279. Perfect Squares

Given an integer n, return the least number of perfect square numbers that sum to n.

A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

class Solution {
    int dp[10001];
    int dfs(int n) {
        if(dp[n] != -1) return dp[n];
        dp[n] = INT_MAX;
        for(int i = 1; i*i <= n; i++) {
            dp[n] = min(dfs(i * i) + dfs(n - i*i), dp[n]);
        }
        return dp[n];
    }
public:
    int numSquares(int n) {
        memset(dp, -1, sizeof(dp));
        dp[0] = 0;
        for(int i = 1; i*i <= n; i++) dp[i*i] = 1;
        return dfs(n);
    }
};