CF1749A.Cowardly Rooks
入门
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×n. m 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×n 的棋盘。在棋盘上放置了 m 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 t (1≤t≤2000) — the number of testcases.
The first line of each testcase contains two integers n and m (1≤n,m≤8) — the size of the chessboard and the number of the rooks.
The i-th of the next m lines contains two integers xi and yi (1≤xi,yi≤n) — the position of the i-th rook: xi is the row and yi 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 t(1≤t≤2000)——测试用例的数量。
每个测试用例的第一行包含两个整数 n 和 m(1≤n,m≤8)——棋盘的大小以及车的数量。
接下来的 m 行中,第 i 行包含两个整数 xi 和 yi(1≤xi,yi≤n)——第 i 辆车的位置:xi 表示行号,yi 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 2×2 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 3×3 board. It has 4 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 2×2 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 3×3 棋盘的中心。它有 4 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?