分治算法，最大子数组问题？？

[LinYF1980]

我按照算法导论写的代码，给定1,3,1,-1,我觉得应该输出5,也就是1,3,1，而算法给出结果是4,有1,3构成。为什么？


package b;

public class FindMaxCrossingSub {
static int nosum=0;
public static final int MAXLEFTID=0,MAXRIGHTID=1,MAXSUM=2;

public static int[] crossSub(int[] A,int low,int mid,int right){
int sum=0;
int[] cross=new int[3];
int leftSum=0,rightSum=0;
int maxLeft=0,maxRight=0;
//find maxleft
for(int i=mid;i>=low;i--){
sum+=A[i];
if(sum>leftSum){
leftSum=sum;
maxLeft=i;
}else{
leftSum=0;
maxLeft=mid;
}

}
//find maxright
sum=0;
for(int i=mid+1;i<=right;i++){
sum+=A[i];
if(sum>rightSum){
rightSum=sum;
maxRight=i;
}else{
rightSum=0;
maxRight=mid;
}
}
//modify value array
cross[MAXLEFTID]=maxLeft;
cross[MAXRIGHTID]=maxRight;
cross[MAXSUM]=leftSum+rightSum;
System.out.println("leftsum:"+leftSum+",rightsum:"+rightSum);
return cross;
}

public static void print(int[] temp){
for(int i=0;i<temp.length;i++){
System.out.println("no "+i+":"+temp[i]);
}
}

public static int[] findMax(int[] A,int left,int right){
nosum++;
System.out.println("第"+nosum+"次递归调用:"+"left:"+left+"right:"+right);
//System.out.println(Thread.currentThread().getStackTrace()[1].getMethodName());
int mid;
int[] valueArray=new int[3];
int[] leftArray=new int[3];
int[] rightArray=new int[3];
int[] crossArray=new int[3];
if(left==right){
valueArray[MAXLEFTID]=left;
valueArray[MAXRIGHTID]=right;
valueArray[MAXSUM]=A[left];
return valueArray;
}else{
mid=(int) Math.floor((left+right)/2);
leftArray=findMax(A,left,mid);
rightArray=findMax(A,mid+1,right);
crossArray=crossSub(A,left,mid,right);
if((leftArray[MAXSUM]>rightArray[MAXSUM])&&(leftArray[MAXSUM]>crossArray[MAXSUM]))
return leftArray;
else if((rightArray[MAXSUM]>leftArray[MAXSUM])&&(rightArray[MAXSUM]>crossArray[MAXSUM]))
return rightArray;
else return crossArray;
}
}

public static void main(String[] args) {
// TODO Auto-generated method stub
int[] value=new int[3];
int[] c={1,3,1,-1};
print(c);
value=findMax(c,0,c.length-1);
//print(cross);
System.out.println("---max subArray---");
for(int i=value[0];i<=value[1];i++)
System.out.println("A["+i+"]:"+c[i]);
System.out.print("最大子数组和为："+value[2]);
}

}

[大羽飞鹤]

package b;

public class FindMaxCrossingSub {
	static int nosum=0;	
	public static final int MAXLEFTID=0,MAXRIGHTID=1,MAXSUM=2;
	
	public static int[] crossSub(int[] A,int low,int mid,int right){
		int sum=0;
		int[] cross=new int[3];
		int leftSum=0,rightSum=0;
		int maxLeft=0,maxRight=0;
		//find maxleft
		for(int i=mid;i>=low;i--){
			sum+=A[i];
			if(sum>leftSum){
				leftSum=sum;
				maxLeft=i;
			}else{
				leftSum=0;
				maxLeft=mid;
			}
				
		}
		//find maxright
		sum=0;
		for(int i=mid+1;i<=right;i++){
			sum+=A[i];
			if(sum>rightSum){
				rightSum=sum;
				maxRight=i;
			}else{
				rightSum=0;
				maxRight=mid;
			}
		}
		//modify value array
		cross[MAXLEFTID]=maxLeft;
		cross[MAXRIGHTID]=maxRight;
		cross[MAXSUM]=leftSum+rightSum;		
		System.out.println("leftsum:"+leftSum+",rightsum:"+rightSum);
		return cross;
	}
	
	public static void print(int[] temp){
		for(int i=0;i<temp.length;i++){
			System.out.println("no "+i+":"+temp[i]);
		}
	}
	
	public static int[] findMax(int[] A,int left,int right){
		nosum++;
		System.out.println("第"+nosum+"次递归调用:"+"left:"+left+"right:"+right);
		//System.out.println(Thread.currentThread().getStackTrace()[1].getMethodName());
		int mid;
		int[] valueArray=new int[3];
		int[] leftArray=new  int[3];
		int[] rightArray=new int[3];
		int[] crossArray=new int[3];
		if(left==right){
			valueArray[MAXLEFTID]=left;
			valueArray[MAXRIGHTID]=right;
			valueArray[MAXSUM]=A[left];
			return 	valueArray;				
		}else{
			mid=(int) Math.floor((left+right)/2);
			leftArray=findMax(A,left,mid);
			rightArray=findMax(A,mid+1,right);
			crossArray=crossSub(A,left,mid,right);
			if((leftArray[MAXSUM]>rightArray[MAXSUM])&&(leftArray[MAXSUM]>crossArray[MAXSUM]))
				return leftArray;
			else if((rightArray[MAXSUM]>leftArray[MAXSUM])&&(rightArray[MAXSUM]>crossArray[MAXSUM]))
				return rightArray;
			else return crossArray;
		}
	}
		
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int[] value=new int[3];
		int[] c={1,3,1,-1};
		print(c);
		value=findMax(c,0,c.length-1);
		//print(cross);
		System.out.println("---max subArray---");
		for(int i=value[0];i<=value[1];i++)
			System.out.println("A["+i+"]:"+c[i]);
		System.out.print("最大子数组和为："+value[2]);
	}

}

[remember1989]

能不能描述一下这段代码要解决的是什么问题

[大羽飞鹤]

求给定数组中最大连续子数组，如：1，3，-1，1，则结果为：1，3 和为4