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.

For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

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Dynamic programming.

dp[i] = min(dp[k*k] + dp[i – k*k]), k = 0,1,2,3,…,sqrt(i)

class Solution {
public:
    int numSquares(int n) {
        int dp[n + 1];
        for(int i = 1; i <= n; i++){
            dp[i] = n;
            int k = 1;
            while(k*k <= i){
                if(k*k == i){
                    dp[i] = 1;
                }
                else{
                    dp[i] = dp[i] > dp[k*k] + dp[i - k*k]? dp[k*k] + dp[i - k*k]: dp[i];
                }
                k++;
            }
        }
        return dp[n];
    }
};