Tower of Hanoi Problem in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to print the source peg name.

DSA C#

Console.WriteLine("Move disk from [1] to destination");

Drag options to blanks, or click blank then click option'

A"aux"

B"dest"

C"source"

D"disk"

Attempts:

3 left

💡 Hint

Common Mistakes

Using the destination peg name instead of source.

Using the auxiliary peg name incorrectly.

The source peg is named "source" in the print statement to indicate where the disk moves from.

2fill in blank

medium

Complete the recursive call to move n-1 disks from source to auxiliary peg.

DSA C#

Hanoi(n - 1, [1], aux, dest);

Drag options to blanks, or click blank then click option'

Adest

Bdisk

Caux

Dsource

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping source and destination pegs.

Using the auxiliary peg as source incorrectly.

The first argument after n-1 is the source peg, so it should be "source".

3fill in blank

hard

Fix the error in the base case condition to stop recursion when no disks remain.

DSA C#

if (n [1] 0) return;

Drag options to blanks, or click blank then click option'

A<=

B==

C>

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' which only stops at exactly zero, missing negative values.

Using '!=' which causes infinite recursion.

The base case should stop recursion when n is less than or equal to zero.

4fill in blank

hard

Fill both blanks to correctly move n-1 disks from auxiliary to destination peg.

DSA C#

Hanoi([1], aux, [2], source);

Drag options to blanks, or click blank then click option'

An - 1

Bn

Cdest

Dsource

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of n-1 for the number of disks.

Swapping source and destination pegs.

We move n-1 disks from auxiliary to destination peg after moving the largest disk.

5fill in blank

hard

Fill all three blanks to complete the recursive Tower of Hanoi function call sequence.

DSA C#

Hanoi([1], [2], aux, [3]);

Drag options to blanks, or click blank then click option'

An - 1

Bsource

Cdest

Daux

Attempts:

3 left

💡 Hint

Common Mistakes

Using n instead of n-1.

Mixing up auxiliary and destination pegs.

The recursive call moves n-1 disks from source to auxiliary peg before moving the largest disk to destination.

Practice

1. What is the minimum number of moves required to solve the Tower of Hanoi problem with 3 disks?

easy

A. 6

B. 7

C. 8

D. 9

Solution

1. Step 1: Understand the formula for minimum moves

   The minimum moves required for n disks is 2^n - 1.

2. Step 2: Calculate for 3 disks

   For 3 disks, minimum moves = 2^3 - 1 = 8 - 1 = 7.

3. Final Answer:

   7 -> Option B

4. Quick Check:

   2^3 - 1 = 7 [OK]

Hint: Use formula 2^n - 1 for minimum moves [OK]

Common Mistakes:

• Confusing total moves with number of disks
• Using n instead of 2^n - 1
• Calculating 2*n - 1 instead of 2^n - 1

2. Which of the following is the correct C# method signature for a recursive Tower of Hanoi function?

easy

A. void TowerOfHanoi(int n, string fromRod, string toRod)

B. int TowerOfHanoi(int n, char fromRod, char toRod, char auxRod)

C. int TowerOfHanoi(int n, string fromRod, string toRod, string auxRod)

D. void TowerOfHanoi(int n, char fromRod, char toRod, char auxRod)

Solution

1. Step 1: Identify correct parameter types

   The Tower of Hanoi function typically uses integer for disk count and characters for rods.

2. Step 2: Check return type and parameters

   The function usually returns void and takes 3 rods as char parameters plus disk count as int.

3. Final Answer:

   void TowerOfHanoi(int n, char fromRod, char toRod, char auxRod) -> Option D

4. Quick Check:

   Correct signature uses void and char rods [OK]

Hint: Use void return and char for rods in signature [OK]

Common Mistakes:

• Using string instead of char for rods
• Returning int instead of void
• Missing auxiliary rod parameter

3. What will be the output sequence of moves for Tower of Hanoi with 2 disks from rod A to rod C using rod B as auxiliary?

medium

A. Move disk 1 from A to B
Move disk 2 from A to C
Move disk 1 from B to C

B. Move disk 2 from A to B
Move disk 1 from A to C
Move disk 2 from B to C

C. Move disk 1 from A to C
Move disk 2 from A to B
Move disk 1 from C to B

D. Move disk 2 from A to C
Move disk 1 from B to A
Move disk 2 from C to B

Solution

1. Step 1: Understand the recursive move sequence for 2 disks

   Move smaller disk 1 to auxiliary rod B, then move disk 2 to target rod C, then move disk 1 from B to C.

2. Step 2: Verify the move order

   Sequence is: 1 from A to B, 2 from A to C, 1 from B to C.

3. Final Answer:

   Move disk 1 from A to B Move disk 2 from A to C Move disk 1 from B to C -> Option A

4. Quick Check:

   Correct move order for 2 disks [OK]

Hint: For 2 disks, move smaller disk first to aux rod [OK]

Common Mistakes:

• Swapping disk numbers in moves
• Confusing auxiliary and target rods
• Reversing move order

4. Identify the error in this Tower of Hanoi recursive call snippet:

void Hanoi(int n, char from, char to, char aux) {
  if (n == 0) return;
  Hanoi(n - 1, from, aux, to);
  Console.WriteLine($"Move disk {n} from {from} to {to}");
  Hanoi(n - 1, aux, to, from);
}

medium

A. Base case should be if (n == 1) return;

B. Recursive calls have wrong rod order in parameters

C. No error, code is correct

D. Console.WriteLine should print disk n-1 instead of n

Solution

1. Step 1: Check base case correctness

   Base case n == 0 means no disks to move, which is correct to stop recursion.

2. Step 2: Verify recursive calls and print statement

   Recursive calls correctly move n-1 disks between rods, and print statement moves disk n from 'from' to 'to'.

3. Final Answer:

   No error, code is correct -> Option C

4. Quick Check:

   Base case and recursion are correctly implemented [OK]

Hint: Base case n==0 is correct to stop recursion [OK]

Common Mistakes:

• Changing base case to n==1 incorrectly
• Mixing up rod parameters in recursive calls
• Printing wrong disk number

5. You want to solve Tower of Hanoi for 4 disks but print only the moves where disk 1 is moved. How many such moves will be printed?

hard

A. 8

B. 15

C. 7

D. 4

Solution

1. Step 1: Calculate total moves for 4 disks

   Total moves = 2^4 - 1 = 15 moves.

2. Step 2: Count moves involving disk 1

   Disk 1 moves every alternate move, so number of moves = (total moves + 1) / 2 = (15 + 1)/2 = 8.

3. Final Answer:

   8 -> Option A

4. Quick Check:

   Disk 1 moves half the times plus one [OK]

Hint: Disk 1 moves on every alternate move, count half plus one [OK]

Common Mistakes:

• Assuming disk 1 moves equal to total moves
• Using total moves minus one
• Confusing disk 1 moves with total disks