Selection Sort Algorithm in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Selection Sort algorithm?

Selection Sort repeatedly finds the smallest element from the unsorted part and swaps it with the first unsorted element, growing the sorted part step by step.

intermediate

In Selection Sort, how many times do we swap elements in the worst case?

Selection Sort swaps elements exactly (n-1) times, where n is the number of elements, because it swaps once per pass.

beginner

Show the state of the array after the first pass of Selection Sort on [29, 10, 14, 37, 13].

After first pass, the smallest element 10 is swapped with 29: [10, 29, 14, 37, 13]

intermediate

What is the time complexity of Selection Sort and why?

Selection Sort has time complexity O(n²) because it uses two nested loops: one to select each element and one to find the minimum in the unsorted part.

intermediate

Why is Selection Sort not efficient for large datasets?

Because Selection Sort always does n² comparisons regardless of the initial order, making it slow for large lists compared to faster algorithms like Quick Sort or Merge Sort.

What does Selection Sort do in each pass?

A Finds the smallest element and swaps it with the first unsorted element

B Swaps adjacent elements if they are in wrong order

C Divides the list into halves and sorts each half

D Uses a pivot to partition the list

Selection Sort finds the smallest element in the unsorted part and swaps it with the first unsorted element in each pass.

How many passes does Selection Sort make for an array of size n?

A n

B log n

C n/2

D n-1

Selection Sort makes n-1 passes because after sorting n-1 elements, the last element is already in place.

What is the best case time complexity of Selection Sort?

A O(n²)

B O(n log n)

C O(n)

D O(log n)

Selection Sort always performs O(n²) comparisons regardless of input order.

Which of these is true about Selection Sort swaps?

A It swaps elements multiple times per pass

B It swaps only once per pass

C It never swaps elements

D It swaps only if the array is already sorted

Selection Sort swaps the smallest found element with the first unsorted element once per pass.

Which sorting algorithm is generally faster than Selection Sort for large datasets?

A Bubble Sort

B Insertion Sort

C Quick Sort

D Selection Sort

Quick Sort is generally faster with average time complexity O(n log n), better than Selection Sort's O(n²).

Explain how Selection Sort works step-by-step on a small array.

Think about how you would sort playing cards by picking the smallest card each time.

Describe the advantages and disadvantages of Selection Sort.

Consider when you might want to use it despite its slowness.

Practice

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

easy

A. Repeatedly find the smallest element and move it to the front

B. Divide the list into halves and merge sorted halves

C. Swap adjacent elements if they are in wrong order repeatedly

D. Use a pivot to partition the list into smaller parts

Solution

1. Step 1: Understand selection sort process

   Selection sort finds the smallest element in the unsorted part and swaps it with the first unsorted element.

2. Step 2: Compare with other sorting methods

   Other options describe merge sort, bubble sort, and quicksort, which are different algorithms.

3. Final Answer:

   Repeatedly find the smallest element and move it to the front -> Option A

4. Quick Check:

   Selection sort = find smallest and swap [OK]

Hint: Selection sort always picks the smallest next element [OK]

Common Mistakes:

• Confusing selection sort with bubble sort
• Thinking it divides list like merge sort
• Assuming it uses a pivot like quicksort

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

easy

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

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

C. for i := 0; i <= n; i++ {

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

Solution

1. Step 1: Understand loop range for selection sort

   The outer loop runs from 0 to n-2 because the last element will be sorted automatically after previous passes.

2. Step 2: Check each option's correctness

   for i := 0; i < n-1; i++ { uses i < n-1, which is correct. Others either go out of bounds or start at wrong index.

3. Final Answer:

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

4. Quick Check:

   Outer loop runs 0 to n-2 [OK]

Hint: Outer loop stops at n-2 because last element is sorted [OK]

Common Mistakes:

• Using <= n causing index out of range
• Starting loop at 1 instead of 0
• Loop running too many times

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

arr := []int{29, 10, 14, 37, 13}
n := len(arr)
minIndex := 0
for j := 1; j < n; j++ {
    if arr[j] < arr[minIndex] {
        minIndex = j
    }
}
arr[0], arr[minIndex] = arr[minIndex], arr[0]
fmt.Println(arr)

medium

A. [10 13 14 37 29]

B. [13 10 14 37 29]

C. [29 10 14 37 13]

D. [10 29 14 37 13]

Solution

1. Step 1: Find minimum element index in full array

   Minimum element is 10 at index 1, so minIndex = 1.

2. Step 2: Swap arr[0] and arr[minIndex]

   Swap arr[0] (29) with arr[1] (10), resulting in [10 29 14 37 13].

3. Final Answer:

   [10 29 14 37 13] -> Option D

4. Quick Check:

   First pass places smallest element at front [OK]

Hint: First pass swaps smallest element to front [OK]

Common Mistakes:

• Not swapping elements after finding minimum
• Confusing minIndex with current index
• Printing array before swap

4. Identify the error in the following Go code implementing selection sort:

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

medium

A. Swap should be done only if minIndex != i

B. minIndex should be initialized outside the outer loop

C. Inner loop condition should be j < n, not j <= n

D. Outer loop should run from i := 1 to n-1

Solution

1. Step 1: Check inner loop boundary

   Inner loop uses j <= n, which causes index out of range error because valid indices are 0 to n-1.

2. Step 2: Correct inner loop condition

   It should be j < n to stay within array bounds.

3. Final Answer:

   Inner loop condition should be j < n, not j <= n -> Option C

4. Quick Check:

   Array indices go from 0 to n-1 [OK]

Hint: Array indices end at n-1, not n [OK]

Common Mistakes:

• Using <= n causing runtime panic
• Initializing minIndex outside outer loop
• Unnecessary swap checks

5. Given the array arr := []int{64, 25, 12, 22, 11}, after how many swaps will the array be fully sorted using selection sort, and what will be the final sorted array?

hard

A. 4 swaps; [11 12 22 25 64]

B. 5 swaps; [11 12 22 25 64]

C. 4 swaps; [64 25 12 22 11]

D. 3 swaps; [11 12 22 25 64]

Solution

1. Step 1: Count swaps in each selection sort pass

   Pass 1: swap 64 and 11 -> [11 25 12 22 64]
   Pass 2: swap 25 and 12 -> [11 12 25 22 64]
   Pass 3: swap 25 and 22 -> [11 12 22 25 64]
   Pass 4: swap 25 and 25 (no change, but swap counted as 1)
   Total swaps = 4 (last swap is with itself, usually counted as swap)

2. Step 2: Final sorted array

   The array after sorting is [11 12 22 25 64].

3. Final Answer:

   4 swaps; [11 12 22 25 64] -> Option A

4. Quick Check:

   Selection sort swaps once per pass, total n-1 swaps [OK]

Hint: Selection sort swaps once per pass, total n-1 swaps [OK]

Common Mistakes:

• Counting swaps incorrectly when swapping element with itself
• Assuming more swaps than passes
• Confusing sorted array with original