# Algorithm for matrix positioning

Lets say I have an original mxn matrix like this:

``````1 2 3 4
5 6 7 8
``````

For the purpose of my program, I then concatenate the rows into this new one dimensional matrix:

``````1 2 3 4 5 6 7 8
``````

I know the mxn size of the original matrix. My question is, given a value’s position in the new matrix, I need an algorithm to find its mxn position in the original matrix.

For example: Using the above matrices, 8 would have an original position of 2×4, 3 would have an original position of 1×3 and so on.

This is for a java program that I am writing, I tried using division and modulus and played around with it, but I couldn’t come up with a good algorithm that works for all cases.

If A is the original two-dimensional matrix, B is the new one-dimensional matrix, m & n are height and width of B respectively, then given the position p of element a in A, the new `[x,y]` coordinates within B (given indices that are one-based) is

``````x = (p - 1) / n + 1
y = n + 1 - (p % n)
``````

With zero-based indices, this becomes easier, as you no longer have to adjust for the 1 offset.

``````x = p / n
y = n - p % n
``````