Selection Sort Algorithm in DSA C++ - Time & Space Complexity

Time Complexity: Selection Sort Algorithm

O(n²)

Understanding Time Complexity

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

How does the number of steps increase when sorting bigger lists?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void selectionSort(int arr[], int n) {
  for (int i = 0; i < n - 1; i++) {
    int minIndex = i;
    for (int j = i + 1; j < n; j++) {
      if (arr[j] < arr[minIndex]) {
        minIndex = j;
      }
    }
    std::swap(arr[i], arr[minIndex]);
  }
}
    

This code sorts an array by repeatedly finding the smallest element and moving it to the front.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Comparing elements inside the inner loop.
• How many times: The inner loop runs fewer times each pass, but overall about n*(n-1)/2 times.

How Execution Grows With Input

As the list size grows, the number of comparisons grows roughly with the square of the size.

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

Pattern observation: Doubling the input size roughly quadruples the work.

Final Time Complexity

Time Complexity: O(n²)

This means the time to sort grows quickly as the list gets bigger, roughly proportional to the square of the list size.

Common Mistake

[X] Wrong: "Selection Sort gets faster if the list is already sorted."

[OK] Correct: Selection Sort always compares elements the same way, so it takes the same time regardless of initial order.

Interview Connect

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

Self-Check

"What if we changed the inner loop to stop early when no smaller element is found? How would the time complexity change?"

Practice

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

easy

A. Divide the array into halves and sort each half recursively

B. Swap adjacent elements if they are in wrong order

C. Repeatedly find the minimum element and place it at the beginning

D. Use a heap data structure to sort elements

Solution

1. Step 1: Understand Selection Sort process

   Selection Sort works by finding the smallest element in the unsorted part and swapping it with the first unsorted element.

2. Step 2: Compare with other sorting methods

   Unlike swapping adjacent elements or dividing arrays, Selection Sort directly selects the minimum element each time.

3. Final Answer:

   Repeatedly find the minimum element and place it at the beginning -> Option C

4. Quick Check:

   Selection Sort = Find minimum and swap [OK]

Hint: Selection Sort picks minimum each pass [OK]

Common Mistakes:

• Confusing with Bubble Sort swapping adjacent elements
• Thinking it divides array like Merge Sort
• Assuming it uses extra data structures like heaps

2. Which of the following is the correct syntax to swap two elements arr[i] and arr[min_idx] in C++ during Selection Sort?

easy

A. swap(arr[i], arr[min_idx]);

B. arr[i] = arr[min_idx]; arr[min_idx] = arr[i];

C. swap(arr[min_idx], arr[j]);

D. arr[i], arr[min_idx] = arr[min_idx], arr[i];

Solution

1. Step 1: Identify correct swap function usage

   In C++, the standard library provides swap(a, b) to exchange values of two variables.

2. Step 2: Check syntax correctness

   swap(arr[i], arr[min_idx]); uses swap(arr[i], arr[min_idx]); which correctly swaps the two elements.

3. Final Answer:

   swap(arr[i], arr[min_idx]); -> Option A

4. Quick Check:

   Use std::swap for swapping [OK]

Hint: Use std::swap(a, b) to swap in C++ [OK]

Common Mistakes:

• Assigning one element twice causing data loss
• Using Python-style tuple swap syntax in C++
• Confusing parameter order in swap function

3. What will be the output array after running Selection Sort on arr = {64, 25, 12, 22, 11}?

medium

A. [11, 22, 12, 25, 64]

B. [64, 25, 12, 22, 11]

C. [25, 11, 12, 22, 64]

D. [11, 12, 22, 25, 64]

Solution

1. Step 1: Perform Selection Sort passes

   Pass 1: Minimum is 11, swap with 64 -> {11, 25, 12, 22, 64}
   Pass 2: Minimum is 12, swap with 25 -> {11, 12, 25, 22, 64}
   Pass 3: Minimum is 22, swap with 25 -> {11, 12, 22, 25, 64}
   Pass 4: Minimum is 25, no swap needed -> {11, 12, 22, 25, 64}

2. Step 2: Final sorted array

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

3. Final Answer:

   [11, 12, 22, 25, 64] -> Option D

4. Quick Check:

   Selection Sort output = Sorted array ascending [OK]

Hint: Selection Sort outputs sorted ascending array [OK]

Common Mistakes:

• Not swapping minimum element correctly
• Confusing sorting order (descending vs ascending)
• Stopping before full array is sorted

4. Identify the error in the following Selection Sort code snippet:

for (int i = 0; i < n-1; i++) {
  int min_idx = i;
  for (int j = i+1; j < n; j++) {
    if (arr[j] > arr[min_idx]) {
      min_idx = j;
    }
  }
  swap(arr[i], arr[min_idx]);
}

medium

A. The inner loop condition should be j <= n

B. The comparison operator should be < to find minimum

C. The swap function is used incorrectly

D. The outer loop should run till i < n

Solution

1. Step 1: Analyze comparison logic

   The code uses if (arr[j] > arr[min_idx]) which finds the maximum, not minimum.

2. Step 2: Correct comparison for Selection Sort

   Selection Sort requires finding the minimum element, so the operator should be <.

3. Final Answer:

   The comparison operator should be < to find minimum -> Option B

4. Quick Check:

   Selection Sort finds minimum using < comparison [OK]

Hint: Use < to find minimum in Selection Sort [OK]

Common Mistakes:

• Using > instead of < for minimum search
• Incorrect loop boundaries causing out-of-range errors
• Misusing swap function parameters

5. Given an array arr = {5, 3, 8, 6, 2}, how many swaps will Selection Sort perform to sort it in ascending order?

hard

A. 2

B. 3

C. 4

D. 5

Solution

1. Step 1: Trace swaps during Selection Sort

   Pass 1: Minimum is 2, swap with 5 -> swap count = 1
   Array: {2, 3, 8, 6, 5}
   Pass 2: Minimum is 3, already at position -> no swap
   Pass 3: Minimum is 5, swap with 8 -> swap count = 2
   Array: {2, 3, 5, 6, 8}
   Pass 4: Minimum is 6, already at position -> no swap

2. Step 2: Count total swaps

   Total swaps performed = 2

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Count swaps only when minimum differs from current [OK]

Hint: Count swaps only when minimum differs from current [OK]

Common Mistakes:

• Counting all passes as swaps
• Ignoring when minimum is already at current position
• Assuming swaps equal number of passes