牛客网暑期ACM多校训练营（第六场） A Singing Contest

题目链接： https://www.nowcoder.com/acm/contest/144/A

时间限制：C/C++ 1秒，其他语言2秒
空间限制：C/C++ 262144K，其他语言524288K
64bit IO Format: %lld

题目描述 

Jigglypuff is holding a singing contest. There are 2n singers indexed from 1 to 2n participating in the contest.

The rule of this contest is like the knockout match. That is, in the first round, singer 1 competes with singer 2, singer 3 competes with singer 4 and so on; in the second round, the winner of singer 1 and singer 2 competes with the winner of singer 3 and singer 4 and so on. There are n rounds in total.

Each singer has prepared n songs before the contest. Each song has a unique pleasantness. In each round, a singer should sing a song among the songs he prepared. In order not to disappoint the audience, one song cannot be performed more than once. The singer who sings the song with higher pleasantness wins.

Now all the singers know the pleasantness of songs prepared by all the others. Everyone wants to win as many rounds as he can. Assuming that singers choose their song optimally, Jigglypuff wants to know which singer will win the contest?

输入描述:

The input starts with one line containing exactly one integer t which is the number of test cases. (1 ≤ t ≤ 10)

For each test case, the first line contains exactly one integer n where 2n is the number of singers. (1 ≤ n ≤ 14)

Each of the next 2n lines contains n integers where aij is the pleasantness of the j-th song of the i-th singer. It is guaranteed that all these 2nx n 
integers are pairwise distinct. (1 ≤ aij ≤ 109)

输出描述:

For each test case, output "Case #x: y" in one line (without quotes), where x is the test case number (starting from 1) and y is the index of the winner.

示例1

输入

复制

2
1
1
2
2
1 8
2 7
3 4
5 6

输出

复制

Case #1: 2
Case #2: 4

题意：首先输入测试样例组数t，接下来输入n，代表我们接下来要进行n轮比赛，每场比赛相邻的两个人进行比赛，也就是1号与2号比，2号与3号比，一轮过后，1,2的获胜方与3,4的获胜方比赛，以此类推，进
行n轮最初就需要2^n个人，每个人都有可能进行n轮比赛之后获得冠军，于是每个人准备了n首歌，每首歌有自己的愉悦值，比赛时，愉悦值高的一定会战胜愉悦值低的。问最后谁会获得冠军。
做法：我们拿1,2比赛为例，假设现在1号不用出自己最大的愉悦值的歌曲，那么有可能2号就有比我愉悦值高的歌曲，此时这一轮我就输了，留着愉悦值高的歌也没有用了，于是，每一次，我们其中一方就要用出
自己最大的愉悦值的歌曲，如果1号愉悦值最高的歌曲的愉悦值大于2的，那么此时1号一定可以赢得这一轮，2号一定要用自己愉悦值最高的歌曲，1号不一定要用自己愉悦值最高的歌曲，只要二分出来比2号的高
就可以，于是，此题用vector可写，并且不断维护现在的入围选手都是第几号即可。
代码如下：

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string.h>
#include<vector>
 
using namespace std;
 
const int maxn = 20004;
 
vector<int>V[maxn];
int ans[maxn] , len;   ///记录此时每一名都是谁 以及现在还剩多少人
///每个人每次都拿出来最大的与对手打 能打过就找到恰好大于对手最大值的去打  打不过就输了 直接淘汰
void init(int n)
{
    for(int i=1; i<=n; i++)
    {
        V[i].clear();
        ans[i] = i;   ///刚开始有n个人  第i名就是第i个人
    }
}
 
int poww(int a , int b)
{
    int res = 1;
    for(int i=1; i<=b; i++)
    {
        res *= a;
    }
    return res;
}
 
void input(int n , int nn)
{
    int tmp;
    for(int i=1; i<=n; i++)
    {
        for(int j=1; j<=nn; j++)
        {
            scanf("%d" , &tmp);
            V[i].push_back(tmp);
        }
        sort(V[i].begin() , V[i].end());   ///没有sort所以错了
    }
}
 
void bi_sai(int x , int y , int num)
{
//    printf("%d..%d..%d..%d..%d..........\n" , x , y , V[x].size() , V[y].size() , num);
    ///题目保证了不会有相同的愉悦值出现
    int L = V[x].size();
    if(V[x][L-1] > V[y][L-1])
    {
        int pos = upper_bound(V[x].begin() , V[x].end() , V[y][L-1])-V[x].begin();
        ans[num] = x;
        V[x].erase(V[x].begin()+pos);
    }
    else
    {
        int pos = upper_bound(V[y].begin() , V[y].end() , V[x][L-1])-V[y].begin();
        ans[num] = y;
        V[y].erase(V[y].begin()+pos);
    }
}
 
void solve(int nn)
{
//    printf("%d..%d..++++\n" , nn , len);
    for(int i=1; i<=nn; i++)   ///一共要打n场
    {
        for(int j=1; j<=len; j+=2)   ///每一场是len个人比赛 第ans[i]个人和第ans[i+1]个人
        {
            int a , b;
            a = ans[j];
            b = ans[j+1];
//            printf("%d/.%d..\n" , a , b);
            bi_sai(a , b , j/2+1);   ///a 和 b比赛 赢了的获得第j/2+1名
//            printf("%d...\n" , ans[j/2+1]);
//            printf("%d...%d..%d..\n" , i , j , len);
        }
        len /= 2;
//        printf("%d+++++++\n" , len);
//        for(int j=1; j<=len; j++)
//        {
//            printf("%d..\n" , ans[j]);
//        }
    }
}
 
void debug1(int n)
{
    for(int i=1; i<=n; i++)
    {
        printf("%d..%d..\n" , i , V[i].size());
        for(int j=0; j<V[i].size(); j++)
        {
            printf("%d " , V[i][j]);
        }
        printf("\n");
    }
}
 
int main()
{
//    printf("%d..\n" , poww(2 , 14));
    int t , n , nn;
    scanf("%d" , &t);
    for(int cas=1; cas<=t; cas++)
    {
        scanf("%d" , &n);
        nn = n;
        n = poww(2 , n);
        len = n;
        init(n);
        input(n , nn);
//        debug1(n);
        solve(nn);
        printf("Case #%d: %d\n" , cas , ans[1]);
    }
 
 
    return 0;
}
 
/*
10
3
1 2 5
2 3 4
3 4 5
1 2 4
6 7 6
8 2 3
0 1 2
1 3 1
这个样例不好 出现了相等的情况
 
 
*/