Sorting Algorithms
Worst Case Average Case
Insertion Sort O (𝑛2 )
O (𝑛2 )
Best Case
In Place
Recursive
Ω (n)
Yes
No
INSERSION-SORT(A)
Ω (nlog 𝑛)
No
Yes
MERGE(A, p, q, r)
MERGE-SORT(A, p, r)
Yes
Yes
Yes
Yes
MAX-HEAPIFY – maintains - Ɵ (log 𝑛)
BUILD-MAX-HEAP- Ɵ (n)
HEAPSORT- Ɵ (nlog 𝑛)
QUICKSORT(A, p, r) O (n log 𝑛)
PARTITION(A, p, r) O (n)
(tight code)
Merge Sort
O (nlog 𝑛) O (nlog 𝑛)
Divide & concur
(Memory usage
grows with input
size)
Heapsort
O (nlog 𝑛)
Quicksort
O (𝑛2 )
Divide & concur
(tight code)
O (n log 𝑛)
if partitioned
randomly
Ω (nlog 𝑛)