Data commit

Task/Josephus-problem/C/josephus-problem.c

@@ -0,0 +1,46 @@
+#include <stdio.h>
+
+// m-th on the reversed kill list; m = 0 is final survivor
+int jos(int n, int k, int m) {
+	int a;
+	for (a = m + 1; a <= n; a++)
+		m = (m + k) % a;
+	return m;
+}
+
+typedef unsigned long long xint;
+
+// same as jos(), useful if n is large and k is not
+xint jos_large(xint n, xint k, xint m) {
+	if (k <= 1) return n - m - 1;
+
+	xint a = m;
+	while (a < n) {
+		xint q = (a - m + k - 2) / (k - 1);
+
+		if (a + q > n)	q = n - a;
+		else if (!q)	q = 1;
+
+		m = (m + q * k) % (a += q);
+	}
+
+	return m;
+}
+
+int main(void) {
+	xint n, k, i;
+
+	n = 41;
+	k = 3;
+	printf("n = %llu, k = %llu, final survivor: %d\n", n, k, jos(n, k, 0));
+
+	n = 9876543210987654321ULL;
+	k = 12031;
+	printf("n = %llu, k = %llu, three survivors:", n, k);
+
+	for (i = 3; i--; )
+		printf(" %llu", jos_large(n, k, i));
+	putchar('\n');
+
+	return 0;
+}