq.sum<0) then yield g])}|>Map.ofSeq
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let n3=[for d1 in die do for d2 in N.[d1] do for d3 in N.[d2] do if List.contains d1 N.[d3] then yield (d1,d2,d3)]
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let d1,d2,d3=List.last n3 in printfn "Solutions found = %d\nLast solution found is %A<%A; %A<%A; %A>%A" (n3.Length) d1 d2 d2 d3 d1 d3
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@ -0,0 +1,5 @@
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// Non-transitive diceNigel Galloway: August 9th., 2020
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let die=[for n0 in [1..7] do for n1 in [n0..7] do for n2 in [n1..7] do for n3 in [n2..7] do for n4 in [n3..7] do for n5 in [n4..7]->[n0;n1;n2;n3;n4;n5]]
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let N=seq{for n in die->(n,[for g in die do if (seq{for n in n do for g in g->compare n g}|>Seq.sum<0) then yield g])}|>Map.ofSeq
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let n3=[for d1 in die do for d2 in N.[d1] do for d3 in N.[d2] do if List.contains d1 N.[d3] then yield (d1,d2,d3)]
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let d1,d2,d3=List.last n3 in printfn "Solutions found = %d\nLast solution found is %A<%A; %A<%A; %A>%A" (n3.Length) d1 d2 d2 d3 d1 d3
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25
Task/Non-transitive-dice/Factor/non-transitive-dice.factor
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25
Task/Non-transitive-dice/Factor/non-transitive-dice.factor
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@ -0,0 +1,25 @@
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USING: grouping io kernel math math.combinatorics math.ranges
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prettyprint sequences ;
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: possible-dice ( n -- seq )
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[ [1,b] ] [ selections ] bi [ [ <= ] monotonic? ] filter ;
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: cmp ( seq seq -- n ) [ - sgn ] cartesian-map concat sum ;
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: non-transitive? ( seq -- ? )
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[ 2 clump [ first2 cmp neg? ] all? ]
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[ [ last ] [ first ] bi cmp neg? and ] bi ;
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: find-non-transitive ( #sides #dice -- seq )
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[ possible-dice ] [ <k-permutations> ] bi*
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[ non-transitive? ] filter ;
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! Task
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"Number of eligible 4-sided dice: " write
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4 possible-dice length . nl
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"All ordered lists of 3 non-transitive dice with 4 sides:" print
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4 3 find-non-transitive . nl
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"All ordered lists of 4 non-transitive dice with 4 sides:" print
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4 4 find-non-transitive .
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108
Task/Non-transitive-dice/Go/non-transitive-dice.go
Normal file
108
Task/Non-transitive-dice/Go/non-transitive-dice.go
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package main
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import (
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"fmt"
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"sort"
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)
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func fourFaceCombs() (res [][4]int) {
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found := make([]bool, 256)
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for i := 1; i <= 4; i++ {
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for j := 1; j <= 4; j++ {
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for k := 1; k <= 4; k++ {
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for l := 1; l <= 4; l++ {
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c := [4]int{i, j, k, l}
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sort.Ints(c[:])
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key := 64*(c[0]-1) + 16*(c[1]-1) + 4*(c[2]-1) + (c[3] - 1)
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if !found[key] {
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found[key] = true
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res = append(res, c)
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}
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}
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}
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}
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}
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return
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}
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func cmp(x, y [4]int) int {
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xw := 0
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yw := 0
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for i := 0; i < 4; i++ {
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for j := 0; j < 4; j++ {
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if x[i] > y[j] {
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xw++
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} else if y[j] > x[i] {
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yw++
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}
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}
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}
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if xw < yw {
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return -1
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} else if xw > yw {
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return 1
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}
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return 0
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}
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func findIntransitive3(cs [][4]int) (res [][3][4]int) {
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var c = len(cs)
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for i := 0; i < c; i++ {
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for j := 0; j < c; j++ {
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for k := 0; k < c; k++ {
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first := cmp(cs[i], cs[j])
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if first == -1 {
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second := cmp(cs[j], cs[k])
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if second == -1 {
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third := cmp(cs[i], cs[k])
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if third == 1 {
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res = append(res, [3][4]int{cs[i], cs[j], cs[k]})
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}
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}
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}
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}
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}
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}
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return
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}
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func findIntransitive4(cs [][4]int) (res [][4][4]int) {
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c := len(cs)
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for i := 0; i < c; i++ {
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for j := 0; j < c; j++ {
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for k := 0; k < c; k++ {
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for l := 0; l < c; l++ {
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first := cmp(cs[i], cs[j])
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if first == -1 {
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second := cmp(cs[j], cs[k])
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if second == -1 {
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third := cmp(cs[k], cs[l])
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if third == -1 {
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fourth := cmp(cs[i], cs[l])
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if fourth == 1 {
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res = append(res, [4][4]int{cs[i], cs[j], cs[k], cs[l]})
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}
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}
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}
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}
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}
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}
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}
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}
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return
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}
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func main() {
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combs := fourFaceCombs()
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fmt.Println("Number of eligible 4-faced dice", len(combs))
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it3 := findIntransitive3(combs)
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fmt.Printf("\n%d ordered lists of 3 non-transitive dice found, namely:\n", len(it3))
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for _, a := range it3 {
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fmt.Println(a)
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}
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it4 := findIntransitive4(combs)
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fmt.Printf("\n%d ordered lists of 4 non-transitive dice found, namely:\n", len(it4))
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for _, a := range it4 {
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fmt.Println(a)
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}
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}
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27
Task/Non-transitive-dice/Haskell/non-transitive-dice.hs
Normal file
27
Task/Non-transitive-dice/Haskell/non-transitive-dice.hs
Normal file
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@ -0,0 +1,27 @@
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{-# language LambdaCase #-}
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import Data.List
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import Control.Monad
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newtype Dice = Dice [Int]
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instance Show Dice where
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show (Dice s) = "(" ++ unwords (show <$> s) ++ ")"
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instance Eq Dice where
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d1 == d2 = d1 `compare` d2 == EQ
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instance Ord Dice where
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Dice d1 `compare` Dice d2 = (add $ compare <$> d1 <*> d2) `compare` 0
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where
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add = sum . map (\case {LT -> -1; EQ -> 0; GT -> 1})
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dices n = Dice <$> (nub $ sort <$> replicateM n [1..n])
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nonTrans dice = filter (\x -> last x < head x) . go
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where
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go 0 = []
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go 1 = sequence [dice]
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go n = do
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(a:as) <- go (n-1)
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b <- filter (< a) dice
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return (b:a:as)
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15
Task/Non-transitive-dice/J/non-transitive-dice-1.j
Normal file
15
Task/Non-transitive-dice/J/non-transitive-dice-1.j
Normal file
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|
@ -0,0 +1,15 @@
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NB. unique list of all y faced dice
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udice=: {{ 1+~./:~"1 (#: ,@i.)y#y }}
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NB. which dice are less than which other dice?
