第四章 分治策略 最大子数组问题

最大子数组问题:找出数组中和最大的最大的非空连续子数组.

这里定义一个ret的类来进行存储三个值.用public只是用来方便读取和使用..

 

#include "stdafx.h"

#include<iostream>

using namespace std;

 

class ret

{

public:

ret(void){};

ret(int x,int y ,int z):max_left(x),max_right(y),right_sum(0){}

int max_left;

int max_right;

int right_sum;

};

 

ret FindMaxCrossingSubarray(int *arr,int low,int mid,int high);

ret findMaxSub(int *arr,int low,int high);

 

int _tmain(int argc, _TCHAR* argv[])

{

int arr[]={-1,-2,2,8,2,1,-2,4};

ret test= findMaxSub(arr,1,sizeof(arr)/sizeof(arr[0]));

cout<<"从第"<<test.max_left<<"个数到第"<<test.max_right<<"的和最大,和为:"<<test.right_sum<<endl;

return 0;

}

ret findMaxSub(int *arr,int low,int high)

{

 

if(low==high){

ret temp1;

temp1.max_left=low;

temp1.max_right=high;

temp1.right_sum=arr[low-1];

return temp1;

}

else

{

int mid = (low +high)/2;

ret temp2 = findMaxSub(arr,low,mid);

ret temp3 = findMaxSub(arr,mid+1,high);

ret temp4 = FindMaxCrossingSubarray(arr,low,mid,high);

if(temp2.right_sum>=temp3.right_sum&&temp2.right_sum>=temp4.right_sum)

return temp2;

else if(temp3.right_sum>=temp2.right_sum&&temp3.right_sum>=temp4.right_sum)

return temp3;

else return temp4;

}

 

}

ret FindMaxCrossingSubarray(int *arr,int low,int mid,int high)

{

ret temp; 

int left_sum =-99999,sum = 0,max_left=0;

for (int i =mid-1;i>=low-1;--i)

{

sum=sum+arr[i];

if(sum>left_sum)

{

left_sum = sum;

max_left = i;

}

}

int right_sum =-99999,rsum = 0,max_right=0;

for (int j =mid;j<=high-1;++j)

{

rsum=rsum+arr[j];

if(rsum>right_sum)

{

right_sum = rsum;

max_right = j;

}

}

 

temp.max_left=max_left+1;

temp.max_right=max_right+1;

temp.right_sum=left_sum+right_sum;

return temp;

}

 

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

class ret
{
public:
	ret(void){};
	ret(int x,int y ,int z):max_left(x),max_right(y),right_sum(0){}
	int max_left;
	int max_right;
	int right_sum;
};

ret FindMaxCrossingSubarray(int *arr,int low,int mid,int high);
ret findMaxSub(int *arr,int low,int high);

int _tmain(int argc, _TCHAR* argv[])
{
	int arr[]={-1,-2,2,8,2,1,-2,4};
	ret test= findMaxSub(arr,1,sizeof(arr)/sizeof(arr[0]));
	cout<<"从第"<<test.max_left<<"个数到第"<<test.max_right<<"的和最大,和为:"<<test.right_sum<<endl;
	return 0;
}
ret findMaxSub(int *arr,int low,int high)
{

	if(low==high){
		ret temp1;
		temp1.max_left=low;
		temp1.max_right=high;
		temp1.right_sum=arr[low-1];
		return temp1;
	}
	else
	{
		int mid = (low +high)/2;
		ret temp2 = findMaxSub(arr,low,mid);
		ret temp3 = findMaxSub(arr,mid+1,high);
		ret temp4 = FindMaxCrossingSubarray(arr,low,mid,high);
		if(temp2.right_sum>=temp3.right_sum&&temp2.right_sum>=temp4.right_sum)
			return temp2;
		else if(temp3.right_sum>=temp2.right_sum&&temp3.right_sum>=temp4.right_sum)
			return temp3;
		else return temp4;
	}

}
ret FindMaxCrossingSubarray(int *arr,int low,int mid,int high)
{
	ret temp; 
	int left_sum =-99999,sum = 0,max_left=0;
	for (int i =mid-1;i>=low-1;--i)
	{
		sum=sum+arr[i];
		if(sum>left_sum)
		{
			left_sum = sum;
			max_left = i;
		}
	}
	int right_sum =-99999,rsum = 0,max_right=0;
	for (int j =mid;j<=high-1;++j)
	{
		rsum=rsum+arr[j];
		if(rsum>right_sum)
		{
			right_sum = rsum;
			max_right = j;
		}
	}

	temp.max_left=max_left+1;
	temp.max_right=max_right+1;
	temp.right_sum=left_sum+right_sum;
	return temp;
}