Sorting is the process of arranging elements in a specific order, usually ascending or descending, to make data easier to search, analyze, and process.

Sorting plays a critical role in computer science because many algorithms perform efficiently only on sorted data.

1. Bubble Sort

Concept

Bubble Sort repeatedly compares adjacent elements and swaps them if they are in the wrong order. Larger elements gradually move to the end of the array, similar to bubbles rising to the surface.

Working Idea

  • Compare adjacent elements
  • Swap them if they are in the wrong order
  • Repeat the process for all elements

Time Complexity

  • Best case: O(n)
  • Average case: O(n²)
  • Worst case: O(n²)

Space Complexity

O(1)

Key Points

  • Very simple to understand
  • Highly inefficient for large datasets

2. Selection Sort

Concept

Selection Sort repeatedly selects the smallest element from the unsorted portion of the array and places it at its correct position.

Working Idea

  • Find the minimum element
  • Swap it with the first unsorted element
  • Repeat for the remaining elements

Time Complexity

  • Best case: O(n²)
  • Average case: O(n²)
  • Worst case: O(n²)

Space Complexity

O(1)

Key Points

  • Requires fewer swaps than Bubble Sort
  • Still slow for large inputs

3. Insertion Sort

Concept

Insertion Sort builds the sorted array one element at a time by inserting each element into its correct position in the already sorted part.

Working Idea

  • Take one element at a time
  • Insert it into the correct position in the sorted portion

Time Complexity

  • Best case: O(n)
  • Average case: O(n²)
  • Worst case: O(n²)

Space Complexity

O(1)

Key Points

  • Efficient for small or nearly sorted datasets
  • Used in real-world hybrid sorting algorithms

4. Merge Sort

Concept

Merge Sort follows the divide-and-conquer approach by dividing the array into halves, sorting each half, and then merging them back together.

Working Idea

  • Divide the array into two halves
  • Recursively sort both halves
  • Merge the sorted halves

Time Complexity

  • Best case: O(n log n)
  • Average case: O(n log n)
  • Worst case: O(n log n)

Space Complexity

O(n)

Key Points

  • Stable sorting algorithm
  • Very efficient for large datasets

5. Quick Sort

Concept

Quick Sort selects a pivot element and arranges elements smaller than the pivot on one side and larger elements on the other side.

Working Idea

  • Choose a pivot element
  • Partition the array around the pivot
  • Recursively sort the subarrays

Time Complexity

  • Best case: O(n log n)
  • Average case: O(n log n)
  • Worst case: O(n²)

Space Complexity

O(log n) due to recursion stack

Key Points

  • Very fast in practice
  • Not stable by default

6. Heap Sort

Concept

Heap Sort uses a heap data structure to repeatedly extract the maximum element and place it at the end of the array.

Working Idea

  • Build a max heap
  • Remove the largest element
  • Place it at the end
  • Repeat the process

Time Complexity

  • Best case: O(n log n)
  • Average case: O(n log n)
  • Worst case: O(n log n)

Space Complexity

O(1)

Key Points

  • In-place sorting algorithm
  • Not stable

7. Counting Sort

Concept

Counting Sort counts the occurrences of each element and uses this information to place elements directly into their correct positions.

Working Idea

  • Count the frequency of each element
  • Compute cumulative counts
  • Place elements in sorted order

Time Complexity

O(n + k), where k is the range of values

Space Complexity

O(n + k)

Key Points

  • Extremely fast for small range data
  • Not a comparison-based sorting algorithm

8. Radix Sort

Concept

Radix Sort sorts numbers digit by digit, starting from the least significant digit and moving to the most significant digit.

Working Idea

  • Sort numbers by each digit
  • Use a stable sorting method at each step

Time Complexity

O(n × d), where d is the number of digits

Space Complexity

O(n)

Key Points

  • Works well for integers
  • Not comparison-based

9. Bucket Sort

Concept

Bucket Sort distributes elements into different buckets, sorts each bucket individually, and then combines all buckets to form the sorted array.

Working Idea

  • Create buckets
  • Distribute elements into buckets
  • Sort each bucket
  • Combine the results

Time Complexity

  • Average case: O(n + k)
  • Worst case: O(n²)

Space Complexity

O(n)

Key Points

  • Efficient for uniformly distributed data

Comparison of Sorting Algorithms

Bubble Sort
Best: O(n)
Average: O(n²)
Worst: O(n²)
Stable: Yes

Selection Sort
Best: O(n²)
Average: O(n²)
Worst: O(n²)
Stable: No

Insertion Sort
Best: O(n)
Average: O(n²)
Worst: O(n²)
Stable: Yes

Merge Sort
Best: O(n log n)
Average: O(n log n)
Worst: O(n log n)
Stable: Yes

Quick Sort
Best: O(n log n)
Average: O(n log n)
Worst: O(n²)
Stable: No

Heap Sort
Best: O(n log n)
Average: O(n log n)
Worst: O(n log n)
Stable: No

Counting Sort
Best: O(n + k)
Average: O(n + k)
Worst: O(n + k)
Stable: Yes

Radix Sort
Best: O(n × d)
Average: O(n × d)
Worst: O(n × d)
Stable: Yes

Choosing the Right Sorting Algorithm

  • Small dataset → Insertion Sort
  • Large dataset → Merge Sort or Quick Sort
  • Memory constraints → Heap Sort
  • Known range of values → Counting Sort
  • Real-world systems → Hybrid algorithms

Conclusion

No single sorting algorithm is best for all situations.

Understanding the strengths and limitations of each sorting algorithm allows you to choose the most efficient approach for a given problem and dataset.