《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 ;
 }