279. Perfect Squares(dp)

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

Example 1:

Input: n = 12
Output: 3 
Explanation: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.

1、自底向下的动态规划

class Solution {
public:
    //子问题、最小个数
    int numSquares(int n) {
        vector<int> dp(n+1,n);
        dp[0] = 0;
        dp[1] = 1;
        for(int i=2;i<=n;i++){
            for(int j=1;j*j<=i;j++){
                dp[i] = min(dp[i],dp[i-j*j]+1);
            }
        }
        return dp[n];
    }
};

法二：

拉格朗日四平方和定理

每个正整数均可表示为四个整数的平方和。证明：https://i.cnblogs.com/posts/edit

279. Perfect Squares(dp)

原文：https://www.cnblogs.com/wsw-seu/p/14017631.html