绳子切割问题：动态规划与贪心算法-优快云博客

本文链接：https://blog.youkuaiyun.com/csdn_zjp/article/details/100714202

本文探讨了绳子切割问题，旨在通过动态规划和贪心算法找到将绳子切割成若干段，使得各段长度的乘积最大的解决方案。动态规划方法通过自底向上计算每个可能长度的最优值，而贪心算法则基于数学规律快速求解。

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public class E14CuttingRope {
    //切割绳子，使得分段长度乘积最大

    public static int maxResultsAfterCutting_Solution1(int length) {
        //基于动态规划
        if (length < 2)
            return -1;
        if (length == 3)
            return 2;
        //被切割成相应长度所得值
        int[] results = new int[length + 1];
        results[0] = 0;
        results[1] = 1;
        results[2] = 2;
        results[3] = 3;
        //至下而上计算最优值
        int max = 0;
        for (int i = 4; i <= length; i++) {
            for (int j = 1; j <= i / 2; j++) {
                results[i] = results[j] * results[i - j];
                if (max < results[i])
                    max = results[i];
            }
            results[i] = max;
        }
        return results[length];
    }

    public static int maxResultsAfterCutting_Solution2(int length){
        //基于贪心算法实现
        int maxThreeTimes = length / 3;
        //余数为1时，即出现最后一个数为4的情况
        if (length % 3 == 1)
            maxThreeTimes -= 1;

        int maxTwoTimes = (length - maxThreeTimes * 3) / 2;
        return  (int)Math.pow(3, maxThreeTimes) * (int)Math.pow(2, maxTwoTimes);
    }

    //测试用例
    public static void main(String[] args){
        System.out.println(E14CuttingRope.maxResultsAfterCutting_Solution1(4));
        System.out.println(E14CuttingRope.maxResultsAfterCutting_Solution1(5));
        System.out.println(E14CuttingRope.maxResultsAfterCutting_Solution2(4));
        System.out.println(E14CuttingRope.maxResultsAfterCutting_Solution2(5));
    }
}

剪绳子（Java实现）