[leetcode] 343. Integer Break

题目

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.

Constraints:

• 2 <= n <= 58

思路

这道题涉及到一个数学问题，一个整数n在拆分为多个e时，所求得的乘积是最大的，不过由于e不是整数，而接近e的有2和3，所有这个问题就变成拆分多少个2和3的问题。

代码

python版本：

class Solution:
    def integerBreak(self, n: int) -> int:
        dp = [0]*(n+1)
        dp[:7] = [0, 0, 1, 2, 4, 6, 9]
        for i in range(7, len(dp)):
            dp[i] = dp[i-3]*3
        return dp[n]