Tower of Hanoi Problem in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Typescript

console.log(`Move disk from [1] to destination`);

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Aauxiliary

Bdestination

Csource

Ddisk

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'destination' instead of 'source' for the starting rod.

Using 'disk' which is not a rod name.

The move is from the source rod to the destination rod, so 'source' is correct.

2fill in blank

medium

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

DSA Typescript

hanoi([1] - 1, source, auxiliary, destination);

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A0

Bn - 1

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Passing 'n - 1 - 1' or other incorrect expressions.

Passing a fixed number like 1 instead of the variable.

We call hanoi with n-1 disks, so the argument should be 'n'.

3fill in blank

hard

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

DSA Typescript

if (n [1] 0) return;

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A>

B<=

C==

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'n > 0' which causes infinite recursion.

Using 'n == 0' which misses negative values.

The recursion stops when n is less than or equal to 0, so 'n <= 0' is correct.

4fill in blank

hard

Fill both blanks to move n-1 disks from auxiliary to destination rod after moving the largest disk.

DSA Typescript

hanoi(n [1] 1, [2], destination, source);

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A-

B+

Cauxiliary

Dsource

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' for disk count.

Using 'source' instead of 'auxiliary' for the starting rod.

We move n-1 disks, so use 'n - 1', and the disks move from auxiliary rod.

5fill in blank

hard

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

DSA Typescript

hanoi([1] - 1, source, [2], destination);
console.log(`Move disk from [3] to destination`);
hanoi([1] - 1, [2], destination, source);

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

An

Bauxiliary

Csource

Ddestination

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up source and auxiliary rods in recursive calls.

Incorrect disk count in recursive calls.

We move n-1 disks from source to auxiliary, then move disk from source to destination, then move n-1 disks from auxiliary 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:

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

2. Which of the following is the correct TypeScript function signature for solving Tower of Hanoi recursively?

easy

A. function towerOfHanoi(n: number, from: string, to: string, aux: string): void

B. function towerOfHanoi(n: string, from: number, to: number, aux: number): number

C. function towerOfHanoi(n: number, from: number, to: number): void

D. function towerOfHanoi(n: number): string

Solution

1. Step 1: Identify parameters needed for Tower of Hanoi

   We need number of disks (number), source peg (string), destination peg (string), and auxiliary peg (string).

2. Step 2: Match with function signature

   function towerOfHanoi(n: number, from: string, to: string, aux: string): void matches all parameters with correct types and returns void as it prints moves.

3. Final Answer:

   function towerOfHanoi(n: number, from: string, to: string, aux: string): void -> Option A

4. Quick Check:

   Correct parameters and return type [OK]

Hint: Check parameter types and count carefully [OK]

Common Mistakes:

• Using wrong parameter types
• Missing auxiliary peg parameter
• Wrong return type

3. What will be the output of the following TypeScript code snippet for Tower of Hanoi with 2 disks?

function towerOfHanoi(n: number, from: string, to: string, aux: string): void {
  if (n === 1) {
    console.log(`Move disk 1 from ${from} to ${to}`);
    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 1 from A to C
Move disk 2 from A to B
Move disk 1 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 B to C
Move disk 2 from A to C
Move disk 1 from A to B

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

Solution

1. Step 1: Trace first recursive call with n=2

   Call towerOfHanoi(1, 'A', 'B', 'C') prints "Move disk 1 from A to B".

2. Step 2: Print move for disk 2

   Prints "Move disk 2 from A to C".

3. Step 3: Trace second recursive call with n=1

   Call towerOfHanoi(1, 'B', 'C', 'A') prints "Move disk 1 from B to C".

4. Final Answer:

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

5. Quick Check:

   Follow recursion steps carefully [OK]

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

Common Mistakes:

• Mixing source and auxiliary pegs
• Printing moves in wrong order
• Confusing disk numbers

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

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

medium

A. Change base case to if (n === 1) and print move for disk 1

B. Change base case to if (n === 0) and remove print statement

C. Remove recursive calls and only print moves

D. Change print statement to print disk 0

Solution

1. Step 1: Analyze base case condition

   Base case should be when n equals 1, not 0, because disk numbering starts at 1.

2. Step 2: Fix base case and print statement

   Change if (n === 0) to if (n === 1) and print move for disk 1.

3. Final Answer:

   Change base case to if (n === 1) and print move for disk 1 -> Option A

4. Quick Check:

   Base case must handle smallest disk [OK]

Hint: Base case is n === 1, not zero [OK]

Common Mistakes:

• Using n === 0 as base case
• Printing move for disk 1 in wrong place
• Skipping base case

5. You want to solve Tower of Hanoi for 4 disks but only print moves where disk 1 is moved. Which modification to the recursive function is correct?

hard

A. Print all moves and filter disk 1 moves after recursion

B. Remove all recursive calls except for n=1

C. Add condition to print only if disk number is 1 inside the print statement

D. Change base case to n=2 and print only disk 1 moves

Solution

1. Step 1: Understand requirement to print only disk 1 moves

   We must keep recursion intact but print moves only when disk number is 1.

2. Step 2: Modify print statement with condition

   Add if (n === 1) before printing move to filter only disk 1 moves.

3. Final Answer:

   Add condition to print only if disk number is 1 inside the print statement -> Option C

4. Quick Check:

   Filter print, keep recursion [OK]

Hint: Use if condition inside print to filter moves [OK]

Common Mistakes:

• Removing recursive calls breaks solution
• Filtering moves after recursion wastes time
• Changing base case incorrectly