剑指offer——面试题14：剪绳子

// 面试题14：剪绳子
// 题目：给你一根长度为n绳子，请把绳子剪成m段（m、n都是整数，n>1并且m≥1）。
// 每段的绳子的长度记为k[0]、k[1]、……、k[m]。k[0]*k[1]*…*k[m]可能的最大乘
// 积是多少？例如当绳子的长度是8时，我们把它剪成长度分别为2、3、3的三段，此
// 时得到最大的乘积18。

#include <iostream>
#include <cmath>

// ====================动态规划====================
int maxProductAfterCutting_solution1(int length)
{
    if(length < )
        return ;
    if(length == )
        return ;
    if(length == )
        return ;

    int* products = new int[length + ];
    products[] = ;
    products[] = ;
    products[] = ;
    products[] = ;

    int max = ;
    for(int i = ; i <= length; ++i)
    {
        max = ;
        for(int j = ; j <= i / ; ++j)
        {
            int product = products[j] * products[i - j];
            if(max < product)
                max = product;

            products[i] = max;
        }
    }

    max = products[length];
    delete[] products;

    return max;
}

// ====================贪婪算法====================
int maxProductAfterCutting_solution2(int length)
{
    if(length < )
        return ;
    if(length == )
        return ;
    if(length == )
        return ;

    // 尽可能多地减去长度为3的绳子段
    int timesOf3 = length / ;

    // 当绳子最后剩下的长度为4的时候，不能再剪去长度为3的绳子段。
    // 此时更好的方法是把绳子剪成长度为2的两段，因为2*2 > 3*1。
    if(length - timesOf3 *  == )
        timesOf3 -= ;

    int timesOf2 = (length - timesOf3 * ) / ;

    return (int) (pow(, timesOf3)) * (int) (pow(, timesOf2));
}

// ====================测试代码====================
void test(const char* testName, int length, int expected)
{
    int result1 = maxProductAfterCutting_solution1(length);
    if(result1 == expected)
        std::cout << "Solution1 for " << testName << " passed." << std::endl;
    else
        std::cout << "Solution1 for " << testName << " FAILED." << std::endl;

    int result2 = maxProductAfterCutting_solution2(length);
    if(result2 == expected)
        std::cout << "Solution2 for " << testName << " passed." << std::endl;
    else
        std::cout << "Solution2 for " << testName << " FAILED." << std::endl;
}

void test1()
{
    int length = ;
    int expected = ;
    test("test1", length, expected);
}

void test2()
{
    int length = ;
    int expected = ;
    test("test2", length, expected);
}

void test3()
{
    int length = ;
    int expected = ;
    test("test3", length, expected);
}

void test4()
{
    int length = ;
    int expected = ;
    test("test4", length, expected);
}

void test5()
{
    int length = ;
    int expected = ;
    test("test5", length, expected);
}

void test6()
{
    int length = ;
    int expected = ;
    test("test6", length, expected);
}

void test7()
{
    int length = ;
    int expected = ;
    test("test7", length, expected);
}

void test8()
{
    int length = ;
    int expected = ;
    test("test8", length, expected);
}

void test9()
{
    int length = ;
    int expected = ;
    test("test9", length, expected);
}

void test10()
{
    int length = ;
    int expected = ;
    test("test10", length, expected);
}

void test11()
{
    int length = ;
    int expected = ;
    test("test11", length, expected);
}

int main(int agrc, char* argv[])
{
    test1();
    test2();
    test3();
    test4();
    test5();
    test6();
    test7();
    test8();
    test9();
    test10();
    test11();

    return ;
}