June 2018 Update
This commit is contained in:
Ingy döt Net
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ba8067c3b7
commit
22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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@ -1,27 +1,21 @@
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function rs = runsum(v)
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for i = 1:numel(v)
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rs(i) = sum(v(1:i));
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function a = spiral(n)
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a = ones(n*n, 1);
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u = -(i = n) * (v = ones(n, 1));
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for k = n-1:-1:1
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j = 1:k;
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a(j+i) = u(j) = -u(j);
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a(j+(i+k)) = v(j) = -v(j);
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i += 2*k;
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endfor
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a(cumsum(a)) = 1:n*n;
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a = reshape(a, n, n)'-1;
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endfunction
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function g = grade(v)
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for i = 1:numel(v)
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g(v(i)+1) = i-1;
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endfor
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endfunction
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>> spiral(5)
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ans =
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function spiral = make_spiral(spirald)
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series = ones(1,spirald^2);
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l = spirald-1; p = spirald+1;
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s = 1;
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while(l>0)
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series(p:p+l-1) *= spirald*s;
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series(p+l:p+l*2-1) *= -s;
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p += l*2;
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l--; s *= -1;
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endwhile
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series(1) = 0;
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spiral = reshape(grade(runsum(series)), spirald, spirald)';
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endfunction
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make_spiral(5)
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0 1 2 3 4
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15 16 17 18 5
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14 23 24 19 6
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13 22 21 20 7
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12 11 10 9 8
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@ -38,3 +38,22 @@ class Turtle {
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}
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}
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}
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# Now we can build the spiral in the normal way from outside-in like this:
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sub MAIN(Int $size = 5) {
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my $t = Turtle.new(dir => 2);
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my $counter = 0;
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$t.forward(-1);
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for 0..^ $size -> $ {
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$t.forward;
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$t.lay-egg($counter++);
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}
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for $size-1 ... 1 -> $run {
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$t.turn-right;
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$t.forward, $t.lay-egg($counter++) for 0..^$run;
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$t.turn-right;
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$t.forward, $t.lay-egg($counter++) for 0..^$run;
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}
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$t.showmap;
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}
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@ -1,16 +1,11 @@
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sub MAIN($size as Int) {
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my $t = Turtle.new(dir => 2);
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my $counter = 0;
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$t.forward(-1);
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for 0..^ $size -> $ {
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sub MAIN(Int $size = 5) {
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my $t = Turtle.new(dir => ($size %% 2 ?? 4 !! 0));
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my $counter = $size * $size;
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while $counter {
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$t.lay-egg(--$counter);
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$t.turn-left;
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$t.turn-right if $t.look;
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$t.forward;
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$t.lay-egg($counter++);
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}
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for $size-1 ... 1 -> $run {
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$t.turn-right;
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$t.forward, $t.lay-egg($counter++) for 0..^$run;
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$t.turn-right;
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$t.forward, $t.lay-egg($counter++) for 0..^$run;
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}
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$t.showmap;
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}
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@ -1,11 +1,19 @@
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sub MAIN($size as Int) {
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my $t = Turtle.new(dir => ($size %% 2 ?? 4 !! 0));
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my $counter = $size * $size;
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while $counter {
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$t.lay-egg(--$counter);
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$t.turn-left;
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$t.turn-right if $t.look;
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$t.forward;
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}
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$t.showmap;
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sub spiral_matrix ( $n ) {
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my @sm;
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my $len = $n;
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my $pos = 0;
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for ^($n/2).ceiling -> $i {
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my $j = $i + 1;
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my $e = $n - $j;
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@sm[$i ][$i + $_] = $pos++ for ^( $len); # Top
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@sm[$j + $_][$e ] = $pos++ for ^(--$len); # Right
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@sm[$e ][$i + $_] = $pos++ for reverse ^( $len); # Bottom
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@sm[$j + $_][$i ] = $pos++ for reverse ^(--$len); # Left
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}
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return @sm;
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}
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say .fmt('%3d') for spiral_matrix(5);
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51
Task/Spiral-matrix/Prolog/spiral-matrix.pro
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51
Task/Spiral-matrix/Prolog/spiral-matrix.pro
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@ -0,0 +1,51 @@
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% Prolog implementation: SWI-Prolog 7.2.3
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replace([_|T], 0, E, [E|T]) :- !.
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replace([H|T], N, E, Xs) :-
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succ(N1, N), replace(T, N1, E, Xs1), Xs = [H|Xs1].
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% True if Xs is the Original grid with the element at (X, Y) replaces by E.
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replace_in([H|T], (0, Y), E, Xs) :- replace(H, Y, E, NH), Xs = [NH|T], !.
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replace_in([H|T], (X, Y), E, Xs) :-
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succ(X1, X), replace_in(T, (X1, Y), E, Xs1), Xs = [H|Xs1].
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% True, if E is the value at (X, Y) in Xs
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get_in(Xs, (X, Y), E) :- nth0(X, Xs, L), nth0(Y, L, E).
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create(N, Mx) :- % NxN grid full of nils
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numlist(1, N, Ns),
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findall(X, (member(_, Ns), X = nil), Ls),
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findall(X, (member(_, Ns), X = Ls), Mx).
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% Depending of the direction, returns two possible coordinates and directions
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% (C,D) that will be used in case of a turn, and (A,B) otherwise.