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NB. y here is a result of udice
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lthan=: {{ 0>*@(+/)@,@:*@(-/)"1/~ y}}
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NB. "less than loops" length x, for y sided non-transitive dice
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cycles=: {{
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ud=. udice y
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lt=. lthan ud
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extend=. [:; lt{{< y,"1 0 y-.~I.m{~{:y }}"1
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r=. ; extend^:(x-1)&.> i.#ud
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ud{~ ~.((i.<./)|.])"1 r #~ lt{~({:,&.>{.)|:r
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}}
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9
Task/Non-transitive-dice/J/non-transitive-dice-2.j
Normal file
9
Task/Non-transitive-dice/J/non-transitive-dice-2.j
Normal file
|
|
@ -0,0 +1,9 @@
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3 cycles 4
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1 1 4 4
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2 2 2 4
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1 3 3 3
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4 cycles 4
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1 1 4 4
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2 2 2 4
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2 2 3 3
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1 3 3 3
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||||
106
Task/Non-transitive-dice/Java/non-transitive-dice.java
Normal file
106
Task/Non-transitive-dice/Java/non-transitive-dice.java
Normal file
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|
@ -0,0 +1,106 @@
|
|||
import java.util.ArrayList;
|
||||
import java.util.HashSet;
|
||||
import java.util.List;
|
||||
import java.util.Set;
|
||||
import java.util.stream.Collectors;
|
||||
import java.util.stream.IntStream;
|
||||
|
||||
public class Main {
|
||||
private static List<List<Integer>> fourFaceCombos() {
|
||||
List<List<Integer>> res = new ArrayList<>();
|
||||
Set<Integer> found = new HashSet<>();
|
||||
|
||||
for (int i = 1; i <= 4; i++) {
|
||||
for (int j = 1; j <= 4; j++) {
|
||||
for (int k = 1; k <= 4; k++) {
|
||||
for (int l = 1; l <= 4; l++) {
|
||||
List<Integer> c = IntStream.of(i, j, k, l).sorted().boxed().collect(Collectors.toList());
|
||||
|
||||
int key = 64 * (c.get(0) - 1) + 16 * (c.get(1) - 1) + 4 * (c.get(2) - 1) + (c.get(3) - 1);
|
||||
if (found.add(key)) {
|
||||
res.add(c);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
private static int cmp(List<Integer> x, List<Integer> y) {
|
||||
int xw = 0;
|
||||
int yw = 0;
|
||||
for (int i = 0; i < 4; i++) {
|
||||
for (int j = 0; j < 4; j++) {
|
||||
if (x.get(i) > y.get(j)) {
|
||||
xw++;
|
||||
} else if (x.get(i) < y.get(j)) {
|
||||
yw++;
|
||||
}
|
||||
}
|
||||
}
|
||||
return Integer.compare(xw, yw);
|
||||
}
|
||||
|
||||
private static List<List<List<Integer>>> findIntransitive3(List<List<Integer>> cs) {
|
||||
int c = cs.size();
|
||||
List<List<List<Integer>>> res = new ArrayList<>();
|
||||
|
||||
for (int i = 0; i < c; i++) {
|
||||
for (int j = 0; j < c; j++) {
|
||||
if (cmp(cs.get(i), cs.get(j)) == -1) {
|
||||
for (List<Integer> kl : cs) {
|
||||
if (cmp(cs.get(j), kl) == -1 && cmp(kl, cs.get(i)) == -1) {
|
||||
res.add(List.of(cs.get(i), cs.get(j), kl));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
private static List<List<List<Integer>>> findIntransitive4(List<List<Integer>> cs) {
|
||||
int c = cs.size();
|
||||
List<List<List<Integer>>> res = new ArrayList<>();
|
||||
|
||||
for (int i = 0; i < c; i++) {
|
||||
for (int j = 0; j < c; j++) {
|
||||
if (cmp(cs.get(i), cs.get(j)) == -1) {
|
||||
for (int k = 0; k < cs.size(); k++) {
|
||||
if (cmp(cs.get(j), cs.get(k)) == -1) {
|
||||
for (List<Integer> ll : cs) {
|
||||
if (cmp(cs.get(k), ll) == -1 && cmp(ll, cs.get(i)) == -1) {
|
||||
res.add(List.of(cs.get(i), cs.get(j), cs.get(k), ll));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
List<List<Integer>> combos = fourFaceCombos();
|
||||
System.out.printf("Number of eligible 4-faced dice: %d%n", combos.size());
|
||||
System.out.println();
|
||||
|
||||
List<List<List<Integer>>> it3 = findIntransitive3(combos);
|
||||
System.out.printf("%d ordered lists of 3 non-transitive dice found, namely:%n", it3.size());
|
||||
for (List<List<Integer>> a : it3) {
|
||||
System.out.println(a);
|
||||
}
|
||||
System.out.println();
|
||||
|
||||
List<List<List<Integer>>> it4 = findIntransitive4(combos);
|
||||
System.out.printf("%d ordered lists of 4 non-transitive dice found, namely:%n", it4.size());
|
||||
for (List<List<Integer>> a : it4) {
|
||||
System.out.println(a);
|
||||
}
|
||||
}
|
||||
}
|
||||
76
Task/Non-transitive-dice/Julia/non-transitive-dice.julia
Normal file
76
Task/Non-transitive-dice/Julia/non-transitive-dice.julia
Normal file
|
|
@ -0,0 +1,76 @@
|
|||
import Base.>, Base.<
|
||||
using Memoize, Combinatorics
|
||||
|
||||
struct Die
|
||||
name::String
|
||||
faces::Vector{Int}
|
||||
end
|
||||
|
||||
""" Compares two die returning 1, -1 or 0 for operators >, < == """
|
||||
function cmpd(die1, die2)
|
||||
# Numbers of times one die wins against the other for all combinations
|
||||
# cmp(x, y) is `(x > y) - (y > x)` to return 1, 0, or -1 for numbers
|
||||
tot = [0, 0, 0]
|
||||
for d in Iterators.product(die1.faces, die2.faces)
|
||||
tot[2 + (d[1] > d[2]) - (d[2] > d[1])] += 1
|
||||
end
|
||||
return (tot[3] > tot[1]) - (tot[1] > tot[3])
|
||||
end
|
||||
|
||||
Base.:>(d1::Die, d2::Die) = cmpd(d1, d2) == 1
|
||||
Base.:<(d1::Die, d2::Die) = cmpd(d1, d2) == -1
|
||||
|
||||
""" True iff ordering of die in dice is non-transitive """
|
||||
isnontrans(dice) = all(x -> x[1] < x[2], zip(dice[1:end-1], dice[2:end])) && dice[1] > dice[end]
|
||||
|
||||
findnontrans(alldice, n=3) = [perm for perm in permutations(alldice, n) if isnontrans(perm)]
|
||||
|
||||
function possible_dice(sides, mx)
|
||||
println("\nAll possible 1..$mx $sides-sided dice")
|
||||
dice = [Die("D $(n+1)", [i for i in f]) for (n, f) in
|
||||
enumerate(Iterators.product(fill(1:mx, sides)...))]
