Perfect Squares

Total Accepted: 18854 Total Submissions: 63048 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.

f(n) = min{f(n-1),f(n-4),f(n-9)...f(n-k*k)}+1,其中k*k <=n && k>=1;

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