How to Solve Quicksort Puzzles: Rules for Logic Solvers

This puzzle I created for the 10th 24-hour Championship. The Quicksort puzzle was the new puzzle that was introduced in the Oguz Atay Puzzle Contest (OAPC). This is a very interesting puzzle. However, this puzzle was not seen in many of the puzzle contests once the OAPC puzzle contest was over. I created a few Quicksort Puzzles, which you can find and solve on this website.

The Rules of the Quicksort Puzzle

Blacken some cells in the diagram so that there is only one blackened square in every outlined region. Black squares cannot touch each other from the side, and all the white cells must be interconnected. Numbers in the diagram indicate the number of white cells seen from that square (in four directions), including themselves. A square with a number cannot be blackened.