June 2018 Update

Task/Josephus-problem/BASIC/josephus-problem-1.basic

@@ -0,0 +1,7 @@
+10 N=41
+20 K=3
+30 M=0
+40 FOR I=M+1 TO N
+50 M=INT(I*((M+K)/I-INT((M+K)/I))+0.5)
+60 NEXT I
+70 PRINT "Survivor is number";M

Task/Josephus-problem/BASIC/josephus-problem-2.basic

@@ -0,0 +1,5 @@
+ 10  DEF  FN MOD(X) = X - INT (X / A) * A
+ 20  LM = 0: INPUT "GIVE N AND K (N,K): ";N,K
+ 30  IF N < 1 or K < 1 THEN GOTO 20
+ 40  FOR A = 1 TO N: LM =  FN MOD(LM + K): NEXT A
+ 50  PRINT "N = ";N;", K = ";K;", SURVIVOR: ";LM

Task/Josephus-problem/BBC-BASIC/josephus-problem.bbc

@@ -0,0 +1,10 @@
+REM >josephus
+PRINT "Survivor is number "; FNjosephus(41, 3, 0)
+END
+:
+DEF FNjosephus(n%, k%, m%)
+LOCAL i%
+FOR i% = m% + 1 TO n%
+  m% = (m% + k%) MOD i%
+NEXT
+= m%

Task/Josephus-problem/Julia/josephus-problem-1.julia

@@ -1 +1,5 @@
-josephus(n, k, m=1) = n == m ? collect(0:m-1) : mod(josephus(n-1, k, m) + k, n)
+using Memoize
+@memoize josephus(n::Integer, k::Integer, m::Integer=1) = n == m ? collect(0:m .- 1) : mod.(josephus(n - 1, k, m) + k, n)
+
+@show josephus(41, 3)
+@show josephus(41, 3, 5)

Task/Josephus-problem/Julia/josephus-problem-2.julia

@@ -1,4 +1,14 @@
-julia> print(josephus(41,3))
-[30]
-julia> print(josephus(41,3,5))
-[3,15,21,30,34]
+function josephus(n::Integer, k::Integer, m::Integer=1)
+    p, i, seq = collect(0:n-1), 0, Vector{typeof(n)}(0)
+    while length(p) > m
+        i = (i + k - 1) % length(p)
+        push!(seq, splice!(p, i + 1))
+    end
+    return seq, p
+end
+
+seq, surv = josephus(41, 3)
+println("Prisoner killing in order: $seq\nSurvivor: $surv")
+
+seq, surv = josephus(41, 3, 3)
+println("Prisoner killing in order: $seq\nSurvivor: $surv")

Task/Josephus-problem/MATLAB/josephus-problem.m

@@ -0,0 +1,38 @@
+function [indAlive] = josephus(numPeople,count)
+% Josephus: Given a circle of numPeople individuals, with a count of count,
+% find the index (starting at 1) of the survivor [see Josephus Problem]
+
+%% Definitions:
+%   0 = dead position
+%   1 = alive position
+%   index = # of person
+
+%% Setting up
+arrPeople = ones(1, numPeople);
+currInd = 0;
+
+%% Counting
+while (length(arrPeople(arrPeople == 1)) > 1)     % While more than 1 person is alive
+    counter = 0;
+    while counter ~= count                       % Counting until we hit the count
+        currInd = currInd + 1;                  % Move to the next person
+
+        if currInd > numPeople                  % If overflow, wraparound
+            currInd = currInd - numPeople;
+        end
+
+        if arrPeople(currInd)                   % If the current person is alive
+            counter = counter + 1;                % Add 1 person to the count
+            %fprintf("Index: %d \t| Counter: %d\n", currInd, counter)           % Uncomment to display index and counter location
+        end
+
+    end
+
+    arrPeople(currInd) = 0;                     % Kill the person we reached
+    %fprintf("Killed person %d \n", currInd)                                   % Uncomment to display order of killing
+    %disp(arrPeople)                                                           % Uncomment to display current status of people
+end
+
+indAlive = find(arrPeople);
+
+end

Task/Josephus-problem/Modula-2/josephus-problem.mod2

@@ -0,0 +1,26 @@
+MODULE Josephus;
+FROM FormatString IMPORT FormatString;
+FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
+
+PROCEDURE Josephus(n,k : INTEGER) : INTEGER;
+VAR a,m : INTEGER;
+BEGIN
+    m := 0;
+    FOR a:=1 TO n DO
+        m := (m + k) MOD a;
+    END;
+    RETURN m
+END Josephus;
+
+VAR
+    buf : ARRAY[0..63] OF CHAR;
+    n,k,i : INTEGER;
+    nl,kl,il : LONGCARD;
+BEGIN
+    n := 41;
+    k := 3;
+    FormatString("n = %i, k = %i, final survivor: %i\n", buf, n, k, Josephus(n, k));
+    WriteString(buf);
+
+    ReadChar
+END Josephus.

Task/Josephus-problem/Perl-6/josephus-problem.pl6

@@ -0,0 +1,16 @@
+sub Execute(@prisoner, $k) {
+    until @prisoner == 1 {
+	@prisoner.=rotate($k - 1);
+	@prisoner.shift;
+    }
+}
+
+my @prisoner = ^41;
+Execute @prisoner, 3;
+say "Prisoner {@prisoner} survived.";
+
+# We don't have to use numbers.  Any list will do:
+
+my @dalton = <Joe Jack William Averell Rantanplan>;
+Execute @dalton, 2;
+say "{@dalton} survived.";

Task/Josephus-problem/PicoLisp/josephus-problem.l

@@ -0,0 +1,23 @@
+#general solution
+(de jo (N K)
+   (if (=1 N)
+      1
+      (inc
+         (%
+            (+ (dec K) (jo (dec N) K))
+            N ) ) ) )
+
+#special case when K is 2; much faster than general version.
+(de jo2(N)
+   (let P 1
+      (while (<= P N)
+         (setq P (* 2 P))
+         (+ (- (* 2 N) P) 1) ) ) )
+
+# find the survivor using an optimal solution
+(de survivor (N K)
+   (if (=0 (% N 2))
+      (jo2 N)
+      (jo N K) ) )
+(print (survivor 5 2))
+(print (survivor 41 3))

Task/Josephus-problem/Python/josephus-problem-4.py

@@ -0,0 +1,33 @@
+from itertools import compress, cycle
+def josephus(prisoner, kill, surviver):
+    p = range(prisoner)
+    k = [0] * kill
+    k[kill-1] = 1
+    s = [1] * kill
+    s[kill -1] = 0
+    queue = p
+
+    queue = compress(queue, cycle(s))
+    try:
+        while True:
+            p.append(queue.next())
+    except StopIteration:
+        pass
+
+    kil=[]
+    killed = compress(p, cycle(k))
+    try:
+        while True:
+            kil.append(killed.next())
+    except StopIteration:
+        pass
+
+    print 'The surviver is: ', kil[-surviver:]
+    print 'The kill sequence is ', kil[:prisoner-surviver]
+
+josephus(41,3,2)
+The surviver is:  [15, 30]
+The kill sequence is  [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 0, 4, 9, 13, 18, 22, 27, 31, 36, 40, 6, 12, 19, 25, 33, 39, 7, 16, 28, 37, 10, 24, 1, 21, 3, 34]
+josephus(5,2,1)
+The surviver is:  [2]
+The kill sequence is  [1, 3, 0, 4]