Sorting Stability and When to Use Which Sort in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean for a sorting algorithm to be stable?

A stable sorting algorithm keeps the original order of equal elements the same after sorting.

beginner

Name a common stable sorting algorithm.

Merge Sort is a common stable sorting algorithm.

intermediate

Why might you choose a stable sort over an unstable sort?

You choose a stable sort when you want to keep the relative order of equal elements, for example, when sorting by multiple keys step-by-step.

intermediate

Which sorting algorithm is generally fastest for small arrays and why?

Insertion Sort is generally fastest for small arrays because it has low overhead and works well when the array is nearly sorted.

intermediate

When should you prefer Quick Sort over Merge Sort?

Prefer Quick Sort when you want an in-place sort with good average performance and less memory use, but be aware it is not stable.

Which of these sorting algorithms is stable?

A Merge Sort

B Quick Sort

C Heap Sort

D Selection Sort

Merge Sort is stable because it preserves the order of equal elements during merging.

Why is Insertion Sort preferred for small or nearly sorted arrays?

A It uses extra memory

B It has low overhead and adapts well to nearly sorted data

C It is unstable

D It always runs in O(n log n)

Insertion Sort is simple and efficient for small or nearly sorted arrays because it minimizes comparisons and swaps.

Which sorting algorithm is NOT stable?

A Bubble Sort

B Merge Sort

C Quick Sort

D Insertion Sort

Quick Sort is generally not stable because it swaps elements without preserving order of equal keys.

When sorting large data that does not fit in memory, which algorithm is preferred?

A Quick Sort

B Insertion Sort

C Selection Sort

D Merge Sort

Merge Sort is preferred for large data and external sorting because it can be implemented to work with data on disk.

Which sorting algorithm uses divide and conquer and is stable?

A Merge Sort

B Heap Sort

C Quick Sort

D Selection Sort

Merge Sort uses divide and conquer and is stable.

Explain what sorting stability means and give an example of when it matters.

Think about sorting a list of people first by age, then by name.

Describe when you would choose Quick Sort, Merge Sort, or Insertion Sort.

Consider memory use, stability, and data size.

Practice

1. Which of the following sorting algorithms is stable by default?

easy

A. Merge Sort

B. Quick Sort

C. Heap Sort

D. Selection Sort

Solution

1. Step 1: Understand stability in sorting

   A stable sort keeps the relative order of equal elements the same as in the input.

2. Step 2: Check common sorting algorithms

   Merge Sort is stable because it merges sorted halves without changing order of equal elements. Quick Sort, Heap Sort, and Selection Sort are not stable by default.

3. Final Answer:

   Merge Sort -> Option A

4. Quick Check:

   Stable sort = Merge Sort [OK]

Hint: Remember: Merge Sort is stable, Quick Sort is not [OK]

Common Mistakes:

• Thinking Quick Sort is stable
• Confusing stability with time complexity
• Assuming all comparison sorts are stable

2. Which syntax correctly declares a stable sort call on a vector v in C++ STL?

easy

A. v.stable_sort();

B. std::sort(v.begin(), v.end(), stable);

C. std::stable_sort(v.begin(), v.end());

D. std::sort_stable(v.begin(), v.end());

Solution

1. Step 1: Recall C++ STL stable sort syntax

   The function is std::stable_sort with two iterators as arguments.

2. Step 2: Check options for correctness

   std::stable_sort(v.begin(), v.end()); matches correct syntax. Options A, B, and D are invalid or do not exist in STL.

3. Final Answer:

   std::stable_sort(v.begin(), v.end()); -> Option C

4. Quick Check:

   Correct stable sort syntax = std::stable_sort(v.begin(), v.end()); [OK]

Hint: Use std::stable_sort with iterators for stable sorting [OK]

Common Mistakes:

• Using std::sort for stable sorting
• Calling non-existent member functions
• Passing wrong arguments to sort functions

3. What is the output of the following C++ code snippet?

struct Item {
  int key;
  char id;
};

std::vector<Item> v = {{2, 'a'}, {1, 'b'}, {2, 'c'}};
std::stable_sort(v.begin(), v.end(), [](Item x, Item y) { return x.key < y.key; });
for (auto &item : v) std::cout << item.key << item.id << ' ';

medium

A. 2c 2a 1b

B. 1b 2c 2a

C. 2a 2c 1b

D. 1b 2a 2c

Solution

1. Step 1: Understand stable_sort behavior

   stable_sort sorts by key ascending but keeps relative order of equal keys.

2. Step 2: Sort vector and trace output

   Keys sorted: 1, 2, 2. For key=2, 'a' comes before 'c' in original, so order stays '2a' then '2c'. Output: "1b 2a 2c "

3. Final Answer:

   1b 2a 2c -> Option D

4. Quick Check:

   Stable sort keeps order of equal keys [OK]

Hint: Stable sort keeps original order for equal keys [OK]

Common Mistakes:

• Assuming equal keys reorder arbitrarily
• Confusing stable_sort with sort
• Ignoring the lambda comparator effect

4. Identify the error in this code snippet that tries to use stable sort on an array:

int arr[] = {3, 1, 2};
std::stable_sort(arr, arr + 3);
for (int i = 0; i < 3; i++) std::cout << arr[i] << ' ';

medium

A. No error; code runs correctly

B. Array pointers used incorrectly in stable_sort

C. stable_sort cannot be used on arrays

D. Missing comparator function causes error

Solution

1. Step 1: Check stable_sort usage on arrays

   std::stable_sort accepts pointers as iterators, so arr and arr+3 are valid.

2. Step 2: Verify code correctness

   Code sorts array {3,1,2} to {1,2,3} and prints correctly. No error present.

3. Final Answer:

   No error; code runs correctly -> Option A

4. Quick Check:

   stable_sort works with array pointers [OK]

Hint: stable_sort works with pointers, no comparator needed for default order [OK]

Common Mistakes:

• Thinking stable_sort needs vector only
• Assuming comparator is mandatory
• Confusing pointers with iterators

5. You have a list of employees with fields name and age. You want to sort them by age but keep the original order for employees with the same age. Which sorting algorithm should you use and why?

hard

A. Heap Sort, because it uses less memory

B. Stable Sort (like Merge Sort), to preserve order of equal ages

C. Quick Sort, because it is faster on average

D. Selection Sort, because it is simple to implement

Solution

1. Step 1: Understand requirement for stability

   We want to keep original order for employees with same age, so sorting must be stable.

2. Step 2: Choose sorting algorithm based on stability

   Merge Sort or any stable sort preserves order of equal keys. Quick Sort, Heap Sort, Selection Sort are not stable by default.

3. Final Answer:

   Stable Sort (like Merge Sort), to preserve order of equal ages -> Option B

4. Quick Check:

   Stable sort needed to keep order [OK]

Hint: Use stable sort to keep order of equal keys [OK]

Common Mistakes:

• Choosing faster but unstable sorts
• Ignoring stability requirement
• Confusing simplicity with correctness