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：

public class Solution {
    public static void main(String[] args) {
        System.out.println(maxProductAfterCutting(5));
    }

    public static int maxProductAfterCutting(int length) {
        // 长度为2,只可能剪成长度为1的两段
        if(length < 2) {
            return 0;
        }

        if(length == 2) {
            return 1;
        }

        if(length == 3) {
            return 2;
        }

        int[] products = new int[length+1];
        products[0] = 0;
        products[1] = 1;
        products[2] = 2;
        products[3] = 3;

        int max = 0;
        for(int k = 4; k <= length; k++) {
            max = 0;
            for(int i = 1; i <= k/2; i++) {
                
                int product = products[i]*products[k-j];
                if(product > max) {
                    max = product;
                }

                products[k] = max;
            }
        }

        return products[length];

    }
}