Merge Sort Algorithm in DSA Go - Build from Scratch

Merge Sort Algorithm

📖 Scenario: You are working on a program that needs to sort a list of numbers efficiently. Merge Sort is a popular sorting method that splits the list into smaller parts, sorts them, and then merges them back together in order.Imagine you have a messy pile of numbered cards, and you want to arrange them from smallest to largest quickly and neatly.

🎯 Goal: Build a Go program that implements the Merge Sort algorithm to sort a list of integers.You will create the initial list, write the merge function, write the merge sort function, and finally print the sorted list.

📋 What You'll Learn

Create a slice of integers called numbers with the exact values: 38, 27, 43, 3, 9, 82, 10

Create a helper function called merge that merges two sorted slices into one sorted slice

Create a recursive function called mergeSort that splits the slice and uses merge to sort

Print the sorted slice after applying mergeSort

💡 Why This Matters

🌍 Real World

Merge Sort is used in many software systems where efficient and stable sorting is needed, such as databases, search engines, and large data processing.

💼 Career

Understanding merge sort helps in technical interviews and improves problem-solving skills for software development roles.

1

Create the initial slice of numbers

Create a slice of integers called numbers with these exact values: 38, 27, 43, 3, 9, 82, 10

DSA Go

# Create the slice called numbers with the given values
# Your code here

Hint

Use numbers := []int{38, 27, 43, 3, 9, 82, 10} to create the slice.

2

Create the merge function

Create a function called merge that takes two sorted slices of integers named left and right and returns a single sorted slice of integers

DSA Go

package main

import "fmt"

func merge(left []int, right []int) []int {
    // Your code here
}

func main() {
    numbers := []int{38, 27, 43, 3, 9, 82, 10}
}

Hint

Use two indexes to compare elements from left and right, append the smaller to result, then append remaining elements.

3

Create the mergeSort function

Create a recursive function called mergeSort that takes a slice of integers named arr and returns a sorted slice of integers. It should split arr into halves, recursively sort each half, and merge them using the merge function

DSA Go

package main

import "fmt"

func merge(left []int, 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++
        }
    }

    for i < len(left) {
        result = append(result, left[i])
        i++
    }

    for j < len(right) {
        result = append(result, right[j])
        j++
    }

    return result
}

func mergeSort(arr []int) []int {
    // Your code here
}

func main() {
    numbers := []int{38, 27, 43, 3, 9, 82, 10}
}

Hint

Split the slice into two halves, recursively call mergeSort on each half, then merge the results.

4

Print the sorted slice

In the main function, call mergeSort with the numbers slice and print the returned sorted slice using fmt.Println

DSA Go

package main

import "fmt"

func merge(left []int, 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++
        }
    }

    for i < len(left) {
        result = append(result, left[i])
        i++
    }

    for j < len(right) {
        result = append(result, right[j])
        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() {
    numbers := []int{38, 27, 43, 3, 9, 82, 10}
    // Your code here
}

Hint

Call mergeSort(numbers) and print the result with fmt.Println.

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