Merge Sort Algorithm in DSA Go

Mental Model

Split the list into smaller parts, sort each part, then join them back together in order.

Analogy: Imagine sorting a big pile of cards by first dividing them into small piles, sorting each small pile, then carefully combining the piles back into one sorted stack.

Unsorted list:
[38, 27, 43, 3, 9, 82, 10]

Split into halves:
[38, 27, 43]    [3, 9, 82, 10]

Split further:
[38] [27, 43]    [3, 9] [82, 10]

Split until single elements:
[38] [27] [43]    [3] [9] [82] [10]

Dry Run Walkthrough

Input: list: [38, 27, 43, 3, 9, 82, 10]

Goal: Sort the list in ascending order using merge sort

Step 1: Split list into two halves

[38, 27, 43]    [3, 9, 82, 10]

Why: We break the problem into smaller parts to sort them easily

Step 2: Split left half into [38] and [27, 43]

[38]    [27, 43]    [3, 9, 82, 10]

Why: Keep splitting until each part has one element

Step 3: Split [27, 43] into [27] and [43]

[38]    [27]    [43]    [3, 9, 82, 10]

Why: Single elements are considered sorted

Step 4: Split right half into [3, 9] and [82, 10]

[38]    [27]    [43]    [3, 9]    [82, 10]

Why: Continue splitting the right half

Step 5: Split [3, 9] into [3] and [9]

[38]    [27]    [43]    [3]    [9]    [82, 10]

Why: Single elements are sorted

Step 6: Split [82, 10] into [82] and [10]

[38]    [27]    [43]    [3]    [9]    [82]    [10]

Why: Single elements are sorted

Step 7: Merge [27] and [43] into [27, 43]

[38]    [27, 43]    [3]    [9]    [82]    [10]

Why: Combine sorted parts in order

Step 8: Merge [3] and [9] into [3, 9]

[38]    [27, 43]    [3, 9]    [82]    [10]

Why: Combine sorted parts in order

Step 9: Merge [82] and [10] into [10, 82]

[38]    [27, 43]    [3, 9]    [10, 82]

Why: Combine sorted parts in order

Step 10: Merge [38] and [27, 43] into [27, 38, 43]

[27, 38, 43]    [3, 9]    [10, 82]

Why: Combine sorted parts in order

Step 11: Merge [3, 9] and [10, 82] into [3, 9, 10, 82]

[27, 38, 43]    [3, 9, 10, 82]

Why: Combine sorted parts in order

Step 12: Merge [27, 38, 43] and [3, 9, 10, 82] into [3, 9, 10, 27, 38, 43, 82]

[3, 9, 10, 27, 38, 43, 82]

Why: Final merge produces fully sorted list

Result:

[3, 9, 10, 27, 38, 43, 82]

Annotated Code

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++        }
    }
    // Append remaining elements
    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{38, 27, 43, 3, 9, 82, 10}
    sorted := mergeSort(arr)
    fmt.Println(sorted)
}

if len(arr) <= 1 { return arr }

stop splitting when array has one or zero elements

mid := len(arr) / 2

find middle index to split array

left := mergeSort(arr[:mid])

recursively sort left half

right := mergeSort(arr[mid:])

recursively sort right half

return merge(left, right)

merge two sorted halves into one sorted array

for i < len(left) && j < len(right) { if left[i] < right[j] { ... } else { ... } }

compare elements from left and right to build sorted result

result = append(result, left[i:]...)

append remaining elements from left if any

result = append(result, right[j:]...)

append remaining elements from right if any

Output

[3 9 10 27 38 43 82]

Complexity Analysis

Time: O(n log n) because the list is repeatedly split in half (log n splits) and merging takes linear time at each level

Space: O(n) because extra space is needed to hold merged arrays during the process

vs Alternative: Compared to simple sorting like bubble sort (O(n²)), merge sort is much faster for large lists but uses extra memory

Edge Cases

empty list

returns empty list immediately without error

DSA Go

if len(arr) <= 1 { return arr }

single element list

returns the single element list as is

DSA Go

if len(arr) <= 1 { return arr }

list with duplicate elements

duplicates are kept and sorted correctly

DSA Go

for i < len(left) && j < len(right) { if left[i] <= right[j] { ... } else { ... } }

When to Use This Pattern

When you need to sort large lists efficiently and can use extra space, look for merge sort because it splits and merges to keep sorting fast.

Common Mistakes

Mistake: Not stopping recursion when array length is 1 or 0, causing infinite recursion
Fix: Add base case: if len(arr) <= 1 { return arr }

Mistake: Merging arrays incorrectly by not handling leftover elements
Fix: After main merge loop, append remaining elements from left and right arrays

Summary

It sorts a list by splitting it into smaller parts, sorting those, and merging them back.

Use it when you want a reliable, efficient sort especially for large lists.

The key is breaking the problem down into smaller sorted pieces and combining them carefully.

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