算法：最大子数组own

转载标明出处：http://i.cnblogs.com/EditPosts.aspx?postid=4726782&update=1

暴力法:

 // maxValue.cpp : 定义控制台应用程序的入口点。
 //

 #include "stdafx.h"
 #include <iostream>

 using namespace std;

 int findMax(int *a,int low,int high,int &sub_left,int &sub_right,int &sub_sum)
 {
     if (low==high)
     {
         if(a[low]>)
         {
             sub_left=low;
             sub_right=high;
             sub_sum=a[low];
         }
         else sub_sum=;
     }

     else
     {
         for(int i=;i<=high;i++)
         {
             int tempSum=;
             for (int j=i;j<=high;j++)
             {
                 tempSum+=a[j];
                 if (tempSum>sub_sum)
                 {
                     sub_sum=tempSum;
                     sub_left=i;
                     sub_right=j;
                 }
             }
         }
     }
     return ;
 }

 int _tmain(int argc, _TCHAR* argv[])
 {
     int sub_left=;
     int sub_right=;
     int sub_sum=;
     int a[]={,-,-,,-,-,-,,,-,,-,-,,-,};
     findMax(a,,,sub_left,sub_right,sub_sum);
     cout<<sub_left<<" "<<sub_right<<" "<<sub_sum<<endl;
     system("pause");
     return ;
 }

时间复杂度：O(n*n);

分治法:

// maxSubArray.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <iostream>

using namespace std;

int Find_Max_cross_subArray(int *a,int low,int middle,int high,int &max_left,int &max_right,int &max_value)
{
    int left_sum=-;
    int sum=;
    for (int i=middle;i>=low;i--)
    {
        sum+=a[i];
        if (sum>left_sum)
        {
            left_sum=sum;
            max_left=i;
        }
    }

    int right_sum=-;
    sum=;
    for (int j=middle+;j<=high;j++)
    {
        sum+=a[j];
        if (sum>right_sum)
        {
            right_sum=sum;
            max_right=j;
        }
    }
    max_value=left_sum+right_sum;
    return ;

}

int Find_Max_subArray(int *a,int low,int high,int &max_left,int &max_right,int &max_vlaue)
{
    if (low==high)
    {
        if (a[low]>)
        {
            max_vlaue=a[low];
            max_left=low;
            max_right=high;
        }
        else max_vlaue=;
    }
    else
    {
        int middle=(low+high)/;
        int tem_left_low;
        int tem_left_high;
        int tem_left_sum;
        Find_Max_subArray(a,low,middle,tem_left_low,tem_left_high,tem_left_sum);

        int tem_right_low;
        int tem_right_high;
        int tem_right_sum;
        Find_Max_subArray(a,middle+,high,tem_right_low,tem_right_high,tem_right_sum);

        int tem_cross_low;
        int tem_cross_high;
        int tem_cross_sum;
        Find_Max_cross_subArray(a,low,middle,high,tem_cross_low,tem_cross_high,tem_cross_sum);

        if (tem_left_sum>=tem_right_sum&&tem_left_sum>=tem_cross_sum)
        {
            max_left=tem_left_low;
            max_right=tem_left_high;
            max_vlaue=tem_left_sum;
        }
        else if (tem_right_sum>=tem_left_sum&&tem_right_sum>=tem_cross_sum)
        {
            max_left=tem_right_low;
            max_right=tem_right_high;
            max_vlaue=tem_right_sum;
        }
        else
        {
            max_left=tem_cross_low;
            max_right=tem_cross_high;
            max_vlaue=tem_cross_sum;
        }
    }
    return ;
}

int _tmain(int argc, _TCHAR* argv[])
{
    int max_left=;
    int max_right=;
    int max_value=;
    int a[]={,-,-,,-,-,-,,,-,,-,-,,-,};
    Find_Max_subArray(a,,,max_left,max_right,max_value);
    cout<<max_left<<" "<<max_right<<" "<<max_value<<endl;
    system("pause");
    return ;
}

递归式： T(n)=2*T(n/2)+Theta(n);n>1

T(n)=theta(1);

非递归线性算法：(4.1-5)

此方是看了我转载的那个伙伴的才有思路,和为负数，就跳过。

 // Max_Value.cpp : 定义控制台应用程序的入口点。
 //

 #include "stdafx.h"
 #include <iostream>
 using namespace std;

 int Max(int *a,int low,int high,int &sub_left,int &sub_right,int &sub_sum)
 {
     if (low==high)
     {
         if (a[low]>)
         {
             sub_sum=a[low];
             sub_left=low;
             sub_right=high;
         }
         else sub_sum=;
     }
     int tempSum=;
     for (int i=low;i<=high;i++)
     {
         tempSum+=a[i];
         if (tempSum<=)
         {
             tempSum=;
             sub_left=i+;
         }
         if (tempSum>sub_sum)
         {
             sub_sum=tempSum;
             sub_right=i;
         }
     }
     return ;
 }
 int _tmain(int argc, _TCHAR* argv[])
 {
     int sub_left=;
     int sub_right=;
     int sub_sum=;
     int a[]={,-,-,,-,-,-,,,-,,-,-,,-,};
     Max(a,,,sub_left,sub_right,sub_sum);
     cout<<sub_left<<" "<<sub_right<<" "<<sub_sum<<endl;
     system("pause");
     return ;
 }

只扫描了一遍，时间复杂度为O(n);

以上方法输出结果都一样：7 10 43