Bubble Sort Algorithm in DSA Go - Time & Space Complexity

Time Complexity: Bubble Sort Algorithm

O(n²)

Understanding Time Complexity

We want to understand how the time taken by Bubble Sort changes as the list size grows.

How many steps does Bubble Sort need to sort a list of numbers?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func bubbleSort(arr []int) {
    n := len(arr)
    for i := 0; i < n-1; i++ {
        for j := 0; j < n-i-1; j++ {
            if arr[j] > arr[j+1] {
                arr[j], arr[j+1] = arr[j+1], arr[j]
            }
        }
    }
}

This code sorts an array by repeatedly swapping adjacent elements if they are in the wrong order.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing and possibly swapping adjacent elements inside nested loops.
• How many times: The inner loop runs about n times for each of the n passes of the outer loop, so roughly n x n = n² times.

How Execution Grows With Input

As the list size grows, the number of comparisons grows much faster.

Input Size (n)	Approx. Operations
10	About 45 comparisons
100	About 4,950 comparisons
1000	About 499,500 comparisons

Pattern observation: Doubling the input size roughly quadruples the work, showing a square growth pattern.

Final Time Complexity

Time Complexity: O(n²)

This means the time to sort grows roughly with the square of the number of items in the list.

Common Mistake

[X] Wrong: "Bubble Sort always takes the same time no matter the list order."

[OK] Correct: If the list is already sorted, Bubble Sort can finish faster because it does fewer swaps and can stop early if optimized.

Interview Connect

Understanding Bubble Sort's time complexity helps you compare it with faster sorting methods and shows your grasp of algorithm efficiency.

Self-Check

"What if we add a flag to stop early when no swaps happen in a pass? How would the time complexity change?"

Practice

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

easy

A. Repeatedly swap adjacent elements if they are in the wrong order

B. Divide the list into halves and sort each half separately

C. Select the smallest element and move it to the beginning

D. Insert each element into its correct position in a sorted sublist

Solution

1. Step 1: Understand Bubble Sort mechanism

   Bubble Sort compares adjacent elements and swaps them if they are out of order.

2. Step 2: Compare with other sorting methods

   Other options describe different algorithms: divide and conquer, selection sort, insertion sort.

3. Final Answer:

   Repeatedly swap adjacent elements if they are in the wrong order -> Option A

4. Quick Check:

   Bubble Sort = swapping adjacent pairs [OK]

Hint: Bubble Sort swaps neighbors repeatedly until sorted [OK]

Common Mistakes:

• Confusing Bubble Sort with Selection Sort
• Thinking it divides the list like Merge Sort
• Assuming it inserts elements like Insertion Sort

2. Which of the following is the correct way to write the outer loop for Bubble Sort in Go to sort an array arr of length n?

easy

A. for i := 0; i < n-1; i++ {}

B. for i := 0; i < n; i++ {}

C. for i := 1; i <= n; i++ {}

D. for i := 1; i < n-1; i++ {}

Solution

1. Step 1: Determine loop range for passes

   Bubble Sort requires n-1 passes to ensure sorting, so loop runs from 0 to n-2 (i < n-1).

2. Step 2: Check options for correct syntax and range

   for i := 0; i < n-1; i++ {} correctly uses i := 0; i < n-1; i++. Others either run too many or incorrect iterations.

3. Final Answer:

   for i := 0; i < n-1; i++ {} -> Option A

4. Quick Check:

   Outer loop runs n-1 times [OK]

Hint: Outer loop runs n-1 times in Bubble Sort [OK]

Common Mistakes:

• Using i <= n causing out-of-range errors
• Starting loop at 1 instead of 0
• Looping n times instead of n-1

