Maximum Subsequence Sum

最新推荐文章于 2025-07-25 20:07:40 发布

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最新推荐文章于 2025-07-25 20:07:40 发布

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分类专栏：浙大陈越数据结构文章标签： C++ 数据结构算法动态数组

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本文介绍了一个改进的最大子列和问题，不仅求出最大子列和，还需输出该子列的首尾元素值。文章提供了一段C++代码实现，通过在线处理方式实时更新最大子列和及其边界值，并考虑了特殊情况处理。

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Given a sequence of $K$ integers { $N_1$ , $N_2$ , ..., $N_K$ }. A continuous subsequence is defined to be { $N_i$ , $N_{i+1}$ , ..., $N_j$ } where $\le i \le j \le K$ . 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 $K$ ( $≤10000\le 10000$ ). 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

就是在最大子列和问题的基础上增加了输出最大子列的第一和最后一个元素的值，不过老师设置了很变态的测试数据，非常考验细心。真是改到怀疑人生，终于全部通过了。

#include <iostream>

using namespace std;

void MaxSubseqSum(int A[],int N)//在线处理，输入一个数据 即时处理一下
{
    int ThisSum=0,MaxSum=0;
    int i,p=A[0],q,s=A[0];
    for(i=0;i<N;i++)
    {
        ThisSum+=A[i];//向右累加
         if(ThisSum<0)//如果发现当前子列为负
            {   ThisSum=0;//则不可能使后面的部分和增大，抛弃之
                if (A[i]!=0)
                    s=A[i+1];
            }
        else  if (ThisSum>MaxSum)
            {   MaxSum=ThisSum;
                q=A[i];
                p=s;
            }//发现更大和则更新当前结果
    }

   if(MaxSum==0)
        {p=A[0];q=A[N-1];
            for(int j=0;j<N;j++)
            {   if(A[j]==0)
                    {p=0;q=0;}
            }
        }
    cout<< MaxSum<<" "<<p<<" "<<q;
}
int main()
{
    int n;
    cin>>n;
    int* a=new int [n];// 使用指针进行数组动态联编
    for(int i=0;i<n;i++)
        cin>>a[i];

    MaxSubseqSum(a,n);//把指针作为参数传进去
    delete [] a;//释放内存空间
    return 0;
}