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Sorting Algorithms

An overview of some commonly used sorting algorithms:

1. Bubble Sort:

  • Compares adjacent elements and swaps them if they are in the wrong order.
  • Repeatedly passes through the list until the list is sorted.
  • Simple to implement but not efficient for large lists.
  • Time Complexity: O(n^2)

2. Selection Sort:

  • Divides the list into a sorted and an unsorted portion.
  • Selects the smallest (or largest) element from the unsorted portion and swaps it with the first element of the unsorted portion.
  • Repeats this process until the entire list is sorted.
  • Time Complexity: O(n^2)

3. Insertion Sort:

  • Builds the final sorted list one element at a time.
  • Takes each element from the unsorted portion and inserts it into the correct position in the sorted portion.
  • Time Complexity: O(n^2), but efficient for small lists or partially sorted lists.

4. Merge Sort:

  • Utilizes the divide-and-conquer approach.
  • Divides the list into smaller sublists, recursively sorts them, and then merges them to obtain the final sorted list.
  • Efficient for large lists and guarantees a time complexity of O(n log n) in all cases.
  • Requires additional space for the merging step.

5. Quick Sort:

  • Utilizes the divide-and-conquer approach.
  • Selects a pivot element, partitions the list into two sublists (elements less than the pivot and elements greater than the pivot), and recursively sorts the sublists.
  • Efficient for large lists, but can have a worst-case time complexity of O(n^2) if the pivot selection is unbalanced.
  • In the average case, it has a time complexity of O(n log n).

6. Heap Sort:

  • Utilizes a binary heap data structure to sort elements.
  • Builds a max-heap from the input list and repeatedly extracts the maximum element to obtain the sorted list.
  • Has a time complexity of O(n log n) in all cases and is an in-place sorting algorithm.
  • Requires additional space for the heap structure.

7. Radix Sort:

  • Sorts elements by processing them digit by digit.
  • Groups elements based on the value of each digit using counting sort or any stable sorting algorithm.
  • Requires a fixed-length representation for elements (e.g., integers or strings).
  • Time complexity depends on the number of digits and the range of digits.