Maximum Subsequence Sum：2004年浙江大学计算机专业考研复试真题

最大连续子序列和：求解与代码实例

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本文介绍如何解决最大连续子序列和问题，通过C++代码实现，并提供一个样例输入输出。重点在于理解算法思路和找到最大子序列的起始和结束位置。

01-复杂度2 Maximum Subsequence Sum (25 分)
Given a sequence of K integers { N1 , N2 , …, NK }. A continuous subsequence is defined to be { Ni , Ni+1 , …, Nj } where 1≤i≤j≤K. The Maximum Subsequence is the continuous subsequence which has the largest sum of its elements. For example, given sequence { -2, 11, -4, 13, -5, -2 }, its maximum subsequence is { 11, -4, 13 } with the largest sum being 20.

Now you are supposed to find the largest sum, together with the first and the last numbers of the maximum subsequence.

Input Specification:
Each input file contains one test case. Each case occupies two lines. The first line contains a positive integer K (≤10000). The second line contains K numbers, separated by a space.

Output Specification:
For each test case, output in one line the largest sum, together with the first and the last numbers of the maximum subsequence. The numbers must be separated by one space, but there must be no extra space at the end of a line. In case that the maximum subsequence is not unique, output the one with the smallest indices i and j (as shown by the sample case). If all the K numbers are negative, then its maximum sum is defined to be 0, and you are supposed to output the first and the last numbers of the whole sequence.

Sample Input:
10
-10 1 2 3 4 -5 -23 3 7 -21
Sample Output:
10 1 4

#include<iostream>
using namespace std;
using std::cout;
using std::cin;
int findMaxSubSeq(int A[], int N, int &left, int &right) {
	int ThisSum, MaxSum;
	int i;
    int count=0;
	ThisSum = 0;
    MaxSum=-1;//-1是为了解决输入有负数和零的问题
    left=0;
    right=N-1;
	for (i = 0;i<N;i++) {
		ThisSum += A[i];
        count++;       //统计序列长度
        
		if (ThisSum>MaxSum) {
			MaxSum = ThisSum;
			right = i;
            left=right-count+1;
		}        
		else if (ThisSum<0){
			ThisSum = 0;
            count=0;//序列和为负数时，重新开始统计序列长度
        }
       
            
	}
    
    if(MaxSum==-1){//全为负数时，序列和为零
        MaxSum=0;
    }

	return MaxSum;
}
 
int main() {
 
	int b[10000] = {};
	int num, left, right;
	cin >> num;
	for (int i = 0;i<num;i++) {
		cin >> b[i];
	}
	int xx = findMaxSubSeq(b, num, left, right);
	cout << xx << " " << b[left] << " " << b[right];
	return 0;
}