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.

Solution:

  1. public class Solution {
  2.   public int numSquares(int n) {
  3.     // dp(i) represents the least number of PS which sum to i
  4.     int[] dp = new int[n + 1];
  6.     Arrays.fill(dp, Integer.MAX_VALUE);
  7.     dp[0] = 0;
  9.     for (int i = 0; i <= n; i++) {
  10.       for (int j = 1; i + j * j <= n; j++) {
  11.         dp[i + j * j] = Math.min(dp[i + j * j], dp[i] + 1);
  12.       }
  13.     }
  15.     return dp[n];
  16.   }
  17. }