|
||||
println(" Created $(length(dice)) dice")
|
||||
println(" Remove duplicate with same bag of numbers on different faces")
|
||||
uniquedice = collect(values(Dict(sort(d.faces) => d for d in dice)))
|
||||
println(" Return $(length(uniquedice)) filtered dice")
|
||||
return uniquedice
|
||||
end
|
||||
|
||||
""" Compares two die returning their relationship of their names as a string """
|
||||
function verbosecmp(die1, die2)
|
||||
# Numbers of times one die wins against the other for all combinations
|
||||
win1 = sum(p[1] > p[2] for p in Iterators.product(die1.faces, die2.faces))
|
||||
win2 = sum(p[2] > p[1] for p in Iterators.product(die1.faces, die2.faces))
|
||||
n1, n2 = die1.name, die2.name
|
||||
return win1 > win2 ? "$n1 > $n2" : win1 < win2 ? "$n1 < $n2" : "$n1 = $n2"
|
||||
end
|
||||
|
||||
""" Dice cmp function with verbose extra checks """
|
||||
function verbosedicecmp(dice)
|
||||
return join([[verbosecmp(x, y) for (x, y) in zip(dice[1:end-1], dice[2:end])];
|
||||
[verbosecmp(dice[1], dice[end])]], ", ")
|
||||
end
|
||||
|
||||
function testnontransitivedice(faces)
|
||||
dice = possible_dice(faces, faces)
|
||||
for N in (faces < 5 ? [3, 4] : [3]) # length of non-transitive group of dice searched for
|
||||
nontrans = unique(map(x -> sort!(x, lt=(x, y)->x.name<y.name), findnontrans(dice, N)))
|
||||
println("\n Unique sorted non_transitive length-$N combinations found: $(length(nontrans))")
|
||||
for list in (faces < 5 ? nontrans : [nontrans[end]])
|
||||
println(faces < 5 ? "" : " Only printing last example for brevity")
|
||||
for (i, die) in enumerate(list)
|
||||
println(" $die$(i < N - 1 ? "," : "]")")
|
||||
end
|
||||
end
|
||||
if !isempty(nontrans)
|
||||
println("\n More verbose comparison of last non_transitive result:")
|
||||
println(" ", verbosedicecmp(nontrans[end]))
|
||||
end
|
||||
println("\n ====")
|
||||
end
|
||||
end
|
||||
|
||||
@time testnontransitivedice(3)
|
||||
@time testnontransitivedice(4)
|
||||
@time testnontransitivedice(5)
|
||||
@time testnontransitivedice(6)
|
||||
102
Task/Non-transitive-dice/Kotlin/non-transitive-dice.kotlin
Normal file
102
Task/Non-transitive-dice/Kotlin/non-transitive-dice.kotlin
Normal file
|
|
@ -0,0 +1,102 @@
|
|||
fun fourFaceCombos(): List<Array<Int>> {
|
||||
val res = mutableListOf<Array<Int>>()
|
||||
val found = mutableSetOf<Int>()
|
||||
for (i in 1..4) {
|
||||
for (j in 1..4) {
|
||||
for (k in 1..4) {
|
||||
for (l in 1..4) {
|
||||
val c = arrayOf(i, j, k, l)
|
||||
c.sort()
|
||||
val key = 64 * (c[0] - 1) + 16 * (c[1] - 1) + 4 * (c[2] - 1) + (c[3] - 1)
|
||||
if (!found.contains(key)) {
|
||||
found.add(key)
|
||||
res.add(c)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
fun cmp(x: Array<Int>, y: Array<Int>): Int {
|
||||
var xw = 0
|
||||
var yw = 0
|
||||
for (i in 0 until 4) {
|
||||
for (j in 0 until 4) {
|
||||
if (x[i] > y[j]) {
|
||||
xw++
|
||||
} else if (y[j] > x[i]) {
|
||||
yw++
|
||||
}
|
||||
}
|
||||
}
|
||||
if (xw < yw) {
|
||||
return -1
|
||||
}
|
||||
if (xw > yw) {
|
||||
return 1
|
||||
}
|
||||
return 0
|
||||
}
|
||||
|
||||
fun findIntransitive3(cs: List<Array<Int>>): List<Array<Array<Int>>> {
|
||||
val c = cs.size
|
||||
val res = mutableListOf<Array<Array<Int>>>()
|
||||
|
||||
for (i in 0 until c) {
|
||||
for (j in 0 until c) {
|
||||
if (cmp(cs[i], cs[j]) == -1) {
|
||||
for (k in 0 until c) {
|
||||
if (cmp(cs[j], cs[k]) == -1 && cmp(cs[k], cs[i]) == -1) {
|
||||
res.add(arrayOf(cs[i], cs[j], cs[k]))
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res
|
||||
}
|
||||
|
||||
fun findIntransitive4(cs: List<Array<Int>>): List<Array<Array<Int>>> {
|
||||
val c = cs.size
|
||||
val res = mutableListOf<Array<Array<Int>>>()
|
||||
|
||||
for (i in 0 until c) {
|
||||
for (j in 0 until c) {
|
||||
if (cmp(cs[i], cs[j]) == -1) {
|
||||
for (k in 0 until c) {
|
||||
if (cmp(cs[j], cs[k]) == -1) {
|
||||
for (l in 0 until c) {
|
||||
if (cmp(cs[k], cs[l]) == -1 && cmp(cs[l], cs[i]) == -1) {
|
||||
res.add(arrayOf(cs[i], cs[j], cs[k], cs[l]))
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return res
|
||||
}
|
||||
|
||||
fun main() {
|
||||
val combos = fourFaceCombos()
|
||||
println("Number of eligible 4-faced dice: ${combos.size}")
|
||||
println()
|
||||
|
||||
val it3 = findIntransitive3(combos)
|
||||
println("${it3.size} ordered lists of 3 non-transitive dice found, namely:")
|
||||
for (a in it3) {
|
||||
println(a.joinToString(", ", "[", "]") { it.joinToString(", ", "[", "]") })
|
||||
}
|
||||
println()
|
||||
|
||||
val it4 = findIntransitive4(combos)
|
||||
println("${it4.size} ordered lists of 4 non-transitive dice found, namely:")
|
||||
for (a in it4) {
|
||||
println(a.joinToString(", ", "[", "]") { it.joinToString(", ", "[", "]") })
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
ClearAll[DieFight]
|
||||
DieFight[d1_List, d2_List] := Module[{sets},
|
||||
sets = Tuples[{d1, d2}];
|
||||
sets = sets[[All, 2]] - sets[[All, 1]];
|
||||
Sign[Total[Sign[sets]]]
|
||||
]
|
||||
ds = DeleteDuplicates[Sort /@ Tuples[Range[4], 4]];
|
||||
ssis = Subsets[Range[Length[ds]], {3}];
|
||||
ssis //= Map[Permutations];
|
||||
