# The Josephus Problem solution

Nov 12th, 2016
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1. import std.algorithm;
2. import std.conv;
3. import std.exception;
4. import std.math;
5. import std.range;
6. import std.stdio;
7. import std.typecons;
8.
9. void main()
10. {
11.     enum count = 100;
12.     enum verbose = false;
13.     iota(1, count + 1)
14.         .map!(i => tuple!("n", "naive", "formula")(i, i.solveNaively(verbose), i.solveViaFormula))
15.         .each!((solution)
16.         {
17.             "n %s -> %s (naive), %s (formula) ".writefln(solution.n, solution.naive, solution.formula);
18.             enforce(solution.naive == solution.formula, "solutions don't match");
19.         });
20. }
21.
22. class Node
23. {
24.     uint n;
25.     Node next;
26.     this(uint n) { this.n = n; }
27. }
28.
29. uint solveNaively(uint n, bool verbose)
30. {
31.     auto ring = makeRing(n);
32.     if (verbose)
33.         "==> %s".writefln(ring.ringToString);
34.     Node node = ring;
35.     while (node.next != node)
36.     {
37.         if (verbose)
38.             "%s -> %s".writefln(node.n, node.next.n);
39.         node = node.next = node.next.next;
40.     }
41.     return node.n;
42. }
43.
44. uint solveViaFormula(uint n)
45. {
46.     return (n - pow(2, cast(uint) log2(n))) * 2 + 1;
47. }
48.
49. Node makeRing(uint count)
50. {
51.     enforce(count);
52.     auto nodes = iota(count).map!(i => new Node(i + 1)).array;
53.     nodes.each!((i, node) => node.next = (i < count - 1 ? nodes[i + 1] : nodes.front));
54.     return nodes.front;
55. }
56.
57. string ringToString(Node ring)
58. {
59.     string s;
60.     Node node = ring;
61.     do
62.     {
63.         s ~= (s.empty ? "" : ", ") ~ node.n.to!string;
64.         node = node.next;
65.     } while (node != ring);
66.     return s;
67. }
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