1007 Maximum Subsequence Sum （25 分)

2019-03-06

1007 Maximum Subsequence Sum （25 分)

Given a sequence of K integers { N1, N2, …, 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 Knumbers, 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:

1 2	10 -10 1 2 3 4 -5 -23 3 7 -21

Sample Output:

10 1 4

作者: CHEN, Yue

单位: 浙江大学

时间限制: 200 ms

内存限制: 64 MB

代码长度限制: 16 KB

题目大意

最大子序列和问题，输出最大和以及相应区间的下标

分析

这个是经典问题了，参见《数据结构与算法分析》，略加改造记录区间下标即可

代码

#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>
#include <map>
#include <cstring>
using namespace std;

int main() {
    int k;
    cin>>k;
    int num[10010];

    for(int i=0;i<k;i++)
        cin>>num[i];
    int start=0,end=0,maxsum=-99999999,thissum=0,tempstart=num[0];
    for(int i=0;i<k;i++){
        thissum+=num[i];
        if(thissum>maxsum) {
            maxsum = thissum;
            end=num[i];
            start=tempstart;
        }
        if(thissum<=0) {
            thissum = 0;
            tempstart=num[i+1];
        }
    }
    if(maxsum<0){
        maxsum=0;
        start=num[0];
        end=num[k-1];
    }
    cout<<maxsum<<" "<<start<<" "<<end;
    return 0;
}