PAT--1007 Maximum Subsequence Sum (25 分)

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 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>
#include <bits/stdc++.h>

using namespace std;
const int maxn = 10010;
int a[maxn],dp[maxn];

int main()
{
    int n;
    cin>>n;
    int flag = 0;
    //int a[n];
    for(int i=0; i<n; i++)
    {

        cin>>a[i];
        if(a[i]>=0)
            flag = 1;
    }

    dp[0] = a[0];
    for(int i=1; i<n; i++)
    {
        dp[i] = max(a[i],dp[i-1]+a[i]);
    }

    int k=0;
    for(int i=1; i<n; i++)
    {
        if(dp[i]>dp[k])
            k = i;
    }


    int s = dp[k];
    int j = k;
    while(s)
    {
        s = s-a[j];
        j--;
    }

    if(dp[k]<0)
    {
        if(flag==0){
            cout<<"0"<<" "<<a[0]<<" "<<a[n-1]<<endl;
        }
    }
    else
    {
        if(dp[k]==0)
            cout<<"0"<<" "<<"0"<<" "<<"0"<<endl;
        else
            cout<<dp[k]<<" "<<a[j+1]<<" "<<a[k]<<endl;
    }

    //cout << "Hello world!" << endl;
    return 0;
}

 排坑：

1. “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.”：如果所有数是负数，则输出0和第一个以及最后一个数；
2. 如果原始序列中有一个是0（只要有一个就成），其他是负数或者0，那么，输出“0 0 0”