Big-O Complexity Chart

Algorithm Last Time Preparation Notes for Time & Space Complexicities of Different Data Structure and Sorting Algorithm.

Common Data Structure Operations

Data Structure Time Complexity Space Complexity
Average Worst Worst
Access Search Insertion Deletion Access Search Insertion Deletion
Array Θ(1) Θ(n) Θ(n) Θ(n) O(1) O(n) O(n) O(n) O(n)
Stack Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n)
Queue Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n)
Singly-Linked List Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n)
Doubly-Linked List Θ(n) Θ(n) Θ(1) Θ(1) O(n) O(n) O(1) O(1) O(n)
Skip List Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n log(n))
Hash Table N/A Θ(1) Θ(1) Θ(1) N/A O(n) O(n) O(n) O(n)
Binary Search Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n)
Cartesian Tree N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(n) O(n) O(n) O(n)
B-Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)
Red-Black Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)
Splay Tree N/A Θ(log(n)) Θ(log(n)) Θ(log(n)) N/A O(log(n)) O(log(n)) O(log(n)) O(n)
AVL Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(log(n)) O(log(n)) O(log(n)) O(log(n)) O(n)
KD Tree Θ(log(n)) Θ(log(n)) Θ(log(n)) Θ(log(n)) O(n) O(n) O(n) O(n) O(n)

Array Sorting Algorithms

Algorithm Time Complexity Space Complexity
Best Average Worst Worst
Quicksort Ω(n log(n)) Θ(n log(n)) O(n^2) O(log(n))
Mergesort Ω(n log(n)) Θ(n log(n)) O(n log(n)) O(n)
Timsort Ω(n) Θ(n log(n)) O(n log(n)) O(n)
Heapsort Ω(n log(n)) Θ(n log(n)) O(n log(n)) O(1)
Bubble Sort Ω(n) Θ(n^2) O(n^2) O(1)
Insertion Sort Ω(n) Θ(n^2) O(n^2) O(1)
Selection Sort Ω(n^2) Θ(n^2) O(n^2) O(1)
Tree Sort Ω(n log(n)) Θ(n log(n)) O(n^2) O(n)
Shell Sort Ω(n log(n)) Θ(n(log(n))^2) O(n(log(n))^2) O(1)
Bucket Sort Ω(n+k) Θ(n+k) O(n^2) O(n)
Radix Sort Ω(nk) Θ(nk) O(nk) O(n+k)
Counting Sort Ω(n+k) Θ(n+k) O(n+k) O(k)
Cubesort Ω(n) Θ(n log(n)) O(n log(n)) O(n)

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