Maximum Subsequence Sum (25 分)

Given a sequence of K integers A continuous subsequence is defined to be 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

code

#include <stdio.h>
#include <stdlib.h>

void maxSubsequence(int arr[],int n);

int main()
{
    int k;
    scanf("%d",&k);
    int num[k];
    for(int i=0;i<k;i++)
    {
        scanf("%d",&num[i]);
    }
    maxSubsequence(num,k);
    return 0;
}

/*求最大子列和*/
void maxSubsequence(int arr[],int n)
{
    int maxSum,thisSum,frist,last,a;//first和last分别为最大子列的第一个和最后一个数，其中a用来记录最后一个数的在数组里的下标
    maxSum = thisSum = 0;
    for(int i =0;i<n;i++)
    {
        thisSum+=arr[i];
        if(thisSum>maxSum)
        {
            last = arr[i]; //每次maxSum更新时，更新last
            a=i;
            maxSum = thisSum;
        }
        if(thisSum<0)
        {
            thisSum = 0;
        }
    }
/*当最大子列和为0时，有两种情况，全为负数，或者存在0和负数，下面对着两种情况进行判断*/
    if(maxSum==0)
    {
        for(int i =0;i<n;i++)
        {
            if(arr[i]==0)
            {
                frist = last =0 ;
                break;
            }else
            {
                frist = arr[0];
                last = arr[n-1];
            }
        }
    }else
    {
        /*当最大子列和不为0时，求最大子列的第一个数字*/
        thisSum = 0;
        for(int j=a;j>=0;j--)
        {
            thisSum += arr[j];
            if(thisSum == maxSum)
            {
                frist = arr[j];
            }
        }
    }
    printf("%d %d %d\n",maxSum,frist,last);
}