Integer Break — LeetCode 343 Python Solution

The problem

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

Input

n = 2

Output

1

Explanation

2 = 1 + 1, 1 × 1 = 1.

Python solution

class Solution:
    def integerBreak(self, n: int) -> int:
        f = [1] * (n + 1)
        for i in range(2, n + 1):
            for j in range(1, i):
                f[i] = max(f[i], f[i - j] * j, (i - j) * j)
        return f[n]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 343. Integer Break is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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