strategy - 16 Two Colored Line up

We have a different type of puzzle which consists of 4x4 board with numbers on it;

Your task is to put numbers in the correct order as given in the diagram above.

In each step, you can take one number from a color and one number from another color and interchange them. In other words, if you take a number from yellow square, you can interchange that number with only white backgrounded numbers.

So what is the minimum number of steps to obtain the correct order given above for the question below?

Answer

You should be able to do it in

14 steps

Because the grid contains

2 cycles of length 8: 4 11 12 8 7 16 15 3 4 and 1 2 9 10 6 5 14 13 1

And each

cycle is correctable in length-1 swaps. e.g. Swap 4 with 3, then with 15, then with 16, then with 7, then with 8, then with 12, then finally with 11, and that cycle is entirely correct.