Leetcode: Perfect Squares

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.

 1 public class Solution {
 2     public int numSquares(int n) {
 3         int[] dp = new int[n+1];
 4         int k = 1;
 5         for (int i=1; i<=n; i++) {
 6             if (i == k*k) {
 7                 dp[i] = 1;
 8                 k++;
 9             }
10             else dp[i] = i;
11         }
12         for (int i=2; i<=n; i++) {
13             int sqrt = (int)Math.sqrt(i);
14             for (int j=1; j<=sqrt; j++) {
15                 dp[i] = Math.min(dp[i], dp[i-j*j]+1);
16             }
17         }
18         return dp[n];
19     }
20 }