【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：

#include <iostream>
#include <cassert>
using namespace std;
const int SIZE = 100;

//最直观的解法，时间复杂度为O(n^3)
int GetMaxSumBasic(const int array[],const int len)
{
    int currentSum = 0;
    int maxSum = 0;
    int i;
    int j;
    int k;

    assert(array != NULL && len >= 0);

    for (i = 0;i < len;++i)
    {
        for (j = i;j < len;++j)
        {
            currentSum = 0;

            for(k = i;k <= j;++k)
            {
                currentSum = currentSum + array[k];
            }

            maxSum = maxSum > currentSum ? maxSum : currentSum;  //更新最大和
        }
    }

    return maxSum;
}

//最直观解法的改进，时间复杂度为O(n^2)
int GetMaxSumImproved(const int array[],const int len)
{
    int currentSum = 0;
    int maxSum = 0;
    int i;
    int j;

    assert(array != NULL && len >= 0);

    for (i = 0;i < len;++i)
    {
        currentSum = 0;
        for (j = i;j < len;++j)
        {
            currentSum = currentSum + array[j];
            maxSum = maxSum > currentSum ? maxSum : currentSum;     //更新最大和
        }
    }

    return maxSum;
}

//有技巧性的解法保存时间复杂度为O(n)
int GetMaxSumAdvaced(const int array[],const int len)
{
    int currentSum = 0;
    int maxSum = 0;
    int i;

    assert(array != NULL && len >= 0);

    for (i = 0;i < len;++i)
    {
        currentSum = currentSum + array[i];
        currentSum = (currentSum < 0) ? 0 : currentSum;    //若当前小于0，则置为0
        maxSum = maxSum > currentSum ? maxSum : currentSum; //更新最大和
    }

    return maxSum;
}

//显示数组元素
void DisplayArray(const int array[],const int len)
{
    assert(array != NULL && len >= 0);
    for (int i = 0;i < len;++i)
    {
        cout<<array[i]<<"	";
    }
    cout<<endl;
}

//测试程序
int main(void)
{
    int array[SIZE];
    int data;
    int len = 0;

    //input array
    cout<<"please enter the data of the array,end with ctrl+z : "<<endl;
    while (cin >> data)
    {
        array[len++] = data;
    }

    cout<<"display the array :"<<endl;
    DisplayArray(array,len);

    //test GetMaxSumBasic
    cout<<"test GetMaxSumBasic..."<<endl;
    cout<<"the max sum is : "<<GetMaxSumBasic(array,len)<<endl;

    //test GetMaxSumImproved
    cout<<"test GetMaxSumImproved..."<<endl;
    cout<<"the max sum is : "<<GetMaxSumImproved(array,len)<<endl;

    //test GetMaxSumAdvaced
    cout<<"test GetMaxSumAdvaced..."<<endl;
    cout<<"the max sum is : "<<GetMaxSumAdvaced(array,len)<<endl;
    
    return 0;
}

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. . .