Tower of Hanoi Problem in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Tower of Hanoi moves for 2 disks

What is the output of the following Tower of Hanoi function call for 2 disks?

DSA Typescript

function towerOfHanoi(n: number, fromRod: string, toRod: string, auxRod: string, moves: string[] = []): string[] {
  if (n === 1) {
    moves.push(`Move disk 1 from ${fromRod} to ${toRod}`);
    return moves;
  }
  towerOfHanoi(n - 1, fromRod, auxRod, toRod, moves);
  moves.push(`Move disk ${n} from ${fromRod} to ${toRod}`);
  towerOfHanoi(n - 1, auxRod, toRod, fromRod, moves);
  return moves;
}

const result = towerOfHanoi(2, 'A', 'C', 'B');
console.log(result.join('\n'));

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

C

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

D

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

💡 Hint

Remember the recursive steps: move n-1 disks to auxiliary, move largest disk, then move n-1 disks to target.

The Tower of Hanoi for 2 disks moves disk 1 from A to B, then disk 2 from A to C, then disk 1 from B to C.

🧠 Conceptual

intermediate

Minimum moves required for Tower of Hanoi

What is the minimum number of moves required to solve the Tower of Hanoi problem with 4 disks?

A 8

B 31

C 15

D 16

💡 Hint

The minimum moves follow the formula 2^n - 1 where n is the number of disks.

For 4 disks, minimum moves = 2^4 - 1 = 16 - 1 = 15.

🔧 Debug

advanced

Identify the error in Tower of Hanoi implementation

What error will this Tower of Hanoi code produce when called with n=3?

DSA Typescript

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

towerOfHanoi(3, 'A', 'C', 'B');

A No error, outputs correct moves

B Stack overflow error due to infinite recursion

C TypeError because of wrong parameter types

D SyntaxError due to missing return statement

💡 Hint

Check the base case and recursive calls carefully.

The base case n===0 stops recursion correctly, so no error occurs and moves print properly.

❓ Predict Output

advanced

Number of moves printed for 3 disks

How many moves will be printed by this Tower of Hanoi function call with 3 disks?

DSA Typescript

function towerOfHanoi(n: number, fromRod: string, toRod: string, auxRod: string, moves: string[] = []): string[] {
  if (n === 1) {
    moves.push(`Move disk 1 from ${fromRod} to ${toRod}`);
    return moves;
  }
  towerOfHanoi(n - 1, fromRod, auxRod, toRod, moves);
  moves.push(`Move disk ${n} from ${fromRod} to ${toRod}`);
  towerOfHanoi(n - 1, auxRod, toRod, fromRod, moves);
  return moves;
}

const result = towerOfHanoi(3, 'A', 'C', 'B');
console.log(result.length);

A 6

B 8

C 9

D 7

💡 Hint

Minimum moves for n disks is 2^n - 1.

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

🚀 Application

expert

Calculate total moves for n disks using formula

Which TypeScript function correctly calculates the minimum number of moves required to solve Tower of Hanoi for n disks?

A function minMoves(n: number): number { return Math.pow(2, n) - 1; }

B function minMoves(n: number): number { return 2 * n + 1; }

C function minMoves(n: number): number { return n * n - 1; }

D function minMoves(n: number): number { return n * 2 - 1; }

💡 Hint

Recall the formula for minimum moves is 2^n - 1.

Option A correctly implements the formula 2^n - 1 for minimum moves.