Added new file in divide and conquer folder

Author: GOURAV-SAHA007

divide_and_conquer/tower_of_hanoi.py

@@ -0,0 +1,66 @@
+"""
+Towers of Hanoi is a mathematical puzzle that is solved using a recursive 
+divide-and-conquer strategy.
+
+It moves a stack of disks from a source pole to a destination pole,
+using an auxiliary pole, subject to these rules:
+1. Only one disk can be moved at a time.
+2. Each move consists of taking the upper disk from one stack and
+   placing it on top of another stack or an empty pole.
+3. No disk may be placed on top of a smaller disk.
+
+More information:
+https://en.wikipedia.org/wiki/Tower_of_Hanoi
+"""
+
+
+def tower_of_hanoi(n: int, source: str = "A", auxiliary: str = "B", destination: str = "C") -> list[tuple[str, str]]:
+    """
+    Pure python implementation of the Towers of Hanoi puzzle (recursive version),
+    returning the sequence of moves required to solve the puzzle.
+
+    >>> tower_of_hanoi(1)
+    [('A', 'C')]
+    >>> tower_of_hanoi(2)
+    [('A', 'B'), ('A', 'C'), ('B', 'C')]
+    >>> tower_of_hanoi(3)
+    [('A', 'C'), ('A', 'B'), ('C', 'B'), ('A', 'C'), ('B', 'A'), ('B', 'C'), ('A', 'C')]
+    >>> tower_of_hanoi(0)
+    []
+    """
+    moves = []
+
+    def solve_hanoi(n: int, source: str, auxiliary: str, destination: str):
+        """Recursive helper function to generate the moves."""
+        if n == 0:
+            return
+
+        # 1. Move n-1 disks from Source to Auxiliary, using Destination as auxiliary.
+        # This is the "Divide" step.
+        solve_hanoi(n - 1, source, destination, auxiliary)
+
+        # 2. Move the largest disk (n) from Source to Destination.
+        # This is the "Conquer" step (base step of the recursion).
+        moves.append((source, destination))
+
+        # 3. Move n-1 disks from Auxiliary to Destination, using Source as auxiliary.
+        # This is the "Combine" step.
+        solve_hanoi(n - 1, auxiliary, source, destination)
+
+    solve_hanoi(n, source, auxiliary, destination)
+    return moves
+
+
+if __name__ == "__main__":
+    try:
+        n_disks = int(input("Enter the number of disks for the Tower of Hanoi: ").strip())
+        if n_disks < 0:
+            print("Please enter a non-negative number of disks.")
+        else:
+            all_moves = tower_of_hanoi(n_disks)
+            print(f"\nTotal moves required: {len(all_moves)}")
+            print("Sequence of Moves (Source -> Destination):")
+            for move in all_moves:
+                print(f"Move disk from {move[0]} to {move[1]}")
+    except ValueError:
+        print("Invalid input. Please enter an integer.")