ssis //= Catenate;
|
||||
|
||||
ssis //= Select[DieFight[ds[[#[[1]]]], ds[[#[[2]]]]] == 1 &];
|
||||
ssis //= Select[DieFight[ds[[#[[2]]]], ds[[#[[3]]]]] == 1 &];
|
||||
ssis //= Select[DieFight[ds[[#[[1]]]], ds[[#[[3]]]]] == -1 &];
|
||||
|
||||
nontransitiveds = Map[ds[[#]] &, ssis, {2}];
|
||||
Column[Row[{#1, "<", #2, " ; ", #2, "<", #3, " ; ", #1, ">", #3}] & @@@ nontransitiveds]
|
||||
|
||||
ssis = Subsets[Range[Length[ds]], {4}];
|
||||
ssis //= Map[Permutations];
|
||||
ssis //= Catenate;
|
||||
|
||||
ssis //= Select[DieFight[ds[[#[[1]]]], ds[[#[[2]]]]] == 1 &];
|
||||
ssis //= Select[DieFight[ds[[#[[2]]]], ds[[#[[3]]]]] == 1 &];
|
||||
ssis //= Select[DieFight[ds[[#[[3]]]], ds[[#[[4]]]]] == 1 &];
|
||||
ssis //= Select[DieFight[ds[[#[[1]]]], ds[[#[[4]]]]] == -1 &];
|
||||
|
||||
nontransitiveds = Map[ds[[#]] &, ssis, {2}];
|
||||
Column[Row[{#1, "<", #2, " ; ", #2, "<", #3, " ; ", #3, "<", #4, " ; ", #1, ">", #4}] & @@@ nontransitiveds]
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
%Non transitive dice. Nigel Galloway, September 14th., 2020
|
||||
int: die; int: faces; set of int: values;
|
||||
predicate pN(array[1..faces] of var values: n, array[1..faces] of var values: g) = sum(i in 1..faces,j in 1..faces)(if n[i]<g[j] then 1 elseif n[i]>g[j] then -1 else 0 endif)>0;
|
||||
predicate pG(array[1..faces] of var values: n) = forall(g in 1..faces-1)(n[g]<=n[g+1]);
|
||||
array[1..die,1..faces] of var values: g;
|
||||
constraint forall(n in 1..die)(pG(g[n,1..faces]));
|
||||
constraint forall(n in 1..die-1)(pN(g[n,1..faces],g[n+1,1..faces]));
|
||||
constraint pN(g[die,1..faces],g[1,1..faces]);
|
||||
output[join(" ",[show(g[n,1..faces])++"<"++show(g[n+1,1..faces]) | n in 1..die-1])," "++show(g[die,1..faces])++">"++show(g[1,1..faces])];
|
||||
132
Task/Non-transitive-dice/Nim/non-transitive-dice.nim
Normal file
132
Task/Non-transitive-dice/Nim/non-transitive-dice.nim
Normal file
|
|
@ -0,0 +1,132 @@
|
|||
import std/[algorithm, sequtils, sets, strformat]
|
||||
import itertools
|
||||
|
||||
type Die = object
|
||||
name: string
|
||||
faces: seq[int]
|
||||
|
||||
|
||||
####################################################################################################
|
||||
# Die functions.
|
||||
|
||||
|
||||
func `$`(die: Die): string =
|
||||
## Return the string representation of a Die.
|
||||
&"({die.name}: {($die.faces)[1..^1]})"
|
||||
|
||||
|
||||
func cmp(die1, die2: Die): int =
|
||||
## Compare two dice returning 1, -1 or 0 for operators >, < ==.
|
||||
var tot: array[3, int]
|
||||
for d in product(die1.faces, die2.faces):
|
||||
inc tot[1 + ord(d[1] < d[0]) - ord(d[0] < d[1])]
|
||||
result = ord(tot[0] < tot[2]) - ord(tot[2] < tot[0])
|
||||
|
||||
|
||||
func verboseCmp(die1, die2: Die): string =
|
||||
## Compare two dice returning a string.
|
||||
var win1, win2 = 0
|
||||
for (d1, d2) in product(die1.faces, die2.faces):
|
||||
inc win1, ord(d1 > d2)
|
||||
inc win2, ord(d2 > d1)
|
||||
result = if win1 > win2: &"{die1.name} > {die2.name}"
|
||||
elif win1 < win2: &"{die1.name} < {die2.name}"
|
||||
else: &"{die1.name} = {die2.name}"
|
||||
|
||||
|
||||
func `>`(die1, die2: Die): bool = cmp(die1, die2) > 0
|
||||
func `<=`(die1, die2: Die): bool = cmp(die1, die2) <= 0
|
||||
|
||||
|
||||
####################################################################################################
|
||||
# Added a permutation iterator as that of "itertools" doesn't allow to specify the length.
|
||||
|
||||
|
||||
iterator permutations[T](values: openArray[T]; r: int): seq[T] {.closure} =
|
||||
## Yield permutations of length "r" with elements taken from "values".
|
||||
let n = values.len
|
||||
if r > n: return
|
||||
var indices = toSeq(0..<n)
|
||||
var cycles = toSeq(countdown(n, n - r + 1))
|
||||
var perm = values[0..<r]
|
||||
yield perm
|
||||
if n == 0: return
|
||||
while true:
|
||||
var exit = true
|
||||
for i in countdown(r - 1, 0):
|
||||
dec cycles[i]
|
||||
if cycles[i] == 0:
|
||||
discard indices.rotateLeft(i..indices.high, 1)
|
||||
cycles[i] = n - i
|
||||
else:
|
||||
let j = cycles[i]
|
||||
swap indices[i], indices[^j]
|
||||
for iperm, ivalues in indices[0..<r]:
|
||||
perm[iperm] = values[ivalues]
|
||||
yield perm
|
||||
exit = false
|
||||
break
|
||||
if exit: return
|
||||
|
||||
|
||||
####################################################################################################
|
||||
# Dice functions.
|
||||
|
||||
|
||||
func isNonTrans(dice: openArray[Die]): bool =
|
||||
## Return true if ordering of die in dice is non-transitive.
|
||||
for i in 1..dice.high:
|
||||
if dice[i] <= dice[i-1]: return false
|
||||
result = dice[0] > dice[^1]
|
||||
|
||||
|
||||
func findNonTrans(allDice: openArray[Die]; n = 3): seq[seq[Die]] =
|
||||
## Return the list of non-transitive dice.
|
||||
for perm in permutations(allDice, n):
|
||||
if perm.isNontrans:
|
||||
result.add perm
|
||||
|
||||
|
||||
proc possibleDice(sides, maxval: Positive): seq[Die] =
|
||||
## Return the list of possible dice with given number of sides and maximum value.
|
||||
|
||||
echo &"All possible 1..{maxval} {sides}-sided dice."
