寻找两个序列的中位数

最新推荐文章于 2024-05-22 16:28:54 发布

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最新推荐文章于 2024-05-22 16:28:54 发布

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分类专栏：算法文章标签：算法

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这篇博客介绍了PAT甲级考试中的一道编程题，题目要求找到两个递增序列的中位数。作者分享了一个简洁的解决方案，通过将两个序列合并并排序，然后直接输出排序后序列的中间元素。尽管官方通过率低，但作者用这种方法快速通过了所有测试用例，对此感到惊讶。

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问题

1029 Median (25 分)
Given an increasing sequence S of N integers, the median is the number at the middle position. For example, the median of S1 = { 11, 12, 13, 14 } is 12, and the median of S2 = { 9, 10, 15, 16, 17 } is 15. The median of two sequences is defined to be the median of the nondecreasing sequence which contains all the elements of both sequences. For example, the median of S1 and S2 is 13.

Given two increasing sequences of integers, you are asked to find their median.

Input Specification:
Each input file contains one test case. Each case occupies 2 lines, each gives the information of a sequence. For each sequence, the first positive integer N (≤2×10
5
) is the size of that sequence. Then N integers follow, separated by a space. It is guaranteed that all the integers are in the range of long int.

Output Specification:
For each test case you should output the median of the two given sequences in a line.

Sample Input:
4 11 12 13 14
5 9 10 15 16 17
结尾无空行
Sample Output:
13

思路

只用一个可变长数组接收这两个序列，然后从小到大排序，最后输出下标为(n+m-1)/2的元素就是中位数。

代码

#include<bits/stdc++.h>
using namespace std;

int main(){
    int n,m,temp;
    vector<long long> seq;
    cin>>n;
    for (int i = 0; i < n; ++i) {
        cin>>temp;
        seq.push_back(temp);
    }
    cin>>m;
    for (int j = 0; j < m; ++j) {
        cin>>temp;
        seq.push_back(temp);
    }

    sort(seq.begin(),seq.end());
    cout<<seq[(n+m-1)/2];
    return 0;
}