Perfect Squares——Leetcode

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.

题目大意：给一个正整数，找出可以由最少个平方数构成的数量是多少。

解题思路：dynamic programming，递推公式F[n]=min{F[n-1]+1,F[n-4]+2,F[n-9]+3,...};

public class Solution {
    int[] f;
    public int numSquares(int n) {
        f=new int[n+1];
        Arrays.fill(f,Integer.MAX_VALUE);
        f[1]=1;
        for(int i=2;i<=n;i++){
            int r = (int)Math.sqrt(i);
            if(i==r*r){
                f[i]=1;
                continue;
            }
            for(int j=1;j<=r;j++){
                f[i]=Math.min(f[i],f[i-j*j]+1);
            }
        }
        return f[n];
    }
}