Leetcode/G家--279.Perfect Squares(DP)

279.Perfect Squares（DP）

• Difficulty: Medium

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.

https://leetcode.com/problems/perfect-squares/ 

解释 https://discuss.leetcode.com/topic/26400/an-easy-understanding-dp-solution-in-java

 

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