Score : $200$ points

问题描述

$N$ 名选手进行了一场循环赛。

给定一个 $N$×$N$ 的表格 $A$，其中记录了比赛结果。令 $A_{i,j}$ 表示 $A$ 中第 $i$ 行第 $j$ 列的元素。
若 $i=j$，则 $A_{i,j}$ 为 -；否则，$A_{i,j}$ 可以为 W、L 或 D。
若 $A_{i,j}$ 为 W，表示选手 $i$ 击败了选手 $j$；若为 L，表示选手 $i$ 输给了选手 $j$；若为 D，表示选手 $i$ 与选手 $j$ 战平。

判断给定的表格是否存在矛盾。

当满足以下任一条件时，该表格被认为存在矛盾：

• 存在一对 $(i,j)$，使得选手 $i$ 击败了选手 $j$，但选手 $j$ 并未输给选手 $i$；
• 存在一对 $(i,j)$，使得选手 $i$ 输给了选手 $j$，但选手 $j$ 并未击败选手 $i$；
• 存在一对 $(i,j)$，使得选手 $i$ 与选手 $j$ 战平，但选手 $j$ 并未与选手 $i$ 战平。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

$N$ players played a round-robin tournament.

You are given an $N$-by-$N$ table $A$ containing the results of the matches. Let $A_{i,j}$ denote the element at the $i$-th row and $j$-th column of $A$.
$A_{i,j}$ is - if $i=j$, and W, L, or D otherwise.
$A_{i,j}$ is W if Player $i$ beat Player $j$, L if Player $i$ lost to Player $j$, and D if Player $i$ drew with Player $j$.

Determine whether the given table is contradictory.

The table is said to be contradictory when some of the following holds:

• There is a pair $(i,j)$ such that Player $i$ beat Player $j$, but Player $j$ did not lose to Player $i$;
• There is a pair $(i,j)$ such that Player $i$ lost to Player $j$, but Player $j$ did not beat Player $i$;
• There is a pair $(i,j)$ such that Player $i$ drew with Player $j$, but Player $j$ did not draw with Player $i$.

Constraints

• $2 \leq N \leq 1000$
• $A_{i,i}$ is -.
• $A_{i,j}$ is W, L, or D, for $i\neq j$.

Input

Input is given from Standard Input in the following format:

$N$

$A_{1,1}A_{1,2}\ldots A_{1,N}$

$A_{2,1}A_{2,2}\ldots A_{2,N}$

$\vdots$

$A_{N,1}A_{N,2}\ldots A_{N,N}$

Output

If the given table is not contradictory, print correct; if it is contradictory, print incorrect.

Sample Input 1

4
-WWW
L-DD
LD-W
LDW-

Sample Output 1

incorrect

Player $3$ beat Player $4$, while Player $4$ also beat Player $3$, which is contradictory.

Sample Input 2

2
-D
D-

Sample Output 2

correct

There is no contradiction.

update @ 2024/3/10 11:03:25