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JosephusProblem.java
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JosephusProblem.java
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/**
* An implementation of the Josephus problem Time complexity: O(n)
*
* @author Micah Stairs
*/
public class JosephusProblem {
// Suppose there are n people in a circle and person
// 0 kill the k'th person, then the k'th person kills
// the 2k'th person and so on until only one person remains.
// The question is who lives?
// Let n be the number of people and k the hop size
public static int josephus(int n, int k) {
int[] dp = new int[n];
for (int i = 1; i < n; i++) dp[i] = (dp[i - 1] + k) % (i + 1);
return dp[n - 1];
}
public static void main(String[] args) {
int n = 41, k = 2;
System.out.println(josephus(n, k));
n = 25;
k = 18;
System.out.println(josephus(n, k));
n = 5;
k = 2;
System.out.println(josephus(n, k));
}
}