[Dynamic Programming] leetcode 343 Integer Break

problem:https://leetcode.com/problems/integer-break/

         Enumerate all integer add, they take the maximum product of the product, and then selecting the largest value.

class Solution {
public:
    int integerBreak(int n) {
        vector<int> dp(n + 1, 0);
        dp[1] = 1;
        for(int i = 2; i <= n;i++)
        {
            for(int j = 1; j <= i/2 ;j++)
            {
                dp[i] = max(dp[i], max(j,dp[j]) * max(i - j, dp[i - j]));
            }
        }
        return dp[n];
    }
};