【编程珠玑】读书笔记第八章算法设计艺术

2013-07-14 16:36:02

本章通过一个实例，展示了算法设计艺术，展示了一些算法设计的常用技术。

问题描述：

输入是具有n个浮点数的向量x，求输入向量的任何连续子向量中的最大和。

下面给出三种实现方法的代码，以及测试结果。

代码：

  1 #include <iostream>
  2 #include <cassert>
  3 using namespace std;
  4 const int SIZE = 100;
  5 
  6 //最直观的解法，时间复杂度为O(n^3)
  7 int GetMaxSumBasic(const int array[],const int len)
  8 {
  9     int currentSum = 0;
 10     int maxSum = 0;
 11     int i;
 12     int j;
 13     int k;
 14 
 15     assert(array != NULL && len >= 0);
 16 
 17     for (i = 0;i < len;++i)
 18     {
 19         for (j = i;j < len;++j)
 20         {
 21             currentSum = 0;
 22 
 23             for(k = i;k <= j;++k)
 24             {
 25                 currentSum = currentSum + array[k];
 26             }
 27 
 28             maxSum = maxSum > currentSum ? maxSum : currentSum;  //更新最大和
 29         }
 30     }
 31 
 32     return maxSum;
 33 }
 34 
 35 //最直观解法的改进，时间复杂度为O(n^2)
 36 int GetMaxSumImproved(const int array[],const int len)
 37 {
 38     int currentSum = 0;
 39     int maxSum = 0;
 40     int i;
 41     int j;
 42 
 43     assert(array != NULL && len >= 0);
 44 
 45     for (i = 0;i < len;++i)
 46     {
 47         currentSum = 0;
 48         for (j = i;j < len;++j)
 49         {
 50             currentSum = currentSum + array[j];
 51             maxSum = maxSum > currentSum ? maxSum : currentSum;     //更新最大和
 52         }
 53     }
 54 
 55     return maxSum;
 56 }
 57 
 58 //有技巧性的解法保存时间复杂度为O(n)
 59 int GetMaxSumAdvaced(const int array[],const int len)
 60 {
 61     int currentSum = 0;
 62     int maxSum = 0;
 63     int i;
 64 
 65     assert(array != NULL && len >= 0);
 66 
 67     for (i = 0;i < len;++i)
 68     {
 69         currentSum = currentSum + array[i];
 70         currentSum = (currentSum < 0) ? 0 : currentSum;    //若当前小于0，则置为0
 71         maxSum = maxSum > currentSum ? maxSum : currentSum; //更新最大和
 72     }
 73 
 74     return maxSum;
 75 }
 76 
 77 //显示数组元素
 78 void DisplayArray(const int array[],const int len)
 79 {
 80     assert(array != NULL && len >= 0);
 81     for (int i = 0;i < len;++i)
 82     {
 83         cout<<array[i]<<"	";
 84     }
 85     cout<<endl;
 86 }
 87 
 88 //测试程序
 89 int main(void)
 90 {
 91     int array[SIZE];
 92     int data;
 93     int len = 0;
 94 
 95     //input array
 96     cout<<"please enter the data of the array,end with ctrl+z : "<<endl;
 97     while (cin >> data)
 98     {
 99         array[len++] = data;
100     }
101 
102     cout<<"display the array :"<<endl;
103     DisplayArray(array,len);
104 
105     //test GetMaxSumBasic
106     cout<<"test GetMaxSumBasic..."<<endl;
107     cout<<"the max sum is : "<<GetMaxSumBasic(array,len)<<endl;
108 
109     //test GetMaxSumImproved
110     cout<<"test GetMaxSumImproved..."<<endl;
111     cout<<"the max sum is : "<<GetMaxSumImproved(array,len)<<endl;
112 
113     //test GetMaxSumAdvaced
114     cout<<"test GetMaxSumAdvaced..."<<endl;
115     cout<<"the max sum is : "<<GetMaxSumAdvaced(array,len)<<endl;
116     
117     return 0;
118 }

测试结果：

please enter the data of the array,end with ctrl+z :
31 -41 59 26 -53 58 97 -93 -23 84 ^Z
display the array :
31      -41     59      26      -53     58      97      -93     -23     84

test GetMaxSumBasic...
the max sum is : 187
test GetMaxSumImproved...
the max sum is : 187
test GetMaxSumAdvaced...
the max sum is : 187
请按任意键继续. . .

测试二：

please enter the data of the array,end with ctrl+z :
-23 24 -1 35 -28 67 -21 10 ^Z
display the array :
-23     24      -1      35      -28     67      -21     10
test GetMaxSumBasic...
the max sum is : 97
test GetMaxSumImproved...
the max sum is : 97
test GetMaxSumAdvaced...
the max sum is : 97
请按任意键继续. . .

【编程珠玑】读书笔记 第八章 算法设计艺术

【编程珠玑】读书笔记第八章算法设计艺术