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名师互学网 > IT > 软件开发 > 后端开发 > Java

Java最大子数组问题

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Java最大子数组问题

伪代码:
FIND-MAX-CROSSING-SUBARRAY(A,low,mid,high)
leftsum=-∞
sum = 0
for i = mid downto low
    sum = sum + A[i]
    if sum > leftsum
        leftsum = sum
        maxleft = i
rightsum=-∞
sum = 0
for j = mid + 1 to high
    sum = sum + A[j]
    if sum > rightsum
        rightsum = sum
        maxright = j
return (maxleft, maxright, leftsum + rightsum)

FIND-MAXIMUM-SUBARRAY(A,low,high)
if high == low
    return (low, high, A[low])
else mid = (low+high)/2
    (leftlow ,lefthigh, leftsum) = FIND-MAXIMUM-SUBARRAY(A, low,mid)
    (rightlow ,righthigh, rightsum) = FIND-MAXIMUM-SUBARRAY(A, mid + 1, high)
    (crosslow ,crosshigh, crosssum) = FIND-MAX-CROSSING-SUBARRAY(A,low,mid,high)
    if leftsum>=rightsum and leftsum>=crosssum
        return (leftlow ,lefthigh, leftsum)
    elseif rightsum>=leftsum and rightsum>=crosssum
        return (rightlow ,righthigh, rightsum)
    else
        return (crosslow ,crosshigh, crosssum)
Java代码:
public class FindMaxSubarray {

	public static int[] Find_Max_Crossing_Subarray(int[] a, int low, int mid, int high) {
		int leftsum = 0;
		int sum = 0;
		int maxleft = 0;
		for(int i = mid ; i > low; i--) {
			sum = sum + a[i];
			if(sum > leftsum) {
				leftsum = sum;
				maxleft = i;
			}
		}
		int rightsum = 0;
		sum = 0;
		int maxright = 0;
		for(int j = mid + 1 ; j < high ; j++) {
			sum = sum + a[j];
			if(sum > rightsum) {
				rightsum = sum;
				maxright = j;
			}
		}
		return new int[] {maxleft, maxright, leftsum + rightsum};
	}
	
	public static int[] Find_Maximum_Subarray(int []a, int low, int high) {
		if(high == low) {
			return new int[] {low, high, a[low]};
		}
		else {
			int mid = (low + high) / 2;
			int[] leftSubarray = Find_Maximum_Subarray(a, low, mid);
			int[] rightSubarray = Find_Maximum_Subarray(a, mid+1, high);
			int[] crossSubarray = Find_Max_Crossing_Subarray(a, low, mid, high);
			if(leftSubarray[2] >= rightSubarray[2] && leftSubarray[2] >= crossSubarray[2]) {
				return leftSubarray;
			}
			else if(rightSubarray[2] >= leftSubarray[2] && rightSubarray[2] >= crossSubarray[2]) {
				return rightSubarray;
			}
			else {
				return crossSubarray;
			}
		}
		
	}
	public static void main(String[]args) {
		int []a = {13,-3,-25,20,-3,-16,-23,18,20,-7,12,-5,-22,15,-4,7};
		int []result = Find_Maximum_Subarray(a, 0, a.length-1);
		System.out.print("最大子数组序列: ");
		for(int i = result[0]; i <= result[1] ; i++) {
			System.out.print(a[i]+" ");
		}
		System.out.println();
		System.out.println("最大子数组和:"+result[2]);
	}
}

 

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