|
||||
var dice: seq[Die]
|
||||
var n = 1
|
||||
for faces in product(toSeq(1..maxval), repeat = sides):
|
||||
dice.add Die(name: &"D{n}", faces: faces)
|
||||
inc n
|
||||
echo &" Created {dice.len} dice."
|
||||
echo " Remove duplicate with same bag of numbers on different faces."
|
||||
var found: HashSet[seq[int]]
|
||||
for d in dice:
|
||||
let count = sorted(d.faces)
|
||||
if count notin found:
|
||||
found.incl count
|
||||
result.add d
|
||||
echo &" Return {result.len} filtered dice."
|
||||
|
||||
|
||||
func verboseDiceCmp(dice: openArray[Die]): string =
|
||||
## Return the verbose comparison of dice.
|
||||
for i in 1..dice.high:
|
||||
result.add verboseCmp(dice[i-1], dice[i]) & ", "
|
||||
result.add verboseCmp(dice[0], dice[^1])
|
||||
|
||||
|
||||
#———————————————————————————————————————————————————————————————————————————————————————————————————
|
||||
|
||||
when isMainModule:
|
||||
|
||||
let dice = possibleDice(sides = 4, maxval = 4)
|
||||
for n in [3, 4]:
|
||||
let nonTrans = dice.findNonTrans(n)
|
||||
echo &"\n Non-transitive length-{n} combinations found: {nonTrans.len}."
|
||||
for list in nonTrans:
|
||||
echo ""
|
||||
for i, die in list:
|
||||
echo " ", if i == 0: '[' else: ' ', die, if i == list.high: "]" else: ","
|
||||
if nonTrans.len != 0:
|
||||
echo &"\n More verbose comparison of last non-transitive result:"
|
||||
echo " ", verboseDiceCmp(nonTrans[^1])
|
||||
echo "\n ===="
|
||||
150
Task/Non-transitive-dice/Perl/non-transitive-dice.pl
Normal file
150
Task/Non-transitive-dice/Perl/non-transitive-dice.pl
Normal file
|
|
@ -0,0 +1,150 @@
|
|||
use strict;
|
||||
use warnings;
|
||||
|
||||
sub fourFaceCombs {
|
||||
my %found = ();
|
||||
my @res = ();
|
||||
for (my $i = 1; $i <= 4; $i++) {
|
||||
for (my $j = 1; $j <= 4; $j++) {
|
||||
for (my $k = 1; $k <= 4; $k++) {
|
||||
for (my $l = 1; $l <= 4; $l++) {
|
||||
my @c = sort ($i, $j, $k, $l);
|
||||
my $key = 0;
|
||||
for my $p (@c) {
|
||||
$key = 10 * $key + $p;
|
||||
}
|
||||
if (not exists $found{$key}) {
|
||||
$found{$key} = 1;
|
||||
push @res, \@c;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return @res;
|
||||
}
|
||||
|
||||
sub compare {
|
||||
my $xref = shift;
|
||||
my $yref = shift;
|
||||
|
||||
my @x = @$xref;
|
||||
my $xw = 0;
|
||||
|
||||
my @y = @$yref;
|
||||
my $yw = 0;
|
||||
|
||||
for my $i (@x) {
|
||||
for my $j (@y) {
|
||||
if ($i < $j) {
|
||||
$yw++;
|
||||
}
|
||||
if ($j < $i) {
|
||||
$xw++;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if ($xw < $yw) {
|
||||
return -1;
|
||||
}
|
||||
if ($yw < $xw) {
|
||||
return 1;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
sub findIntransitive3 {
|
||||
my $dice_ref = shift;
|
||||
my @dice = @$dice_ref;
|
||||
my $len = scalar @dice;
|
||||
|
||||
my @res = ();
|
||||
for (my $i = 0; $i < $len; $i++) {
|
||||
for (my $j = 0; $j < $len; $j++) {
|
||||
my $first = compare($dice[$i], $dice[$j]);
|
||||
if ($first == 1) {
|
||||
for (my $k = 0; $k < $len; $k++) {
|
||||
my $second = compare($dice[$j], $dice[$k]);
|
||||
if ($second == 1) {
|
||||
my $third = compare($dice[$k], $dice[$i]);
|
||||
if ($third == 1) {
|
||||
my $d1r = $dice[$i];
|
||||
my $d2r = $dice[$j];
|
||||
my $d3r = $dice[$k];
|
||||
my @itd = ($d1r, $d2r, $d3r);
|
||||
push @res, \@itd;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return @res;
|
||||
}
|
||||
|
||||
sub findIntransitive4 {
|
||||
my $dice_ref = shift;
|
||||
my @dice = @$dice_ref;
|
||||
my $len = scalar @dice;
|
||||
|
||||
my @res = ();
|
||||
for (my $i = 0; $i < $len; $i++) {
|
||||
for (my $j = 0; $j < $len; $j++) {
|
||||
for (my $k = 0; $k < $len; $k++) {
|
||||
for (my $l = 0; $l < $len; $l++) {
|
||||
my $first = compare($dice[$i], $dice[$j]);
|
||||
if ($first == 1) {
|
||||
my $second = compare($dice[$j], $dice[$k]);
|
||||
if ($second == 1) {
|
||||
my $third = compare($dice[$k], $dice[$l]);
|
||||
if ($third == 1) {
|
||||
my $fourth = compare($dice[$l], $dice[$i]);
|
||||
if ($fourth == 1) {
|
||||
my $d1r = $dice[$i];
|
||||
my $d2r = $dice[$j];
|
||||
my $d3r = $dice[$k];
|
||||
my $d4r = $dice[$l];
|
||||
my @itd = ($d1r, $d2r, $d3r, $d4r);
|
||||
push @res, \@itd;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return @res;
|
||||
}
|
||||
|
||||
sub main {
|
||||
my @dice = fourFaceCombs();
|
||||
my $len = scalar @dice;
|
||||
print "Number of eligible 4-faced dice: $len\n\n";
|
||||
|
||||
my @it3 = findIntransitive3(\@dice);
|
||||
my $count3 = scalar @it3;
|
||||
print "$count3 ordered lists of 3 non-transitive dice found, namely:\n";
|
||||
for my $itref (@it3) {
|
||||
print "[ ";
|
||||
for my $r (@$itref) {
|
||||
print "[@$r] ";
|
||||
}
|
||||
print "]\n";
|
||||
}
|
||||
print "\n";
|
||||
|
||||
my @it4 = findIntransitive4(\@dice);
|
||||
my $count = scalar @it4;
|
||||
print "$count ordered lists of 4 non-transitive dice found, namely:\n";
|
||||
for my $itref (@it4) {
|
||||
print "[ ";
|
||||
for my $r (@$itref) {
|
||||
print "[@$r] ";
|
||||
}
|
||||
print "]\n";
|
||||
}
|
||||
}
|
||||
|
||||
main();
|
||||
221
Task/Non-transitive-dice/Phix/non-transitive-dice-1.phix
Normal file
221
Task/Non-transitive-dice/Phix/non-transitive-dice-1.phix
Normal file
|
|
@ -0,0 +1,221 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"0.8.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (added sq_cmp() builtin that returns nested -1/0/+1 compare() results, just like the existing sq_eq() does for equal().)</span>
|
||||
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- max number of a die side (later set to 6)</span>
|
||||
<span style="color: #000000;">mn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- min number of a die side (later set to 0)</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">sides</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">--
|
||||
-- construct all non-descending permutes of mn..mx,
|
||||
-- ie/eg {1,1,1,1}..{4,4,4,4} with (say), amongst
|
||||
-- others, {1,1,2,4} but not {1,1,4,2}.
