Merge Sort Algorithm in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Merge Sort on a small array

What is the output of the following Go code that implements merge sort on the array [4, 1, 3, 2]?

DSA Go

package main
import "fmt"

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i < len(left) && j < len(right) {
        if left[i] < right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[j:]...)
    return result
}

func mergeSort(arr []int) []int {
    if len(arr) <= 1 {
        return arr
    }
    mid := len(arr) / 2
    left := mergeSort(arr[:mid])
    right := mergeSort(arr[mid:])
    return merge(left, right)
}

func main() {
    arr := []int{4, 1, 3, 2}
    sorted := mergeSort(arr)
    fmt.Println(sorted)
}

A [1 3 2 4]

B [4 3 2 1]

C [1 2 3 4]

D [2 1 3 4]

💡 Hint

Think about how merge sort splits the array and merges sorted halves.

Merge sort splits the array into halves recursively until single elements remain, then merges them back in sorted order. The final sorted array is [1 2 3 4].

🧠 Conceptual

intermediate

Time Complexity of Merge Sort

What is the time complexity of the merge sort algorithm in the average and worst cases?

A O(log n)

B O(n log n)

C O(n^2)

D O(n)

💡 Hint

Consider how many times the array is split and merged.

Merge sort divides the array into halves log n times and merges n elements each time, resulting in O(n log n) complexity.

🔧 Debug

advanced

Identify the bug in this merge function

What error will occur when running this merge function in Go?

DSA Go

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i <= len(left) && j <= len(right) {
        if left[i] < right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[j:]...)
    return result
}

A runtime error: index out of range

B compilation error: missing return statement

C infinite loop

D no error, runs correctly

💡 Hint

Check the loop condition and array indexing carefully.

The loop condition uses <= which allows i or j to equal the length of the slice, causing index out of range error when accessing left[i] or right[j].

🚀 Application

advanced

Merge Sort on Linked List

Which of the following statements about applying merge sort to a singly linked list is TRUE?

A Merge sort cannot be applied to linked lists.

B Merge sort is inefficient on linked lists because random access is slow.

C Merge sort requires converting the linked list to an array first.

D Merge sort can be implemented efficiently on linked lists without extra space by changing pointers.

💡 Hint

Think about how merging works with linked lists compared to arrays.

Merge sort works well on linked lists because merging can be done by rearranging pointers without extra arrays, making it space efficient.

❓ Predict Output

expert

Output of Merge Sort with Duplicate Elements

What is the output of the following Go code after sorting the array [5, 3, 8, 3, 9, 1, 5] using merge sort?

DSA Go

package main
import "fmt"

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i < len(left) && j < len(right) {
        if left[i] <= right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[j:]...)
    return result
}

func mergeSort(arr []int) []int {
    if len(arr) <= 1 {
        return arr
    }
    mid := len(arr) / 2
    left := mergeSort(arr[:mid])
    right := mergeSort(arr[mid:])
    return merge(left, right)
}

func main() {
    arr := []int{5, 3, 8, 3, 9, 1, 5}
    sorted := mergeSort(arr)
    fmt.Println(sorted)
}

A [1 3 3 5 5 8 9]

B [1 3 5 3 5 8 9]

C [1 3 3 5 8 9]

D [9 8 5 5 3 3 1]

💡 Hint

Check how duplicates are handled and the stability of merge sort.

Merge sort is stable and sorts duplicates in order, resulting in [1 3 3 5 5 8 9].

Practice

1. What is the main idea behind the Merge Sort algorithm?

easy

A. Compare each element with every other element and swap if needed

B. Pick the smallest element and place it at the beginning repeatedly

C. Divide the list into halves, sort each half, then merge them

D. Use a pivot to partition the list and sort partitions recursively

Solution

1. Step 1: Understand the divide and conquer approach

   Merge Sort splits the list into two halves recursively until single elements remain.

2. Step 2: Merge sorted halves

   It then merges these halves back together in sorted order.

3. Final Answer:

   Divide the list into halves, sort each half, then merge them -> Option C

4. Quick Check:

   Merge Sort = Divide and Conquer [OK]

Hint: Remember: split, sort halves, then merge [OK]

Common Mistakes:

• Confusing Merge Sort with Bubble Sort
• Thinking Merge Sort uses a pivot like Quick Sort
• Believing Merge Sort sorts in place without extra space

2. Which of the following is the correct way to declare a function for merge sort in Go?

easy

A. func mergeSort(arr []int) []int {}

B. func mergeSort(arr int[]) int[] {}

C. func mergeSort(arr array of int) array of int {}

D. func mergeSort(arr []int) int {}

Solution

1. Step 1: Check Go function syntax for slices

   In Go, slices are declared as []int for integer slices.

