added tower_of_hanoi algo in the backtracking

backtracking/tower_of_hanoi.py

@@ -0,0 +1,56 @@
+def tower_of_hanoi(n, source, destination, auxiliary):
+    """
+    Solves the Tower of Hanoi problem using backtracking.
+
+    Args:
+        n: The number of disks to be moved.
+        source: The index of the source peg.
+        destination: The index of the destination peg.
+        auxiliary: The index of the auxiliary peg.
+
+    Returns:
+        None
+    """
+
+    if n == 1:
+        print(f"Move disk 1 from peg {source} to peg {destination}")
+        return
+
+    tower_of_hanoi(n - 1, source, auxiliary, destination)
+    print(f"Move disk {n} from peg {source} to peg {destination}")
+    tower_of_hanoi(n - 1, auxiliary, destination, source)
+
+
+# Example usage:
+n = 3  # Number of disks
+tower_of_hanoi(n, 1, 3, 2)
+
+# Explanation:
+
+# tower_of_hanoi function:
+
+# Takes four arguments:
+# n: The number of disks to be moved.
+# source: The index of the source peg.
+# destination: The index of the destination peg.
+# auxiliary: The index of the auxiliary peg.
+# If n is 1, it means there's only one disk to move, so it directly prints the move.
+# Otherwise, it recursively calls itself:
+# Moves n-1 disks from the source to the auxiliary peg using the destination as the temporary peg.
+# Moves the largest disk (n) from the source to the destination.
+# Moves the n-1 disks from the auxiliary to the destination using the source as the temporary peg.
+# Example usage:
+
+# Sets n to 3 (the number of disks).
+# Calls the tower_of_hanoi function with the initial pegs: source (1), destination (3), and auxiliary (2).
+# Output:
+
+# Move disk 1 from peg 1 to peg 3
+# Move disk 2 from peg 1 to peg 2
+# Move disk 1 from peg 3 to peg 2
+# Move disk 3 from peg 1 to peg 3
+# Move disk 1 from peg 2 to peg 1
+# Move disk 2 from peg 2 to peg 3
+# Move disk 1 from peg 1 to peg
+#  3
+# This output demonstrates the correct sequence of moves to solve the Tower of Hanoi problem with 3 disks.