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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.