Selection Sort Algorithm in DSA C++ - 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.

beginner

How many passes does Selection Sort make through the array?

Selection Sort makes n-1 passes through an array of n elements, because after placing n-1 elements, the last one is already sorted.

intermediate

What is the time complexity of Selection Sort in the best, average, and worst cases?

Selection Sort has a time complexity of O(n²) in all cases because it always compares each element with the rest, regardless of initial order.

beginner

Does Selection Sort require extra memory for sorting?

No, Selection Sort is an in-place sorting algorithm, meaning it sorts the array without needing extra memory beyond a few variables.

intermediate

Why is Selection Sort not efficient for large datasets?

Because Selection Sort always does n² comparisons, it becomes slow for large datasets compared to faster algorithms like Quick Sort or Merge Sort.

What does Selection Sort do in each pass?

A Divides the array into halves and sorts each half

B Swaps adjacent elements if they are in the wrong order

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

D Uses a pivot to partition the array

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

How many swaps does Selection Sort perform in the worst case?

A n-1 swaps

B n² swaps

C 0 swaps

D n swaps

Selection Sort performs exactly n-1 swaps because it swaps once per pass after finding the minimum.

Which of these is true about Selection Sort's space complexity?

A It sorts in-place using constant extra space

B It requires extra space proportional to n

C It needs a temporary array to store sorted elements

D It uses recursion and stack space

Selection Sort sorts the array in-place and uses only a few variables, so it has constant extra space.

What is the best case time complexity of Selection Sort?

A O(n log n)

B O(n)

C O(log n)

D O(n²)

Selection Sort always does n² comparisons, so its best case time complexity is O(n²).

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

A Bubble Sort

B Quick Sort

C Selection Sort

D Insertion Sort

Quick Sort is generally faster than Selection Sort for large arrays due to better average time complexity.

Explain step-by-step how Selection Sort sorts the array [4, 2, 7, 1].

Think about how the smallest number moves to the front each time.

Describe why Selection Sort is considered an in-place sorting algorithm and what that means for memory use.

Focus on how the array is changed directly.

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