Comparison based Algorithms (compare elements inside array for sorting)

Selection Sort

Insertion Sort

Bubble Sort

Quick Sort

Merge Sort

Non-Comparison based Algorithms

Bucket Sort

Radix Sort

Time Complexity Overview for Every Algorithm

1. Selection Sort Best Case: O (n^2) even if the list is already sorted, we still have to traverse every element. Worst Case: O (n^2) every element is swapped, that results in quadratic time complexity.
2. Insertion Sort Best Case: O (n) even if the list is already sorted, it still makes n-1 comparisons without swaps. Worst Case: O (n^2) if list is sorted in reverse order, in makes max swaps and comparisons.
3. Bubble Sort Best Case: O (n) when list is sorted and only pass is needed. Worst Case: O (n^2) when list is sorted in reverse order, max swaps and comparisons required.
4. Quick Sort Best Case: O (nlogn) when the selected pivot divides array into two equal parts. Worst Case: O (n^2) when selected pivot is either smallest or largest element.
5. Merge Sort Best Case: O (nlogn) continue dividing the array into halves until each half contains 1 element. Worst Case: O (nlogn) continue dividing the array into halves until each half contains 1 element.
6. Bucket Sort Best Case: O (n+k) elements are uniformly distributed across buckets. Worst Case: O (n^2) all elements are placed in a single bucket, quadratic sorting is used.
7. Radix Sort Best Case: O (kn) when elements have same number of digits or significant positions. Worst Case: O (kn) each element has different number of digits or significant positions.
8. Heap Sort Best Case: O (nlogn) heap is already balanced and only heapify operations are required. Worst Case: O (nlogn) heap is unbalanced, heapify operations are required for every element.