Tower of Hanoi Problem in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to print the move from source to destination.

DSA Javascript

console.log('Move disk from ' + [1] + ' to ' + dest);

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

Adest

Bsource

Ctemp

Ddisk

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'dest' instead of 'source' for the starting peg.

Using an undefined variable like 'disk'.

The move is from the source peg to the destination peg, so we print the source variable.

2fill in blank

medium

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

DSA Javascript

towerOfHanoi([1] - 1, source, temp, dest);

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

An

Bn - 1

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Passing n instead of n - 1.

Passing 1 or 0 incorrectly.

We call the function with n-1 disks, so the argument is n - 1.

3fill in blank

hard

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

DSA Javascript

if ([1] === 0) return;

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

Adest

Bsource

Cn

Dtemp

Attempts:

3 left

💡 Hint

Common Mistakes

Checking source or dest instead of n.

Using wrong comparison operators.

The base case checks if n is zero, meaning no disks to move.

4fill in blank

hard

Fill both blanks to correctly move the largest disk and then move n-1 disks from temp to dest.

DSA Javascript

console.log('Move disk from ' + [1] + ' to ' + [2]);
towerOfHanoi(n - 1, temp, dest, source);

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

Asource

Bdest

Ctemp

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping source and temp.

Using n instead of peg names.

The largest disk moves from source to dest, so blanks are source and dest.

5fill in blank

hard

Fill all three blanks to complete the recursive calls and print statement for Tower of Hanoi.

DSA Javascript

towerOfHanoi([1] - 1, [2], [3], dest);
console.log('Move disk from ' + source + ' to ' + dest);
towerOfHanoi([1] - 1, temp, dest, [2]);

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

An

Bsource

Ctemp

Ddest

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up peg names in recursive calls.

Using dest instead of temp in the first call.

First call moves n-1 disks from source to temp, then print move from source to dest, then move n-1 disks from temp to dest using source as temp.

Practice

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

easy

A. 7

B. 6

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 A

4. Quick Check:

   2^3 - 1 = 7 [OK]

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

Common Mistakes:

• Forgetting to subtract 1
• Using n instead of 2^n - 1
• Confusing number of disks with moves

2. Which of the following is the correct base case condition in a recursive Tower of Hanoi function in JavaScript?

easy

A. if (n < 0) return;

B. if (n === 1) moveDisk();

C. if (n > 1) return;

D. if (n === 0) return;

Solution

1. Step 1: Identify base case for recursion

   The recursion stops when there are no disks to move, i.e., n === 0.

2. Step 2: Check the options

   if (n === 0) return; correctly returns when n is 0, stopping recursion.

3. Final Answer:

   if (n === 0) return; -> Option D

4. Quick Check:

   Base case is n === 0 [OK]

Hint: Base case stops recursion at zero disks [OK]

Common Mistakes:

• Using n === 1 as base case incorrectly
• Not stopping recursion causing infinite calls
• Using invalid conditions like n < 0

3. What will be the output sequence of moves for 2 disks in the Tower of Hanoi problem using this code snippet?

function towerOfHanoi(n, from, to, aux) {
  if (n === 0) return;
  towerOfHanoi(n - 1, from, aux, to);
  console.log(`Move disk ${n} from ${from} to ${to}`);
  towerOfHanoi(n - 1, aux, to, from);
}
towerOfHanoi(2, 'A', 'C', 'B');

medium

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

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

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

Solution

1. Step 1: Trace recursive calls for n=2

   First move disk 1 from A to B, then disk 2 from A to C, then disk 1 from B to C.

2. Step 2: Match output with options

   "Move disk 1 from A to B" "Move disk 2 from A to C" "Move disk 1 from B to C" matches the exact sequence of moves printed by the code.

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 C

4. Quick Check:

   Correct move sequence for 2 disks = "Move disk 1 from A to B" "Move disk 2 from A to C" "Move disk 1 from B to C" [OK]

Hint: Follow recursion calls step-by-step [OK]

Common Mistakes:

• Mixing source and auxiliary rods
• Confusing disk numbers in moves
• Ignoring order of recursive calls

4. Identify the error in this Tower of Hanoi recursive function and select the fix:

function towerOfHanoi(n, from, to, aux) {
  if (n === 1) {
    console.log(`Move disk 1 from ${from} to ${to}`);
    return;
  }
  towerOfHanoi(n - 1, from, to, aux);
  console.log(`Move disk ${n} from ${from} to ${to}`);
  towerOfHanoi(n - 1, aux, to, from);
}

medium

A. Swap 'to' and 'aux' in the first recursive call

B. Change base case to n === 0

C. Remove the second recursive call

D. Add an extra console.log before recursion

Solution

1. Step 1: Analyze recursive calls

   The first recursive call should move n-1 disks from 'from' to 'aux' using 'to' as auxiliary, but here 'to' and 'aux' are swapped.

2. Step 2: Correct the argument order

   Swapping 'to' and 'aux' in the first recursive call fixes the logic to move disks correctly.

3. Final Answer:

   Swap 'to' and 'aux' in the first recursive call -> Option A

4. Quick Check:

   Correct recursive call order fixes error [OK]

Hint: Check recursive call parameters carefully [OK]

Common Mistakes:

• Mixing auxiliary and target rods
• Incorrect base case causing infinite recursion
• Removing necessary recursive calls

5. You want to solve the Tower of Hanoi problem for 4 disks but only want to print moves where disk 1 is moved. How would you modify this function?

function towerOfHanoi(n, from, to, aux) {
  if (n === 0) return;
  towerOfHanoi(n - 1, from, aux, to);
  console.log(`Move disk ${n} from ${from} to ${to}`);
  towerOfHanoi(n - 1, aux, to, from);
}

hard

A. Change base case to n === 1 and print only then

B. Add an if condition to print only when n === 1 inside the function

C. Remove recursive calls and print only disk 1 move

D. Print all moves but filter output outside the function

Solution

1. Step 1: Understand the requirement

   We want to print moves only when disk 1 moves, but still perform all recursive calls to solve the problem.

2. Step 2: Modify print statement with condition

   Add an if condition to print only when n === 1, so other moves are not printed but recursion continues.

3. Final Answer:

   Add an if condition to print only when n === 1 inside the function -> Option B

4. Quick Check:

   Conditional print inside recursion solves problem [OK]

Hint: Use if (n === 1) to print selectively [OK]

Common Mistakes:

• Changing base case breaks recursion
• Removing recursive calls stops solution
• Filtering output outside misses recursion logic