|
||||
--</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">die</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sides</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (main work area)</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die</span><span style="color: #0000FF;">)}</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000080;font-style:italic;">-- find rightmost incrementable side
|
||||
-- ie/eg {1,2,4,4} -> set rdx to 2 (if 1-based indexing)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">rdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rfind</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_lt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mx</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">rdx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- set that and all later to that incremented
|
||||
-- ie/eg {1,2,4,4} -> {1,3,3,3}</span>
|
||||
<span style="color: #000000;">die</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rdx</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">die</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rdx</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"There are %d possible %d..%d %d-sided dice\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #000000;">mn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sides</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">Dnn</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">die</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- reconstruct the python die numbering (string)
|
||||
-- essentially just treat it as a base-N number.</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (sides)</span>
|
||||
<span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mx</span><span style="color: #0000FF;">-</span><span style="color: #000000;">mn</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (base)</span>
|
||||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (result)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">die</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">mn</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">N</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"D%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">cmpd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">die1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">die2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- compares two die returning -1, 0, or +1 for <, =, ></span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die1</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">die2</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sign</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">low_rotation</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">),</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">..$]&</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">rotations</span>
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">sk</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sk1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">set</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (indexes to dice)</span>
|
||||
<span style="color: #000000;">cache</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span><span style="color: #000000;">l</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">bool</span> <span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">sk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">sk1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">][</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cmpd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">],</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">][</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">!=-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">valid</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
|
||||
<span style="color: #000080;font-style:italic;">-- force k+1 to be incremented next:</span>
|
||||
<span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">l</span>
|
||||
<span style="color: #008080;">exit</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">valid</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">sk</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">sk1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">[$]</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">][</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cmpd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">],</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #000000;">cache</span><span style="color: #0000FF;">[</span><span style="color: #000000;">sk</span><span style="color: #0000FF;">][</span><span style="color: #000000;">sk1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">low_rotation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- find rightmost incrementable die index
|
||||
-- ie/eg if l is 35 and set is {1,2,35,35}
|
||||
-- -> set rdx to 2 (if 1-based indexing)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">rdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rfind</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_lt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">rdx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- increment that and reset all later
|
||||
-- ie/eg {1,2,35,35} -> {1,3,1,1}</span>
|
||||
<span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rdx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rdx</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"working... (%d/%d)\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">l</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">progress</span><span style="color: #0000FF;">(</span><span style="color: #008000;">""</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">rotations</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">unique</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">rotations</span> <span style="color: #0000FF;">-=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">verbose_cmp</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">die1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">die2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- compares two die returning their relationship of their names as a string</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cmpd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">die2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">op</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"<"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"="</span><span style="color: #0000FF;">,</span><span style="color: #008000;">">"</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span>
|
||||
<span style="color: #000000;">n1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Dnn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die1</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">n2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Dnn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">die2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%s %s %s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n2</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">verbose_dice_cmp</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">set</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">d1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d2</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">set</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">d1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]]</span>
|
||||
<span style="color: #000000;">d2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">verbose_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d2</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">d1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span>
|
||||
<span style="color: #000000;">d2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">set</span><span style="color: #0000FF;">[$]]</span>
|
||||
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">verbose_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d2</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">non_trans</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">non_trans</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">omissions</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">N</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n Non_transitive length-%d combinations found: %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">N</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">rotations</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">object</span> <span style="color: #000000;">ni</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">non_trans</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ni</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">5</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ni</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dice</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ni</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]]</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %s:%v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">Dnn</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">),</span><span style="color: #000000;">d</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">omissions</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">omissions</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" (%d omitted)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">omissions</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">rotations</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" (%d rotations omitted)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rotations</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">last</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">mx</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">6</span> <span style="color: #008080;">and</span> <span style="color: #000000;">mn</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" More verbose comparison of last result:\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">verbose_dice_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">non_trans</span><span style="color: #0000FF;">[</span><span style="color: #000000;">last</span><span style="color: #0000FF;">])})</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n ====\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">),</span><span style="color: #000000;">N</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- From the numberphile video (Efron's dice):</span>
|
||||
<span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">6</span>
|
||||
<span style="color: #000000;">mn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">--show_dice(dice,find_non_trans(dice,4),4)
|
||||
-- ok, dunno about you but I'm not waiting for power(924,4) permutes...
