343. Integer Break (分割整数的最大乘积)

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.

分析：很直观的就能看出这道题用的是动态规划；因为dp[3]需要dp[2]和dp[1]的结果。

时间复杂度：o（n*2）                  空间复杂度：o(n)