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leetcode@ [343] Integer Break (Math & Dynamic Programming)

时间:2016-06-30 01:12:54      阅读:285      评论:0      收藏:0      [点我收藏+]

https://leetcode.com/problems/integer-break/

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:

Show Hint

  1. There is a simple O(n) solution to this problem.Show More Hint
  2. You may check the breaking results of n ranging from 7 to 10 to discover the regularities.
技术分享
public class Solution {
    public int integerBreak(int n) {
        
        if(n <= 2) {
            return 1;
        } else if (n == 3) {
            return 2;
        }
        
        double radical = Math.sqrt((double) n);
        int rad = (int) Math.floor(radical);
        
        int rs = 0, power = 0;
        for(int i=1; i<=rad+1; ++i) {
            int times = n / i;
            int remain = n - i*times;
            
            if(remain == 0) {
                power = (int) Math.pow(i, times);
                rs = Math.max(rs, power);
            } else {
                int power_1 = (int) Math.pow(i, times-1) * (remain + i);
                int power_2 = (int) Math.pow(i, times) * remain;
                rs = Math.max(rs, Math.max(power_1, power_2));
            }
        }
        
        return rs;
    }
}
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leetcode@ [343] Integer Break (Math & Dynamic Programming)

原文:http://www.cnblogs.com/fu11211129/p/5628645.html

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