//尋找最大子陣列的和，分成三種情況來討論
/*
在陣列A[low...high]中，任何連續子陣列A[i...j]的位置有三種
一、完全位於陣列A[low...mid]中，因此low<=i<=j<=mid
二、完全位於陣列A[mid+1...high]中，因此mid<i<=j<=mid
三、跨越了中點，因此low<=i<=mid<j<=high
*/

class FindMaxSubarray
{
public:
	//尋找跨越中點的陣列，得到的是crossLow,crossHigh,crossSum
	void findMaxCrossingSubarray(int *,int,int,int);
	//尋找和最大的子陣列，得到的是lLow,hHigh,sSum,
	void findMaxSubarray(int *,int,int);

	int getLow(){return lLow;}
	int getHigh(){return hHigh;}
	int getSum(){return sSum;}

private:
	int leftLow,leftHigh,leftSum;
	int rightLow,rightHigh,rightSum;
	int crossLow,crossHigh,crossSum;
	
	int lLow,hHigh,sSum;
};

void FindMaxSubarray::findMaxCrossingSubarray(int *sPtr,int low,int mid,int high)
{
	int sum=0;//臨時子陣列和,sum不賦值就蛋疼了！！！！！！！！！！
	
	//mid左邊的最大和
	int left_sum = sPtr[mid];//最接近mid位置的數作為left_sum

	for(int k=mid;k>=low;k--)
	{
		sum = sum + sPtr[k];
		if(sum>left_sum)//尋找mid左邊最大和
		{
			left_sum = sum;
			lLow = k;
		}
	}

	int right_sum = sPtr[mid+1];//最接近mid位置的數作為right_sum
	sum = 0;
	for(int k=mid+1;k<=high;k++)
	{
		sum = sum + sPtr[k];
		if(sum>right_sum)//尋找mid右邊最大和
		{
			right_sum = sum;
			hHigh = k;
		}
	}
    
	//得到跨越mid的字串最大和
	sSum = left_sum + right_sum;
}


void FindMaxSubarray::findMaxSubarray(int * sPtr,int low,int high)
{
	if(low == high)//只有一個元素的起情況
	{
		lLow = low;
		hHigh = high;
		sSum = sPtr[low];
	}
	else
	{
		int mid = (low+high)/2;

		findMaxSubarray(sPtr,low,mid);//找出mid左邊最大陣列和
		leftLow = lLow;
		leftHigh = hHigh;
		leftSum = sSum;

		findMaxSubarray(sPtr,mid+1,high);//找出mid右邊最大陣列和
		rightLow = lLow;
		rightHigh = hHigh;
		rightSum = sSum;

		findMaxCrossingSubarray(sPtr,low,mid,high);//找出跨越mid的最大陣列和
		crossLow = lLow;
		crossHigh = hHigh;
		crossSum = sSum;

		//比較leftSum,rightSum,crossSum的大小來確定sSum
		if((leftSum>=rightSum)&&(leftSum>=crossSum))
		{
			lLow = leftLow;
			hHigh = leftHigh;
			sSum = leftSum;
		}
		else if((rightSum>=leftSum)&&(rightSum>=crossSum))
		{
			lLow = rightLow;
			hHigh = rightHigh;
			sSum = rightSum;
		}
		else
		{
			lLow = crossLow;
			hHigh = crossHigh;
			sSum = crossSum;
		}
 	}
}