├── README.md └── Tables.html /README.md: -------------------------------------------------------------------------------- 1 | BigOCheatSheet 2 | ============== -------------------------------------------------------------------------------- /Tables.html: -------------------------------------------------------------------------------- 1 |

Searching

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Algorithm	Data Structure	Time Complexity			Space Complexity
		Best	Average	Worst	Worst
Depth First Search (DFS)	Tree	`O(1)`	`-`	`O(b^d)`	`O(\|V\|)`
Breadth First Search (BFS)	Tree	`O(1)`	`-`	`O(b^d)`	`O(b^d)`
Binary	Tree	40 \| `O(1)` 41 \|	43 \| `O(log(n))` 44 \|	46 \| `O(log(n))` 47 \|	49 \| `O(1)` 50 \|
Interpolation	-	`O(1)`	`O(log(log(n)))`	`O(n)`	`O(1)`
Linear (Brute Force)	Array	`O(1)`	`O(n)`	`O(n)`	`O(1)`

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Sorting

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Algorithm	Data Structure	Time Complexity			Space Complexity
		Best	Average	Worst	Worst
Quicksort	Array	`O(n log(n))`	`O(n log(n))`	`O(n^2)`	`O(log(n))`
Mergesort	Array	`O(n log(n))`	`O(n log(n))`	`O(n log(n))`	`O(n)`
Bubble Sort	Array	`O(n)`	`O(n^2)`	`O(n^2)`	`O(1)`
Insertion Sort	Array	`O(n)`	`O(n^2)`	`O(n^2)`	`O(1)`
Bucket Sort	Array	`O(n+k)`	`O(n+k)`	`O(n^2)`	`O(nk)`
Radix Sort	Array	`O(nk)`	`O(nk)`	`O(nk)`	`O(n+k)`

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Data Structures

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Data Structure	Time Complexity								Space Complexity
	Average				Worst				Worst
	Indexing	Search	Insertion	Deletion	Indexing	Search	Insertion	Deletion
Basic Array	`O(1)`	`O(n)`	`-`	`-`	`O(1)`	`O(n)`	`-`	`-`	`O(n)`
Dynamic Array	`O(1)`	`O(n)`	`O(n)`	`-`	`O(1)`	`O(n)`	`O(n)`	`-`	`O(n)`
Singly-Linked List	`O(n)`	`O(n)`	`O(1)`	`O(1)`	`O(n)`	`O(n)`	`O(1)`	`O(1)`	`O(n)`
Doubly-Linked List	`O(n)`	`O(n)`	`O(1)`	`O(1)`	`O(n)`	`O(n)`	`O(1)`	`O(1)`	`O(n)`
Hash Table	`-`	`O(1)`	`O(1)`	`O(1)`	`-`	`O(n)`	`O(n)`	`O(n)`	`O(n)`
Binary Search Tree	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`-`	`O(n)`	`O(n)`	`O(n)`	`O(n)`
B-Tree	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(n)`
Red-Black Tree	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(n)`
AVL Tree	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(n)`

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Heaps

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Heaps	Time Complexity
	Heapify	Find Max	Extract Max	Increase Key	Insert	Delete	Merge
Linked List (sorted)	`-`	`O(1)`	`O(1)`	`O(n)`	`O(n)`	`O(1)`	`O(m+n)`
Linked List (unsorted)	`-`	`O(n)`	`O(n)`	`O(1)`	`O(1)`	`O(1)`	`O(1)`
Binary Heap	`O(log(n))`	`O(1)`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(m+n)`
Binomial Heap	`-`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(log(n))`	`O(log(n))`
Fibonacci Heap	`-`	`O(1)`	`O(log(n))*`	`O(1)*`	`O(1)`	`O(log(n))*`	`O(1)`

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Graphs

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Node / Edge Management	Storage	Add Vertex	Add Edge	Remove Vertex	Remove Edge	Query
Adjacency list	`O(\|V\|+\|E\|)`	`O(1)`	`O(1)`	`O(\|E\|)`	`O(\|E\|)`	`O(\|V\|)`
Incidence list	`O(\|V\|+\|E\|)`	`O(1)`	`O(1)`	`O(\|E\|)`	`O(\|E\|)`	`O(\|E\|)`
Adjacency matrix	`O(\|V\|^2)`	`O(\|V\|^2)`	`O(1)`	`O(\|V\|^2)`	`O(1)`	`O(1)`
Incidence matrix	`O(\|V\| ⋅ \|E\|)`	`O(\|V\| ⋅ \|E\|)`	`O(\|V\| ⋅ \|E\|)`	`O(\|V\| ⋅ \|E\|)`	`O(\|V\| ⋅ \|E\|)`	`O(\|E\|)`

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