102416: [AtCoder]ABC241 G - Round Robin

Problem Statement

$N$ players numbered $1$ through $N$ will participate in a round-robin tournament.
Specifically, for every pair $(i,j) (1\leq i \lt j \leq N)$, Player $i$ and Player $j$ play a match against each other once, for a total of $\frac{N(N-1)}{2}$ matches.
In every match, one of the players will be a winner and the other will be a loser; there is no draw.

$M$ matches have already ended. In the $i$-th match, Player $W_i$ won Player $L_i$.

List all the players who may become the unique winner after the round-robin tournament is completed.
A player is said to be the unique winner if the number of the player's wins is strictly greater than that of any other player.

Constraints

• $2\leq N \leq 50$
• $0\leq M \leq \frac{N(N-1)}{2}$
• $1\leq W_i,L_i\leq N$
• $W_i \neq L_i$
• If $i\neq j$, then $(W_i,L_i) \neq (W_j,L_j)$.
• $(W_i,L_i) \neq (L_j,W_j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$W_1$ $L_1$
$W_2$ $L_2$
$\vdots$
$W_M$ $L_M$

Output

Let $A=(A_1,A_2,\dots,A_K) (A_1\lt A_2 \lt \dots \lt A_K)$ be the set of indices of players that may become the unique winner. Print $A$ in the increasing order, with spaces in between.
In other words, print in the following format.

$A_1$ $A_2$ $\dots$ $A_K$

Sample Input 1

4 2
2 1
2 3

Sample Output 1

2 4

Players $2$ and $4$ may become the unique winner, while Players $1$ and $3$ cannot.
Note that output like 4 2 is considered to be incorrect.

Sample Input 2

3 3
1 2
2 3
3 1

Sample Output 2

It is possible that no player can become the unique winner.

Sample Input 3

7 9
6 5
1 2
3 4
5 3
6 2
1 5
3 2
6 4
1 4

Sample Output 3

1 3 6 7

问题描述

编号为$1$到$N$的$N$名选手将参加一个循环赛。

具体来说，对于每一对$(i,j) (1\leq i \lt j \leq N)$，选手$i$和选手$j$将互相比赛一次，总共比赛$\frac{N(N-1)}{2}$场。

每场比赛中，其中一名选手将是胜者，另一名将是负者；没有平局。

已经结束了$M$场比赛。在第$i$场比赛中，选手$W_i$赢了选手$L_i$。

列出所有可能在循环赛结束后成为唯一胜者的选手。

如果一名选手的胜利次数严格多于其他任何选手，那么该选手被认为是唯一胜者。

约束

• $2\leq N \leq 50$
• $0\leq M \leq \frac{N(N-1)}{2}$
• $1\leq W_i,L_i\leq N$
• $W_i \neq L_i$
• 如果$i\neq j$，则$(W_i,L_i) \neq (W_j,L_j)$。
• $(W_i,L_i) \neq (L_j,W_j)$
• 输入中的所有值都是整数。

输入

从标准输入给出以下格式的输入：

$N$ $M$
$W_1$ $L_1$
$W_2$ $L_2$
$\vdots$
$W_M$ $L_M$

输出

令$A=(A_1,A_2,\dots,A_K) (A_1\lt A_2 \lt \dots \lt A_K)$表示可能成为唯一胜者的选手的索引集合。按照递增顺序打印$A$，并在其中间用空格分隔。

换句话说，按照以下格式打印：

$A_1$ $A_2$ $\dots$ $A_K$

样例输入 1

4 2
2 1
2 3

样例输出 1

2 4

选手$2$和$4$可能成为唯一胜者，而选手$1$和$3$不可能成为唯一胜者。

请注意，像4 2这样的输出被认为是错误的。

样例输入 2

3 3
1 2
2 3
3 1

样例输出 2

有可能没有选手可以成为唯一胜者。

样例输入 3

7 9
6 5
1 2
3 4
5 3
6 2
1 5
3 2
6 4
1 4

样例输出 3

1 3 6 7