PAT甲级-1007. Maximum Subsequence Sum (25)最大子序列和

太过爱你忘了你带给我的痛 2022-05-31 09:39 145阅读 0赞

# 1007. Maximum Subsequence Sum (25) #

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

计算所给序列的最大子序列和，输出和及子序列首尾项。

题目最后一句说如果所给序列全是负数，默认和为0，且输出序列首尾项。

例如

4
    -2 0 0 -1

输出

0 0 0

而不是

0 -2 -1

#include<bits/stdc++.h>
    using namespace std;
    #define INF 0xfffffff
    #define MAXN 10010
    int a[MAXN],n,x,y,ans,sum;
    void maxsequence()//最大子序列和
    {
        ans=sum=a[0];
        for (int i=1; i<n; i++)
        {
            if(sum<=0) sum=a[i];
            else sum+=a[i];
            if (sum>ans) ans=sum;
        }
    }
    int main()
    {
    #ifdef ONLINE_JUDGE
    #else
        freopen("F:/cb/read.txt","r",stdin);
    //freopen("F:/cb/out.txt","w",stdout);
    #endif
        ios::sync_with_stdio(false);
        cin.tie(0);
        cin>>n;
        for(int i=0; i<n; ++i)
            cin>>a[i];
        int cnt=1;
        maxsequence();
        if(ans<0) cout<<"0 "<<a[0]<<" "<<a[n-1]<<endl;
        else
        {
            sum=0;
            for(int i=0; i<n; i++)
            {
                if(sum<=0) cnt=1,sum=a[i];
                else ++cnt,sum+=a[i];
                if(sum==ans)
                {
                    y=a[i];
                    x=a[i-cnt+1];
                    break;
                }
            }
            cout<<ans<<" "<<x<<" "<<y<<endl;
        }
    }