Sorting Techniques Complexities

Sorting AlgorithmTime ComplexitySpace Complexity
Best CaseAverage CaseWorst CaseWorst Case
Bubble SortΩ(N)Θ(N2)O(N2)O(1)
Selection SortΩ(N2)Θ(N2)O(N2)O(1)
Insertion SortΩ(N)Θ(N2)O(N2)O(1)
Merge SortΩ(N log N)Θ(N log N)O(N log N)O(N)
Heap SortΩ(N log N)Θ(N log N)O(N log N)O(1)
Quick SortΩ(N log N)Θ(N log N)O(N2)O(log N)
Radix SortΩ(N k)Θ(N k)O(N k)O(N + k)
Count SortΩ(N + k)Θ(N + k)O(N + k)O(k)
Bucket SortΩ(N + k)Θ(N + k)O(N2)O(N)

Sort stability, Efficiency, Passes Comparison Table :

Sorting algorithmEfficiencyPassesSort stability
Bubble sort0(n2)n-1stable
Selection sort0(n2)n-1unstable
Insertion sort0(n)n-1stable
Quick sort0(n log n)log nunstable
Merge sort0(n log n)log nstable
Shell sort0(n)log nunstable
Radix sort0(n)No. of digits in the largest numberstable