Solution 18: 约瑟夫环问题

public class JosephLoop {
	public int josephLoopByList(int n, int m) {
		if (n <= 0 || m <= 0) {
			return -1;
		}

		int cnt = n;
		boolean[] p = new boolean[n];
		int k = 0;

		while (cnt > 1) {
			for (int i = 0; i < p.length; i++) {
				if (!p[i]) {
					++k;
					if (k == m) {
						p[i] = true;
						--cnt;
						k = 0;
					}
				}
			}
		}

		for (int i = 0; i < p.length; i++) {
			// get the last one
			if (!p[i]) {
				return i + 1;
			}
		}

		return -1;
	}
	
	// recursion
	public int josephLoopRec(int n, int m) {
		if (n <= 0 || m <= 0) {
			return -1;
		}
		return helper(n, m, n) + 1;
	}

	private int helper(int n, int m, int i) {
		if (i == 1) {
			return (m - 1) % n;
		}
		return (helper(n - 1, m, i - 1) + m) % n;
	}
}