剪绳子

题目：

给你一段长度为n的绳子，请把绳子剪成m段，每段绳子的长度记为：k[0]、k[1]、...。请问它们的乘积最大值是多少？

解答：

 1 public class Solution {
 2     public static void main(String[] args) {
 3         System.out.println(maxProductAfterCutting(5));
 4     }
 5 
 6     public static int maxProductAfterCutting(int length) {
 7         // 长度为2,只可能剪成长度为1的两段
 8         if(length < 2) {
 9             return 0;
10         }
11 
12         if(length == 2) {
13             return 1;
14         }
15 
16         if(length == 3) {
17             return 2;
18         }
19 
20         int[] products = new int[length+1];
21         products[0] = 0;
22         products[1] = 1;
23         products[2] = 2;
24         products[3] = 3;
25 
26         int max = 0;
27         for(int k = 4; k <= length; k++) {
28             max = 0;
29             for(int i = 1; i <= k/2; i++) {
30                 
31                 int product = products[i]*products[k-j];
32                 if(product > max) {
33                     max = product;
34                 }
35 
36                 products[k] = max;
37             }
38         }
39 
40         return products[length];
41 
42     }
43 }