The Push_Swap project aims to sort a set of integers using a specific set of instructions on two stacks. This program generates a sequence of push_swap instructions to achieve the desired sorting.

The following instructions are utilized for sorting:

For stacks with a size less than 6, a simple sorting method is employed (found in the src folder).

The primary algorithm used is Radix sort. This efficient algorithm sorts non-negative integers with a time complexity of O(n). It operates by distributing numbers into "boxes" based on their digits and then rearranging them based on the box order.

• Sort starts from the least significant digit.
• Each number is placed in the box corresponding to its digit.
• Numbers are then connected in order of the boxes.

This process is repeated for each digit, resulting in a fully sorted array.

The push_swap algorithm achieves:

• 3 numbers sorted in a maximum of 3 instructions
• 4 numbers sorted in a maximum of 7 instructions
• 5 numbers sorted in a maximum of 11 instructions
• 100 numbers sorted in a maximum of 1084 instructions (3 points)
• 500 numbers sorted in a maximum of 6785 instructions (4 points)

The algorithm is sufficient for project requirements and can exceed 105% with bonus completion.

The bonus task involves writing a program named checker that takes stack A as an argument (formatted as a list of integers). Checker reads instructions from standard input, executes them on the stack, and then verifies the sorting.

• If stack A is sorted and stack B is empty, checker displays "OK."
• Otherwise, it displays "KO."
• Invalid arguments result in an "Error" message.