3. What will be the output of the following Go code snippet after applying one full pass of Bubble Sort on the array?

arr := []int{5, 3, 8, 4, 2}
n := len(arr)
for j := 0; j < n-1; j++ {
    if arr[j] > arr[j+1] {
        arr[j], arr[j+1] = arr[j+1], arr[j]
    }
}
fmt.Println(arr)

medium

A. [2 3 4 5 8]

B. [3 5 8 4 2]

C. [3 5 4 2 8]

D. [5 3 8 4 2]

Solution

1. Step 1: Perform one pass of Bubble Sort

   Compare and swap adjacent elements: - Compare 5 & 3: swap -> [3 5 8 4 2] - Compare 5 & 8: no swap - Compare 8 & 4: swap -> [3 5 4 8 2] - Compare 8 & 2: swap -> [3 5 4 2 8]

2. Step 2: Final array after one pass

   After one pass, largest element 8 moves to the end. Array is [3 5 4 2 8].

3. Final Answer:

   [3 5 4 2 8] -> Option C

4. Quick Check:

   One pass moves largest to end [OK]

Hint: One pass pushes largest element to the end [OK]

Common Mistakes:

• Assuming full sort after one pass
• Not swapping correctly
• Confusing indices in swaps

4. Identify the error in the following Bubble Sort code snippet in Go:

arr := []int{4, 2, 7, 1}
n := len(arr)
for i := 0; i < n; i++ {
    for j := 0; j < n; j++ {
        if arr[j] > arr[j+1] {
            arr[j], arr[j+1] = arr[j+1], arr[j]
        }
    }
}
fmt.Println(arr)

medium

A. Outer loop should start from 1 instead of 0

B. Inner loop runs out of range causing runtime error

C. Swap condition should be arr[j] < arr[j+1]

D. Array length n is incorrect

Solution

1. Step 1: Analyze inner loop range

   Inner loop runs j from 0 to n-1, but accesses arr[j+1]. When j = n-1, arr[j+1] is out of range causing runtime error.

2. Step 2: Correct inner loop range

   Inner loop should run from 0 to n-2 (j < n-1) to avoid out-of-range access.

3. Final Answer:

   Inner loop runs out of range causing runtime error -> Option B

4. Quick Check:

   Index out of range error = inner loop limit [OK]

Hint: Inner loop must stop before last index to avoid out-of-range [OK]

Common Mistakes:

• Not adjusting inner loop limit
• Swapping with wrong comparison
• Misunderstanding loop boundaries

5. Given the array arr := []int{3, 1, 4, 5, 2}, how many total swaps will Bubble Sort perform to fully sort the array in ascending order?

hard

A. 5

B. 7

C. 6

D. 4

Solution

1. Step 1: Trace swaps in each pass

   Initial array: [3,1,4,5,2] Pass 1: - 3 > 1 swap -> [1,3,4,5,2] (1 swap) - 3 > 4 no swap - 4 > 5 no swap - 5 > 2 swap -> [1,3,4,2,5] (2 swaps total) Pass 2: - 1 > 3 no swap - 3 > 4 no swap - 4 > 2 swap -> [1,3,2,4,5] (3 swaps total) Pass 3: - 1 > 3 no swap - 3 > 2 swap -> [1,2,3,4,5] (4 swaps total) Pass 4: - 1 > 2 no swap - 2 > 3 no swap No swaps, sorting done.

2. Step 2: Count total swaps

   Pass 1: 2 swaps Pass 2: 1 swap Pass 3: 1 swap Total = 4 swaps Recheck carefully: Pass 1: swaps at (3,1) and (5,2) = 2 Pass 2: swap at (4,2) = 1 Pass 3: swap at (3,2) = 1 Total swaps = 4

3. Step 3: Verify if more swaps needed

   Sorting completes after pass 4 with no swaps. Total swaps = 4

4. Final Answer:

   4 -> Option D

5. Quick Check:

   Count swaps carefully per pass [OK]

Hint: Count swaps each pass until no swaps remain [OK]

Common Mistakes:

• Counting comparisons instead of swaps
• Missing swaps in later passes
• Assuming swaps equal to array length