《OFFER14》14_CuttingRope

 

 // 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 ;

 }