Score : $600$ points

问题描述

$N$ 名编号为 $1$ 至 $N$ 的选手将参加一场循环赛。
具体来说，对于每一对 $(i,j) (1\leq i < j \leq N)$，选手 $i$ 和选手 $j$ 之间会进行一次对决，总共进行 $\frac{N(N-1)}{2}$ 场比赛。
在每场比赛中，会有唯一的胜者和败者，不存在平局。

目前已经结束了 $M$ 场比赛。在第 $i$ 场比赛中，选手 $W_i$ 击败了选手 $L_i$。

请列出循环赛结束后可能成为唯一冠军的所有选手。
若选手的胜场数严格大于任何其他选手，则称该选手为唯一冠军。

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 10:24:17