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In-place transposition of a matrix

Recently attended an Technical Written Interview. Came through the following question.

I have an array as say

testArray = {a1,a2,a3,...an,b1,b2,b3,....bn,c1,c2,c3,.....,cn}

I need to sort this array as `

testArray = {a1,b1,c1,a2,b2,c2,a3,b3,c3,.....,an,bn,cn}

Constraint is I should not use extra memory, should not use any inbuilt function.
Should write complete code, it can be in any language and can also use any data structure.

eg:

Input: {1,2,3,4,5,6,7,8,9}, n = 3

Output: {1,4,7,2,5,8,3,6,9}

I could not get any solution within the constraint, can anyone provide solution or suggestion?

Answer 1

This is just a matrix transpose operation. And there is even a problem and solution for in-place matrix transposition on Wikipedia.

No extra space is impossible, since you need to at least go through the array. O(1) additional memory is possible, with heavy penalty on the time complexity.

The solution is built on follow-the-cycle algorithm in the Wikipedia page: for each cell, we will find the cell with the smallest index in the cycle. If the cell with the smallest index is greater than or equal (>=) to the index of the current cell, we will perform chain swapping. Otherwise, we ignore the cell, since it has been swapped correctly. The (loosely analyzed) upper bound on time complexity can go as high as O((MN)²) (we go through M * N cells, and the cycle can only be as long as the total number of cells).