Step by Step solution about How to resolve the algorithm Towers of Hanoi step by step in the PHP programming language

The provided PHP function, move, is an implementation of the Towers of Hanoi puzzle. It demonstrates the iterative solution to the puzzle using recursion.

Purpose: The function move solves the Towers of Hanoi puzzle by moving disks from one pole to another, following specific rules. The puzzle involves three poles and n disks of different sizes. The aim is to move all the disks from one pole to another, observing the following rules:

• Only one disk can be moved at a time.
• A disk can only be placed on a larger disk or an empty pole.

Implementation Details:

• The function takes four parameters:

  • $n: The number of disks to move.
  • $from: The starting pole.
  • $to: The destination pole.
  • $via: The intermediate pole.

• The function uses recursion to solve the puzzle. The recursive calls are based on the following logic:

  • If $n is equal to 1 (i.e., only one disk), it prints the instruction to move the disk from the $from pole to the $to pole.
  • If $n is greater than 1:
    • It recursively calls the move function to move $n-1 disks from the $from pole to the $via pole, using the $to pole as the intermediate.
    • It then calls move to move the remaining disk (1) from the $from pole to the $to pole.
    • Finally, it recursively calls move to move the $n-1 disks from the $via pole to the $to pole, using the $from pole as the intermediate.

• The recursive calls continue until all disks are moved from the $from pole to the $to pole, following the rules of the puzzle.

Overall, the move function provides an elegant and efficient recursive solution to the Towers of Hanoi puzzle. It demonstrates the power of recursion in solving complex problems by breaking them down into smaller subproblems.

function move($n,$from,$to,$via) {
    if ($n === 1) {
        print("Move disk from pole $from to pole $to");
    } else {
        move($n-1,$from,$via,$to);
        move(1,$from,$to,$via);
        move($n-1,$via,$to,$from);
    }
}