leetcode 279. 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.

Example 1:

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

Example 2:

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

思路：dp[i]表示和为i的最少的完全平方数个数。

class Solution {
public:
    int numSquares(int n) {
        if (n <= 0)
            return 0;
        vector<int> dp(n + 1, 0);
        dp[0] = 0;
        for (int i = 1; i <= n; i++) {
            dp[i] = INT_MAX;
            for (int j = 1; j * j <= i; j++) {
                dp[i] = min(dp[i], dp[i - j * j] + 1);
            }
        }
        return dp[n];
    }
};

static dynamic programming:

class Solution {
public:
    int numSquares(int n) {
        if (n <= 0)
            return 0;
        static vector<int> dp({0});
        while (dp.size() <= n) {
            int m = dp.size();
            int cnt = INT_MAX;
            for (int j = 1; j * j <= m; j++) {
                cnt = min(cnt, dp[m - j * j] + 1);
            }
            dp.push_back(cnt);
        }
        return dp[n];
    }
};

思路三：数学方法：勒让德多项式。