|
||||
-- limit to the ones discussed, plus another 4 random ones
|
||||
-- (hopefully it'll just pick out the right ones...)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nEfron's dice\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- (rand)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- (rand)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- (rand)</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}</span> <span style="color: #000080;font-style:italic;">-- (rand)</span>
|
||||
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- and from wp:</span>
|
||||
<span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">9</span>
|
||||
<span style="color: #000000;">mn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nFrom wp\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}}</span>
|
||||
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000080;font-style:italic;">-- Miwin's dice</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Miwin's dice\n"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span>
|
||||
<span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">}}</span>
|
||||
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">))</span>
|
||||
<!--
|
||||
15
Task/Non-transitive-dice/Phix/non-transitive-dice-2.phix
Normal file
15
Task/Non-transitive-dice/Phix/non-transitive-dice-2.phix
Normal file
|
|
@ -0,0 +1,15 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">6</span>
|
||||
<span style="color: #000000;">mn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">))</span>
|
||||
|
||||
<span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #000000;">mx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">6</span>
|
||||
<span style="color: #000000;">mn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #000000;">dice</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">possible_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">show_dice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">find_non_trans</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dice</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">))</span>
|
||||
<!--
|
||||
32
Task/Non-transitive-dice/Python/non-transitive-dice-1.py
Normal file
32
Task/Non-transitive-dice/Python/non-transitive-dice-1.py
Normal file
|
|
@ -0,0 +1,32 @@
|
|||
from itertools import combinations_with_replacement as cmbr
|
||||
from time import time
|
||||
|
||||
def dice_gen(n, faces, m):
|
||||
dice = list(cmbr(faces, n))
|
||||
|
||||
succ = [set(j for j, b in enumerate(dice)
|
||||
if sum((x>y) - (x<y) for x in a for y in b) > 0)
|
||||
for a in dice]
|
||||
|
||||
def loops(seq):
|
||||
s = succ[seq[-1]]
|
||||
|
||||
if len(seq) == m:
|
||||
if seq[0] in s: yield seq
|
||||
return
|
||||
|
||||
for d in (x for x in s if x > seq[0] and not x in seq):
|
||||
yield from loops(seq + (d,))
|
||||
|
||||
yield from (tuple(''.join(dice[s]) for s in x)
|
||||
for i, v in enumerate(succ)
|
||||
for x in loops((i,)))
|
||||
|
||||
t = time()
|
||||
for n, faces, loop_len in [(4, '1234', 3), (4, '1234', 4), (6, '123456', 3), (6, '1234567', 3)]:
|
||||
for i, x in enumerate(dice_gen(n, faces, loop_len)): pass
|
||||
|
||||
print(f'{n}-sided, markings {faces}, loop length {loop_len}:')
|
||||
print(f'\t{i + 1}*{loop_len} solutions, e.g. {" > ".join(x)} > [loop]')
|
||||
t, t0 = time(), t
|
||||
print(f'\ttime: {t - t0:.4f} seconds\n')
|
||||
75
Task/Non-transitive-dice/Python/non-transitive-dice-2.py
Normal file
75
Task/Non-transitive-dice/Python/non-transitive-dice-2.py
Normal file
|
|
@ -0,0 +1,75 @@
|
|||
from collections import namedtuple
|
||||
from itertools import permutations, product
|
||||
from functools import lru_cache
|
||||
|
||||
|
||||
Die = namedtuple('Die', 'name, faces')
|
||||
|
||||
@lru_cache(maxsize=None)
|
||||
def cmpd(die1, die2):
|
||||
'compares two die returning 1, -1 or 0 for >, < =='
|
||||
# Numbers of times one die wins against the other for all combinations
|
||||
# cmp(x, y) is `(x > y) - (y > x)` to return 1, 0, or -1 for numbers
|
||||
tot = [0, 0, 0]
|
||||
for d1, d2 in product(die1.faces, die2.faces):
|
||||
tot[1 + (d1 > d2) - (d2 > d1)] += 1
|
||||
win2, _, win1 = tot
|
||||
return (win1 > win2) - (win2 > win1)
|
||||
|
||||
def is_non_trans(dice):
|
||||
"Check if ordering of die in dice is non-transitive returning dice or None"
|
||||
check = (all(cmpd(c1, c2) == -1
|
||||
for c1, c2 in zip(dice, dice[1:])) # Dn < Dn+1
|
||||
and cmpd(dice[0], dice[-1]) == 1) # But D[0] > D[-1]
|
||||
return dice if check else False
|
||||
|
||||
def find_non_trans(alldice, n=3):
|
||||
return [perm for perm in permutations(alldice, n)
|
||||
if is_non_trans(perm)]
|
||||
|
||||
def possible_dice(sides, mx):
|
||||
print(f"\nAll possible 1..{mx} {sides}-sided dice")
|
||||
dice = [Die(f"D{n+1}", faces)
|
||||
for n, faces in enumerate(product(range(1, mx+1), repeat=sides))]
|
||||
print(f' Created {len(dice)} dice')
|
||||
print(' Remove duplicate with same bag of numbers on different faces')
|
||||
found = set()
|
||||
filtered = []
|
||||
for d in dice:
|
||||
count = tuple(sorted(d.faces))
|
||||
if count not in found:
|
||||
found.add(count)
|
||||
filtered.append(d)
|
||||
l = len(filtered)
|
||||
print(f' Return {l} filtered dice')
|
||||
return filtered
|
||||
|
||||
#%% more verbose extra checks
|
||||
def verbose_cmp(die1, die2):
|
||||
'compares two die returning their relationship of their names as a string'
|
||||
# Numbers of times one die wins against the other for all combinations
|
||||
win1 = sum(d1 > d2 for d1, d2 in product(die1.faces, die2.faces))
|
||||
win2 = sum(d2 > d1 for d1, d2 in product(die1.faces, die2.faces))
|
||||
n1, n2 = die1.name, die2.name
|
||||
return f'{n1} > {n2}' if win1 > win2 else (f'{n1} < {n2}' if win1 < win2 else f'{n1} = {n2}')
|
||||
|
||||
def verbose_dice_cmp(dice):
|
||||
c = [verbose_cmp(x, y) for x, y in zip(dice, dice[1:])]
|
||||
c += [verbose_cmp(dice[0], dice[-1])]
|
||||
return ', '.join(c)
|
||||
|
||||
|
||||
#%% Use
|
||||
if __name__ == '__main__':
|
||||
dice = possible_dice(sides=4, mx=4)
|
||||
for N in (3, 4): # length of non-transitive group of dice searched for
|
||||
non_trans = find_non_trans(dice, N)
|
||||
print(f'\n Non_transitive length-{N} combinations found: {len(non_trans)}')
|
||||
for lst in non_trans:
|
||||
print()
|
||||
for i, die in enumerate(lst):
|
||||
print(f" {' ' if i else '['}{die}{',' if i < N-1 else ']'}")
|
||||
if non_trans:
|
||||
print('\n More verbose comparison of last non_transitive result:')
|
||||
print(' ', verbose_dice_cmp(non_trans[-1]))
|
||||
print('\n ====')
|
||||
36
Task/Non-transitive-dice/R/non-transitive-dice.r
Normal file
36
Task/Non-transitive-dice/R/non-transitive-dice.r
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
findNonTrans <- function()
|
||||
{
|
||||
diceSet <- unique(t(apply(expand.grid(1:4, 1:4, 1:4, 1:4), 1, sort))) #By construction, each row is a unique dice.
|
||||
winningDice <- function(X, Y) #Recall 'Example 1' in the task.
|
||||
{
|
||||
comparisonTable <- data.frame(X = rep(X, each = length(X)), Y = rep(Y, times = length(Y)))
|
||||
rowWinner <- ifelse(comparisonTable["X"] > comparisonTable["Y"], "X",
|
||||
ifelse(comparisonTable["X"] == comparisonTable["Y"], "-", "Y"))
|
||||
netXWins <- sum(rowWinner == "X") - sum(rowWinner == "Y")
|
||||
if(netXWins > 0) "X" else if(netXWins == 0) "Draw" else "Y"
|
||||
}
|
||||
rows <- seq_len(nrow(diceSet)) #Recall that each row of diceSet is a dice.
