Score : $200$ points

问题描述

给定一个 $H$×$W$ 的矩阵 $A$。

$A$ 中从上数第 $i$ 行、从左数第 $j$ 列的元素为 $A_{i,j}$。

令 $B$ 为一个 $W$×$H$ 的矩阵，其中从上数第 $i$ 行、从左数第 $j$ 列的元素等于 $A_{j, i}$。

即，矩阵 $B$ 是矩阵 $A$ 的转置。

输出矩阵 $B$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an $H$-by-$W$ matrix $A$.
The element at the $i$-th row from the top and $j$-th column from the left of $A$ is $A_{i,j}$.

Let $B$ be a $W$-by-$H$ matrix whose element at the $i$-th row from the top and $j$-th column from the left equals $A_{j, i}$.
That is, $B$ is the transpose of $A$.

Print $B$.

Constraints

• $1\leq H,W \leq 10^5$
• $H \times W \leq 10^5$
• $1 \leq A_{i,j} \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$H$ $W$

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

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

$\vdots$

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

Output

Print $B$ in the following format:

$B_{1,1}$ $B_{1,2}$ $\ldots$ $B_{1,H}$

$B_{2,1}$ $B_{2,2}$ $\ldots$ $B_{2,H}$

$\vdots$

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

Sample Input 1

4 3
1 2 3
4 5 6
7 8 9
10 11 12

Sample Output 1

1 4 7 10
2 5 8 11
3 6 9 12

For example, we have $A_{2,1}=4$, so the element at the $1$-st row from the top and $2$-nd column from the left of the transpose $B$ is $4$.

Sample Input 2

2 2
1000000000 1000000000
1000000000 1000000000

Sample Output 2

1000000000 1000000000
1000000000 1000000000

update @ 2024/3/10 10:15:12