343. Integer Break 【M】

原创于 2016-04-23 17:16:57 发布 · 441 阅读

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探讨如何将一个正整数拆分为至少两个正整数之和，并最大化这些整数的乘积。通过分析发现，尽量将整数拆分为3可以得到最大的乘积结果，特殊情况除外。

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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.

For example, given n = 2, return 1 (2 = 1 + 1); given n = 10, return 36 (10 = 3 + 3 + 4).

Note: you may assume that n is not less than 2.

Hint:

There is a simple O(n) solution to this problem.
You may check the breaking results of n ranging from 7 to 10 to discover the regularities.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

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其实就是一道小学奥数题，尽可能多的分成3，如果最后剩下的是1，那就变成两个2

class Solution(object):
    def integerBreak(self, n):
        if n == 2:
            return 1
        if n == 3:
            return 2
        p = n / 3

        rest = n % 3

        #print p,rest

        if rest == 1:
            return 3 ** (p-1) * 4
        elif rest == 0:
            return 3 ** (p)
        else:
            return (3 ** p) * rest