Score : $600$ points

问题描述

我们有一个具有 $H$ 行（水平）和 $W$ 列（垂直）的网格。我们用格子 $(i,j)$ 表示从上数第 $i$ 行、从左数第 $j$ 列的格子。

我们希望使用 $1 \times 1$ 的瓷砖和 $1 \times 2$ 的瓷砖覆盖这个网格，使得没有瓷砖重叠且每个位置都被至少一块瓷砖覆盖。（瓷砖可以旋转摆放。）

每个格子上写有数字 1、2 或者 ?，其中格子 $(i, j)$ 上所写的字符为 $c_{i,j}$。

• 写有数字 1 的格子必须被一块 $1 \times 1$ 的瓷砖覆盖；
• 写有数字 2 的格子必须被一块 $1 \times 2$ 的瓷砖覆盖；
• 写有 ? 的格子可以用任意类型的瓷砖进行覆盖。

请确定是否存在这样的瓷砖放置方案。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have a grid with $H$ horizontal rows and $W$ vertical columns. We denote by square $(i,j)$ the square at the $i$-th row from the top and $j$-th column from the left.

We want to cover this grid with $1 \times 1$ tiles and $1 \times 2$ tiles so that no tiles overlap and everywhere is covered by a tile. (A tile can be rotated.)

Each square has 1, 2, or ? written on it. The character written on square $(i, j)$ is $c_{i,j}$.
A square with 1 written on it must be covered by a $1 \times 1$ tile, and a square with 2 by a $1 \times 2$ tile. A square with ? may be covered by any kind of tile.

Determine if there is such a placement of tiles.

Constraints

• $1 \leq H,W \leq 300$
• $H$ and $W$ are integers.
• $c_{i,j}$ is one of 1, 2, and ?.

Input

The input is given from Standard Input in the following format:

$H$ $W$

$c_{1,1}c_{1,2}\ldots c_{1,W}$

$\vdots$

$c_{H,1}c_{H,2}\ldots c_{H,W}$

Output

Print Yes if there is a placement of tiles to satisfy the conditions in the Problem Statement; print No otherwise.

Sample Input 1

3 4
2221
?1??
2?21

Sample Output 1

Yes

For example, the following placement satisfies the conditions.

Sample Input 2

3 4
2?21
??1?
2?21

Sample Output 2

No

There is no placement that satisfies the conditions.

Sample Input 3

5 5
11111
11111
11211
11111
11111

Sample Output 3

No

update @ 2024/3/10 11:56:30