Tower of Hanoi Problem in DSA Go - 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 Go

package main
import "fmt"

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 1 {
        fmt.Printf("Move disk 1 from %s to %s\n", from, to)
        return
    }
    towerOfHanoi(n-1, from, aux, to)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

func main() {
    towerOfHanoi(2, "A", "C", "B")
}

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

For 2 disks, the moves are: move disk 1 from A to B, move disk 2 from A to C, then move disk 1 from B to C.

🧠 Conceptual

intermediate

Minimum moves required for Tower of Hanoi with 4 disks

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

A 15

B 8

C 16

D 31

💡 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 this Tower of Hanoi code snippet

What error will this Go code produce when run?

DSA Go

package main
import "fmt"

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 0 {
        fmt.Printf("Move disk 0 from %s to %s\n", from, to)
        return
    }
    towerOfHanoi(n-1, from, aux, to)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

func main() {
    towerOfHanoi(3, "A", "C", "B")
}

A Compilation error: missing return statement

B Stack overflow due to infinite recursion

C Prints moves including disk 0, which is invalid

D Runs correctly with no errors

💡 Hint

Check the base case condition and what happens when n=0.

The base case incorrectly handles n==0 by printing a move for disk 0, which does not exist. This is logically incorrect but does not cause runtime error.

🚀 Application

advanced

Number of moves for 5 disks after 10 moves

If you have solved 10 moves in the Tower of Hanoi problem with 5 disks, how many moves remain to complete the puzzle?

A 21

B 22

C 23

D 24

💡 Hint

Total moves for 5 disks is 2^5 - 1. Subtract moves done.

Total moves for 5 disks = 2^5 - 1 = 31. Remaining moves = 31 - 10 = 21.

❓ Predict Output

expert

Output of Tower of Hanoi moves for 3 disks with custom peg names

What is the output of the Tower of Hanoi function call for 3 disks with pegs named X, Y, Z?

DSA Go

package main
import "fmt"

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 1 {
        fmt.Printf("Move disk 1 from %s to %s\n", from, to)
        return
    }
    towerOfHanoi(n-1, from, aux, to)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

func main() {
    towerOfHanoi(3, "X", "Z", "Y")
}

A

Move disk 1 from X to Y
Move disk 2 from X to Y
Move disk 1 from Y to Z
Move disk 3 from X to Z
Move disk 1 from Y to X
Move disk 2 from Y to Z
Move disk 1 from X to Z

B

Move disk 1 from X to Y
Move disk 2 from X to Z
Move disk 1 from Y to Z
Move disk 3 from X to Z
Move disk 1 from Y to X
Move disk 2 from Z to Y
Move disk 1 from X to Y

C

Move disk 1 from X to Y
Move disk 2 from X to Z
Move disk 1 from Y to Z
Move disk 3 from X to Y
Move disk 1 from Z to X
Move disk 2 from Z to Y
Move disk 1 from X to Y

D

Move disk 1 from X to Z
Move disk 2 from X to Y
Move disk 1 from Z to Y
Move disk 3 from X to Z
Move disk 1 from Y to X
Move disk 2 from Y to Z
Move disk 1 from X to Z

💡 Hint

Follow the recursive pattern carefully with the given peg names.

The correct sequence follows the classic Tower of Hanoi moves with pegs X, Y, Z as source, auxiliary, and target respectively.

Practice

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

easy

A. 6

B. 9

C. 8

D. 7

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 D

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 number of disks with moves

2. Which of the following Go function signatures correctly represents the Tower of Hanoi recursive function?

easy

A. func towerOfHanoi(n string, from int, to int, aux int)

B. func towerOfHanoi(n int, from string, to string, aux string)

C. func towerOfHanoi(n int, from int, to int)

D. func towerOfHanoi(n int, from string, to string)

Solution

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

   We need number of disks (int), and names of three rods (strings): from, to, auxiliary.

2. Step 2: Match function signature

   func towerOfHanoi(n int, from string, to string, aux string) matches with n as int and three string rods. Others miss parameters or have wrong types.

3. Final Answer:

   func towerOfHanoi(n int, from string, to string, aux string) -> Option B

4. Quick Check:

   Correct parameters and types = func towerOfHanoi(n int, from string, to string, aux string) [OK]

Hint: Tower of Hanoi needs 4 params: disks and 3 rods [OK]

Common Mistakes:

• Using wrong parameter types
• Missing auxiliary rod parameter
• Using fewer than 4 parameters

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

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 1 {
        fmt.Printf("Move disk 1 from %s to %s\n", from, to)
        return
    }
    towerOfHanoi(n-1, from, aux, to)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

func main() {
    towerOfHanoi(2, "A", "C", "B")
}

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

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

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 A

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: Trace recursion carefully for small n [OK]

Common Mistakes:

• Swapping auxiliary and target rods
• Printing moves in wrong order
• Confusing disk numbers

4. Identify the error in the following Tower of Hanoi Go function and select the correct fix:

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 0 {
        return
    }
    towerOfHanoi(n-1, from, to, aux)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

medium

A. Remove base case entirely

B. Change base case to if n == 1 and adjust recursive calls accordingly

C. Swap 'to' and 'aux' in first recursive call

D. Change print statement to use 'aux' instead of 'to'

Solution

1. Step 1: Analyze recursive calls and base case

   Base case with n==0 is okay, but first recursive call uses wrong rod order: it should move disks from 'from' to 'aux' using 'to' as auxiliary.

2. Step 2: Correct first recursive call

   Swap 'to' and 'aux' in first recursive call to towerOfHanoi(n-1, from, aux, to).

3. Final Answer:

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

4. Quick Check:

   Correct rod order in recursion = Swap 'to' and 'aux' in first recursive call [OK]

Hint: First recursive call moves disks to auxiliary rod [OK]

Common Mistakes:

• Confusing auxiliary and target rods
• Incorrect base case condition
• Wrong print statement parameters

5. You want to solve the Tower of Hanoi problem for 4 disks but print only the moves where disk 1 is moved. Which modification to the Go recursive function below will achieve this?

func towerOfHanoi(n int, from string, to string, aux string) {
    if n == 1 {
        fmt.Printf("Move disk 1 from %s to %s\n", from, to)
        return
    }
    towerOfHanoi(n-1, from, aux, to)
    fmt.Printf("Move disk %d from %s to %s\n", n, from, to)
    towerOfHanoi(n-1, aux, to, from)
}

hard

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

B. Change base case to n == 0 and print only in recursive calls

C. Remove the print statement in the base case

D. Print only when from == "A" and to == "C"

Solution

1. Step 1: Understand when disk 1 moves are printed

   Disk 1 moves are printed only in base case when n == 1.

2. Step 2: Modify print statements to print only for disk 1

   Add an if condition around print statements to print only when n == 1, skipping other disks.

3. Final Answer:

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

4. Quick Check:

   Print only disk 1 moves = Add an if condition to print only when n == 1 inside the function [OK]

Hint: Print only when disk number is 1 inside recursion [OK]

Common Mistakes:

• Removing base case print
• Printing based on rod names instead of disk number
• Changing base case incorrectly