|
||||
XvsAllY <- function(X) sapply(rows, function(i) winningDice(X, diceSet[i, ]))
|
||||
winners <- as.data.frame(lapply(rows, function(i) XvsAllY(diceSet[i, ])),
|
||||
row.names = paste("Y=Dice", rows), col.names = paste("X=Dice", rows), check.names = FALSE)
|
||||
solutionCount <- 0
|
||||
for(S in rows)
|
||||
{
|
||||
beatsS <- which(winners[paste("X=Dice", S)] == "Y") #Finds the indices of all T such that S<T.
|
||||
beatsT <- lapply(beatsS, function(X) which(winners[paste("X=Dice", X)] == "Y")) #To begin finding U such that T<U.
|
||||
beatenByS <- which(winners[paste("X=Dice", S)] == "X") #Finds the indices of all U such that S>U.
|
||||
potentialU <- lapply(beatsT, function(X) intersect(X, beatenByS)) #Combining previous two lines.
|
||||
nonEmptyIndices <- lengths(potentialU) != 0 #Most of potentialU is usually empty lists.
|
||||
if(any(nonEmptyIndices)) #If any lists in potentialU are non-empty, then their entry is the index of a U with S>U & T<U.
|
||||
{
|
||||
solutionCount <- solutionCount + 1
|
||||
diceUIndex <- potentialU[nonEmptyIndices][[1]] #Assumes that there is only one valid U for this S.
|
||||
diceTIndex <- beatsS[nonEmptyIndices][[1]] #Finds the T corresponding to the chosen U.
|
||||
cat("Solution", solutionCount, "is:\n")
|
||||
output <- rbind(S = diceSet[S,], T = diceSet[diceTIndex,], U = diceSet[diceUIndex,])
|
||||
colnames(output) <- paste("Dice", 1:4)
|
||||
print(output)
|
||||
}
|
||||
}
|
||||
}
|
||||
findNonTrans()
|
||||
36
Task/Non-transitive-dice/Raku/non-transitive-dice.raku
Normal file
36
Task/Non-transitive-dice/Raku/non-transitive-dice.raku
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
# 20201225 Raku programming solution
|
||||
|
||||
my @dicepool = ^4 xx 4 ;
|
||||
|
||||
sub FaceCombs(\N, @dp) { # for brevity, changed to use 0-based dice on input
|
||||
my @res = my @found = [];
|
||||
for [X] @dp {
|
||||
unless @found[ my \key = [+] ( N «**« (N-1…0) ) Z* .sort ] {
|
||||
@found[key] = True;
|
||||
@res.push: $_ »+» 1
|
||||
}
|
||||
}
|
||||
@res
|
||||
}
|
||||
|
||||
sub infix:<⚖️>(@x, @y) { +($_{Less} <=> $_{More}) given (@x X<=> @y).Bag }
|
||||
|
||||
sub findIntransitive(\N, \cs) {
|
||||
my @res = [];
|
||||
race for [X] ^+cs xx N -> @lot {
|
||||
my $skip = False;
|
||||
for @lot.rotor(2 => -1) {
|
||||
{ $skip = True and last } unless cs[ @_[0] ] ⚖️ cs[ @_[1] ] == -1
|
||||
}
|
||||
next if $skip;
|
||||
if cs[ @lot[0] ] ⚖️ cs[ @lot[*-1] ] == 1 { @res.push: [ cs[ @lot ] ] }
|
||||
}
|
||||
@res
|
||||
}
|
||||
|
||||
say "Number of eligible 4-faced dice : ", +(my \combs = FaceCombs(4,@dicepool));
|
||||
for 3, 4 {
|
||||
my @output = findIntransitive($_, combs);
|
||||
say +@output, " ordered lists of $_ non-transitive dice found, namely:";
|
||||
.say for @output;
|
||||
}
|
||||
91
Task/Non-transitive-dice/Wren/non-transitive-dice.wren
Normal file
91
Task/Non-transitive-dice/Wren/non-transitive-dice.wren
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
import "/sort" for Sort
|
||||
|
||||
var fourFaceCombs = Fn.new {
|
||||
var res = []
|
||||
var found = List.filled(256, false)
|
||||
for (i in 1..4) {
|
||||
for (j in 1..4) {
|
||||
for (k in 1..4) {
|
||||
for (l in 1..4) {
|
||||
var c = [i, j, k, l]
|
||||
Sort.insertion(c)
|
||||
var key = 64*(c[0]-1) + 16*(c[1]-1) + 4*(c[2]-1) + (c[3]-1)
|
||||
if (!found[key]) {
|
||||
found[key] = true
|
||||
res.add(c)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
var cmp = Fn.new { |x, y|
|
||||
var xw = 0
|
||||
var yw = 0
|
||||
for (i in 0..3) {
|
||||
for (j in 0..3) {
|
||||
if (x[i] > y[j]) {
|
||||
xw = xw + 1
|
||||
} else if (y[j] > x[i]) {
|
||||
yw = yw + 1
|
||||
}
|
||||
}
|
||||
}
|
||||
return (xw - yw).sign
|
||||
}
|
||||
|
||||
var findIntransitive3 = Fn.new { |cs|
|
||||
var c = cs.count
|
||||
var res = []
|
||||
for (i in 0...c) {
|
||||
for (j in 0...c) {
|
||||
for (k in 0...c) {
|
||||
var first = cmp.call(cs[i], cs[j])
|
||||
if (first == -1) {
|
||||
var second = cmp.call(cs[j], cs[k])
|
||||
if (second == -1) {
|
||||
var third = cmp.call(cs[i], cs[k])
|
||||
if (third == 1) res.add([cs[i], cs[j], cs[k]])
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
var findIntransitive4 = Fn.new { |cs|
|
||||
var c = cs.count
|
||||
var res = []
|
||||
for (i in 0...c) {
|
||||
for (j in 0...c) {
|
||||
for (k in 0...c) {
|
||||
for (l in 0...c) {
|
||||
var first = cmp.call(cs[i], cs[j])
|
||||
if (first == -1) {
|
||||
var second = cmp.call(cs[j], cs[k])
|
||||
if (second == -1) {
|
||||
var third = cmp.call(cs[k], cs[l])
|
||||
if (third == -1) {
|
||||
var fourth = cmp.call(cs[i], cs[l])
|
||||
if (fourth == 1) res.add([cs[i], cs[j], cs[k], cs[l]])
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
var combs = fourFaceCombs.call()
|
||||
System.print("Number of eligible 4-faced dice: %(combs.count)")
|
||||
var it = findIntransitive3.call(combs)
|
||||
System.print("\n%(it.count) ordered lists of 3 non-transitive dice found, namely:")
|
||||
System.print(it.join("\n"))
|
||||
it = findIntransitive4.call(combs)
|
||||
System.print("\n%(it.count) ordered lists of 4 non-transitive dice found, namely:")
|
||||
System.print(it.join("\n"))
|
||||
Loading…
Add table
Add a link
Reference in a new issue