分治法解决最大子数组问题

/*
* 对于给定的整数数组A，求出数组中具有最大和的子数组，最大和以及左右下标
* 思路：采用分治的方法，将数组分为两部分，则有最大和的子数组共有三种情况
* 在数组左边，在数组右边，跨越数组中点
*/

#include <iostream>
using namespace std;

//存放左右边界值以及sum值的结构体
/*特别注意结构体的使用！！！！！！！！！！！*/
struct SumBorder
{
int left; //左部边界下标
int right; //右部边界下标
int sum; //左右边界之间的数组元素和
};

//找到横跨中点mid，在数组A[low..high]之间的最大子数组的和
SumBorder *findMaxCrossSubarray(int *ptrA, int low, int mid, int high)
{
/*得到mid左边的最大和*/
int leftSum = ptrA[mid]; //左部最大和
int maxLeft = mid; //左边界
int sum = 0;
for (int i = mid; i >= low; i--)
{
sum += ptrA[i];
if (sum >= leftSum)
{
leftSum = sum;
maxLeft = i;
}
}
/*得到mid+1及右边最大和*/
int rightSum = ptrA[mid + 1];
int maxRight = mid + 1;
sum = 0;
for (int j = mid + 1; j <= high; j++)
{
sum += ptrA[j];
if (sum >= rightSum)
{
rightSum = sum;
maxRight = j;
}
}
/*统计汇总*/
SumBorder sumBorder;
SumBorder *ptr = &sumBorder;
ptr->left = maxLeft;
ptr->right = maxRight;
ptr->sum = leftSum + rightSum;
cout << ptr->left << "-" << ptr->right << " sum:" << ptr->sum << endl;
return ptr;
}

/*得到数组A(从low到high)的最大子数组和*/
SumBorder *findMaxSubarray(int *ptrA, int low, int high)
{
SumBorder sumBorder;
SumBorder *sumBorderPtr = &sumBorder;
if (high == low)
{
sumBorder.left = low;
sumBorder.right = high;
sumBorder.sum = ptrA[low];
}
else
{
int mid = (low + high) / 2;
//得到三种情况下的结构体指针变量并进行进一步的判断
SumBorder *left = findMaxSubarray(ptrA, low, mid);
SumBorder *right = findMaxSubarray(ptrA, mid + 1, high);
SumBorder *cross = findMaxCrossSubarray(ptrA, low, mid, high);
if (left->sum >= right->sum  && left->sum >= cross->sum)
{
sumBorder.left = left->left;
sumBorder.right = left->right;
sumBorder.sum = left->sum;
}
else if (right->sum >= left->sum && right->sum >= cross->sum)
{
sumBorder.left = right->left;
sumBorder.right = right->right;
sumBorder.sum = right->sum;
}
else
{
sumBorder.left = cross->left;
sumBorder.right = cross->right;
sumBorder.sum = cross->sum;
}
}
cout << sumBorderPtr->left << "-" << sumBorderPtr->right
<< " 最大值为:" << sumBorderPtr->sum << endl;
return sumBorderPtr;
}

int main()
{
//给定的数组
int A[] = {0, 13, -3, -25, 20, -3, -16, -23, 18,
20, -7, 12, -5, -22, 15, -4, -7};
SumBorder sumBorder;
SumBorder *Ptr = &sumBorder;
SumBorder *test = findMaxSubarray(A, 1, 16); //吃过大亏！
Ptr->left = test->left;
Ptr->right = test->right;
Ptr->sum = test->sum;

/* 把上面的替换成这样是错误的，仔细学习一下struct结构体！！
SumBorder *Ptr = findMaxSubarray(A, 1, 16);
cout << "left:" << Ptr->left << endl;
cout << "right:" << Ptr->right << endl;
cout << "sum:" << Ptr->sum << endl;
*/

cout << "数组A的最大子数组和为：" << endl;
cout << "left:" << Ptr->left << endl;
cout << "right:" << Ptr->right << endl;
cout << "sum:" << Ptr->sum << endl;
system("pause >> cout");
return 0;
}