[LeetCode]Perfect Squares

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.

DP问题，计算1-n的每个值得perfect squares，从小到大计算。

递推公式f[i]=min(f[i],f[i-j*j]+1)。

class Solution {
public:
    int numSquares(int n) {
        vector<int> f(n+1,0);
        f[1]=1;
        for(int i=2;i<=n;i++)
        {
            int local_min = INT_MAX;
            int j=1;
            while(j*j<=i)
            {
                if(j*j==i)
                {
                    local_min = 1;
                    break;
                }
                else
                {
                    local_min = min(local_min,f[i-j*j]+1);
                    j++;
                }
            }
            f[i]=local_min;
        }
        return f[n];
    }
};