Question $1$: Exploring a Matrix $(25$ points$)$

$$ Given a matrix with m rows and n columns. The entrance of the matrix is at position

$[0,0],$ whereas the exit at position $[$m $1,$ n $1].$ In the matrix, you can only move

right or down.

$$ Design an algorithm that takes as input the number of rows $($m$)$ and columns $($n$)$ of

the matrix, and outputs all unique paths from the entrance to the exit. The example

of such paths can be seen in the two test cases.

$$ The time complexity of the algorithm should not be worse than O$($m $$ n$).$

$$ For this question, you should provide:

$1.$ The pseudocode, along with a brief explanation of each step

$2.$ The explanation of the time complexity

$3.$ The Java or Python implementation