2. Step 2: Verify return type matches input type

   Merge sort returns a sorted slice, so return type is also []int.

3. Final Answer:

   func mergeSort(arr []int) []int {} -> Option A

4. Quick Check:

   Go slice syntax = []int [OK]

Hint: Go slices use []type syntax, not array of type [OK]

Common Mistakes:

• Using array syntax like int[] which is invalid in Go
• Returning int instead of []int for sorted slice
• Using incorrect parameter types like 'array of int'

3. What will be the output of the following Go code snippet using merge sort?

package main
import "fmt"

func mergeSort(arr []int) []int {
    if len(arr) <= 1 {
        return arr
    }
    mid := len(arr) / 2
    left := mergeSort(arr[:mid])
    right := mergeSort(arr[mid:])
    return merge(left, right)
}

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i < len(left) && j < len(right) {
        if left[i] < right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[j:]...)
    return result
}

func main() {
    arr := []int{5, 3, 8, 4, 2}
    sorted := mergeSort(arr)
    fmt.Println(sorted)
}

medium

A. [5 3 8 4 2]

B. [2 3 4 5 8]

C. [8 5 4 3 2]

D. [2 3 5 4 8]

Solution

1. Step 1: Trace the recursive splitting

   The array splits into halves until single elements: [5,3,8,4,2] -> [5,3] and [8,4,2], then further splits.

2. Step 2: Merge sorted halves step-by-step

   Merge [5] and [3] -> [3,5]; merge [8] and [4,2] -> [2,4,8]; finally merge [3,5] and [2,4,8] -> [2,3,4,5,8].

3. Final Answer:

   [2 3 4 5 8] -> Option B

4. Quick Check:

   Sorted array = [2 3 4 5 8] [OK]

Hint: Merge halves sorted individually to get full sorted array [OK]

Common Mistakes:

• Assuming original array prints without sorting
• Mixing up merge order causing wrong output
• Forgetting to append remaining elements after loop

4. Identify the bug in this merge function snippet and select the fix:

func merge(left, right []int) []int {
    result := []int{}
    i, j := 0, 0
    for i < len(left) && j < len(right) {
        if left[i] <= right[j] {
            result = append(result, left[i])
            i++
        } else {
            result = append(result, right[j])
            j++
        }
    }
    result = append(result, left[i:]...)
    result = append(result, right[i:]...)
    return result
}

medium

A. Remove the last two append statements

B. Change comparison from <= to <

C. Initialize result with length of left + right

D. Change last append from right[i:] to right[j:]

Solution

1. Step 1: Analyze the append of remaining elements

   After merging common parts, remaining elements from left[i:] and right[j:] must be appended.

2. Step 2: Spot the incorrect slice used

   The code incorrectly appends right[i:] instead of right[j:], which can cause wrong elements or panic.

3. Final Answer:

   Change last append from right[i:] to right[j:] -> Option D

4. Quick Check:

   Append remaining right elements using j index [OK]

Hint: Use correct index variable when appending leftover elements [OK]

Common Mistakes:

• Using wrong index variable for right slice leftover
• Removing leftover appends causing incomplete merge
• Changing comparison operator unnecessarily

5. You want to sort a large list of 1 million integers using merge sort in Go. Which approach is best to optimize memory usage and performance?

hard

A. Use a bottom-up iterative merge sort to avoid deep recursion

B. Use recursive merge sort with slices copied at each step

C. Use merge sort but create new slices for every merge step

D. Use bubble sort instead for simplicity

Solution

1. Step 1: Understand recursion overhead in large data

   Recursive merge sort can cause deep call stacks and many slice copies, increasing memory use.

2. Step 2: Bottom-up iterative merge sort reduces recursion

   Bottom-up merge sort merges pairs iteratively, reducing recursion and memory overhead.

3. Final Answer:

   Use a bottom-up iterative merge sort to avoid deep recursion -> Option A

4. Quick Check:

   Iterative merge sort = better memory for large data [OK]

Hint: Iterative merge sort saves stack and memory for big lists [OK]

Common Mistakes:

• Ignoring recursion limits on large inputs
• Copying slices unnecessarily increasing memory
• Choosing inefficient sorts like bubble sort for big data