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

what about getting the diagonal out, then binary search over the diagonal, start bottom right check if it is above, if yes take the diagonal array position as the column it is in, if not then check if it is below. each time running a binary search on the column once you have a hit on the diagonal (using the array position of the diagonal as the column index). I think this is what was stated by @user942640

you could get the running time of the above and when required (at some point) swap the algo to do a binary search on the initial diagonal array (this is taking into consideration its n * n elements and getting x or y length is O(1) as x.length = y.length. even on a million * million binary search the diagonal if it is less then half step back up the diagonal, if it is not less then binary search back towards where you where (this is a slight change to the algo when doing a binary search along the diagonal). I think the diagonal is better than the binary search down the rows, Im just to tired at the moment to look at the maths :)

by the way I believe running time is slightly different to analysis which you would describe in terms of best/worst/avg case, and time against memory size etc. so the question would be better stated as in 'what is the best running time in worst case analysis', because in best case you could do a brute linear scan and the item could be in the first position and this would be a better 'running time' than binary search...