CF1749A.Cowardly Rooks

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通过率:0%

时间限制:2.00s

内存限制:256MB

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题目描述

There's a chessboard of size n×nn \times n. mm rooks are placed on it in such a way that:

  • no two rooks occupy the same cell;
  • no two rooks attack each other.

A rook attacks all cells that are in its row or column.

Is it possible to move exactly one rook (you can choose which one to move) into a different cell so that no two rooks still attack each other? A rook can move into any cell in its row or column if no other rook stands on its path.

有一个 n×nn \times n 的棋盘。在棋盘上放置了 mm 个车(rook),满足以下条件:

  • 任意两个车不占据同一格子;
  • 任意两个车互不攻击。

一个车会攻击其所在行和列上的所有格子。

是否可能恰好移动一个车(你可以任选其中一个车来移动)到另一个不同的格子,使得移动后仍满足:任意两个车互不攻击?
一个车可以沿其所在行或列移动到任意格子,前提是其路径上没有其他车阻挡。

输入格式

The first line contains a single integer tt (1≤t≤20001 \le t \le 2000) — the number of testcases.

The first line of each testcase contains two integers nn and mm (1≤n,m≤81 \le n, m \le 8) — the size of the chessboard and the number of the rooks.

The ii-th of the next mm lines contains two integers xix_i and yiy_i (1≤xi,yi≤n1 \le x_i, y_i \le n) — the position of the ii-th rook: xix_i is the row and yiy_i is the column.

No two rooks occupy the same cell. No two rooks attack each other.

第一行包含一个整数 tt(1≤t≤20001 \le t \le 2000)——测试用例的数量。

每个测试用例的第一行包含两个整数 nn 和 mm(1≤n,m≤81 \le n, m \le 8)——棋盘的大小以及车的数量。

接下来的 mm 行中,第 ii 行包含两个整数 xix_i 和 yiy_i(1≤xi,yi≤n1 \le x_i, y_i \le n)——第 ii 辆车的位置:xix_i 表示行号,yiy_i 表示列号。

任意两辆车不占据同一格子,且任意两辆车互不攻击。

输出格式

For each testcase, print "YES" if it's possible to move exactly one rook into a different cell so that no two rooks still attack each other. Otherwise, print "NO".

对于每个测试用例,如果可以通过恰好移动一个车(rook)到另一个不同的格子,使得任意两个车之间仍然互不攻击,则输出 "YES";否则输出 "NO"。

输入输出样例

  • 输入#1

    2
    2 2
    1 2
    2 1
    3 1
    2 2

    输出#1

    NO
    YES

说明/提示

In the first testcase, the rooks are in the opposite corners of a 2×22 \times 2 board. Each of them has a move into a neighbouring corner, but moving there means getting attacked by another rook.

In the second testcase, there's a single rook in a middle of a 3×33 \times 3 board. It has 44 valid moves, and every move is fine because there's no other rook to attack it.

在第一个测试用例中,车位于 2×22 \times 2 棋盘的对角角落。每个车均可移动至相邻的角落,但若如此移动,则会被另一辆车攻击。

在第二个测试用例中,一辆车位于 3×33 \times 3 棋盘的中心。它有 44 种合法移动方式,且每次移动均安全,因为棋盘上没有其他车可攻击它。

输入解题思路,AI测评打分。不知道怎么写?

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