Most efficient way to search a sorted matrix?

Question

I have an assignment to write an algorithm (not in any particular language, just pseudo-code) that receives a matrix [size: M x N] that is sorted in a way that all of it\'s

Answer 1

this is wrong answer

I am really not sure if any of the answers are the optimal answers. I am going at it.

1. binary search first row, and first column and find out the row and column where "x" could be. you will get 0,j and i,0. x will be on i row or j column if x is not found in this step.
2. binary search on the row i and the column j you found in step 1.

I think the time complexity is 2* (log m + log n).

You can reduce the constant, if the input array is a square (n * n), by binary searching along the diagonal.