integer_break

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343. Integer Break (Medium)

Given a positive integer n, break it into the sum of at least two positive integers and maximize the product of those integers. Return the maximum product you can get.

Example 1:

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

Example 2:

Input: 10
Output: 36
Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.

Note: You may assume that n is not less than 2 and not larger than 58.

Related Topics

[Math] [Dynamic Programming]

Hints

Hint 1

There is a simple O(n) solution to this problem.

Hint 2

You may check the breaking results of n ranging from 7 to 10 to discover the regularities.