343 - Integer Break

#medium

Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.

Return the maximum product you can get.

Example 1:
Input: n = 2
Output: 1
Explanation: 2 = 1 + 1, 1 × 1 = 1.

Example 2:
Input:** n = 10
Output: 36
Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.

https://www.bilibili.com/video/BV1Mg411q7YJ

class Solution {
public:
    int integerBreak(int n) {
        // 三種一況，一種不拆，第二種拆兩個數，第三種拆三個數 j x (i-j)
        vector<int> dp( n + 1, 0 );
        dp[0] = 0;
        dp[1] = 0;
        dp[2] = 1;
        for ( int i = 3; i <= n; i++ ) {
            for ( int j = 1; j <= i; j++ ) {
                dp[i] = max( dp[i], max( j*(i-j), j * dp[i-j] ) );
            }
        }

        return dp[n];
    }
};