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ops(right, (X,Y), (A,B), (C,D), D1, D2) :-
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A is X, B is Y+1, D1 = right, C is X+1, D is Y, D2 = down.
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ops(left, (X,Y), (A,B), (C,D), D1, D2) :-
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A is X, B is Y-1, D1 = left, C is X-1, D is Y, D2 = up.
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ops(up, (X,Y), (A,B), (C,D), D1, D2) :-
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A is X-1, B is Y, D1 = up, C is X, D is Y+1, D2 = right.
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ops(down, (X,Y), (A,B), (C,D), D1, D2) :-
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A is X+1, B is Y, D1 = down, C is X, D is Y-1, D2 = left.
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% True if NCoor is the right coor in spiral shape. Returns a new direction also.
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next(Dir, Mx, Coor, NCoor, NDir) :-
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ops(Dir, Coor, C1, C2, D1, D2),
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(get_in(Mx, C1, nil) -> NCoor = C1, NDir = D1
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; NCoor = C2, NDir = D2).
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% Returns an spiral with [H|Vs] elements called R, only work if the length of
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% [H|Vs], is the square of the size of the grid.
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spiralH(Dir, Mx, Coor, [H|Vs], R) :-
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replace_in(Mx, Coor, H, NMx),
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(Vs = [] -> R = NMx
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; next(Dir, Mx, Coor, NCoor, NDir),
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spiralH(NDir, NMx, NCoor, Vs, R)).
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% True if Mx is the grid in spiral shape of the numbers from 0 to N*N-1.
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spiral(N, Mx) :-
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Sq is N*N-1, numlist(0, Sq, Ns),
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create(N, EMx), spiralH(right, EMx, (0,0), Ns, Mx).
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46
Task/Spiral-matrix/Ring/spiral-matrix.ring
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46
Task/Spiral-matrix/Ring/spiral-matrix.ring
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@ -0,0 +1,46 @@
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# Project : Spiral matrix
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# Date : 2018/03/23
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# Author : Gal Zsolt [~ CalmoSoft ~]
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# Email : <calmosoft@gmail.com>
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load "stdlib.ring"
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n = 5
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result = newlist(n,n)
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k = 1
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top = 1
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bottom = n
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left = 1
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right = n
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while (k<=n*n)
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for i=left to right
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result[top][i]=k
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k = k + 1
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next
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top = top + 1
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for i=top to bottom
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result[i][right]=k
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k = k + 1
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next
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right = right - 1
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for i=right to left step -1
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result[bottom][i]=k
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k = k + 1
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next
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bottom = bottom - 1
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for i=bottom to top step -1
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result[i][left] = k
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k = k + 1
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next
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left = left + 1
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end
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for m = 1 to n
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for p = 1 to n
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if m = 1
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see " " + result[m][p]
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else
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see "" + result[m][p] + " "
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ok
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next
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see nl
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next
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see nl
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@ -1,22 +1,25 @@
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// Spiral Matrix
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n=10
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mat=zeros(n,n);
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botcol=1; topcol=n
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botrow=1; toprow=n
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ndir=0; col=1; row=1;
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for i=0:n*n-1
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mat(row,col)=i;
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if ndir==0
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if col<topcol then col=col+1; else ndir=1, row=row+1; botrow=botrow+1; end
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elseif ndir==1
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if row<toprow then row=row+1; else ndir=2, col=col-1; topcol=topcol-1; end
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elseif ndir==2
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if col>botcol then col=col-1; else ndir=3, row=row-1; toprow=toprow-1; end
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elseif ndir==3
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if row>botrow then row=row-1; else ndir=0, col=col+1; botcol=botcol+1; end
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end
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end i
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printf("n=%4d\n",n);
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for i=1:n;
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for j=1:n; printf("%4d",mat(i,j)); end j; printf("\n");
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end i;
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function a = spiral(n)
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a = ones(n*n, 1)
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v = ones(n, 1)
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u = -n*v;
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i = n
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for k = n-1:-1:1
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j = 1:k
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u(j) = -u(j)
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a(j+i) = u(j)
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v(j) = -v(j)
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a(j+(i+k)) = v(j)
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i = i+2*k
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end
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a(cumsum(a)) = (1:n*n)'
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a = matrix(a, n, n)'-1
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endfunction
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-->spiral(5)
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ans =
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0. 1. 2. 3. 4.
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15. 16. 17. 18. 5.
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14. 23. 24. 19. 6.
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13. 22. 21. 20. 7.
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12. 11. 10. 9. 8.
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21
Task/Spiral-matrix/Stata/spiral-matrix.stata
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21
Task/Spiral-matrix/Stata/spiral-matrix.stata
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@ -0,0 +1,21 @@
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function spiral_mat(n) {
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a = J(n*n, 1, 1)
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u = J(n, 1, -n)
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v = J(n, 1, 1)
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for (k=(i=n)-1; k>=1; i=i+2*k--) {
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j = 1..k
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a[j:+i] = u[j] = -u[j]
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a[j:+(i+k)] = v[j] = -v[j]
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}
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return(rowshape(invorder(runningsum(a)),n):-1)
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}
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spiral_mat(5)
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1 2 3 4 5
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+--------------------------+
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1 | 0 1 2 3 4 |
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2 | 15 16 17 18 5 |
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3 | 14 23 24 19 6 |
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4 | 13 22 21 20 7 |
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5 | 12 11 10 9 8 |
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+--------------------------+
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