Given a positive integer n, find the least number of perfect square numbers (for example, 1, 4, 9, 16, ...) which sum to n.

For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.

Solution

public class Solution {
    public int numSquares(int n) {
        int dp[] = new int[n + 1];
        dp[0] = 0;
        for(int i = 1; i <= n; i++) {
            int min = Integer.MAX_VALUE;
            int offset = 1;
            while(i - offset*offset >= 0) {
                min = Integer.min(min, dp[i - offset*offset]);
                offset++;
            }
            dp[i] = min + 1;
        }
        return dp[n];
    }
}