Integer Break

Problem Statement

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.

Leetcode Link

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

Code

Python Code

class Solution(object):
    def integerBreak(self, n):
        dp = [None, 1]
        for m in range (2, n + 1):
            j = m - 1
            i = 1
            max_product = 0
            while i <= j:
                max_product = max(max_product, max(i, dp[i]) * max(j, dp[j]))
                j -= 1
                i += 1
            dp.append(max_product)
        return dp[n]