Do you really remember the complexity of all the algorithms?

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The growth order of the algorithms specified in the big O notation.

Source: Big O Cheat Sheet.

Here is a list of some of the most common big O notations and how they compare to input data of different sizes.

Big O notation	Count 10 elements	Count 100 elements	Count 1000 elements
O(1)	1	1	1
O(log N)	3	6	9
O(N)	10	100	1000
O(N log N)	30	600	9000
O(N^2)	100	10000	1000000
O(2^N)	1024	1.26 e+29	1.07 e+301
O(N!)	3628800	9.3 e+157	4.02 e+2567

The data structure	The connection	To find the	insert	delete	note
An array of	1	n	n	n
The stack	n	n	1	1
The queue	n	n	1	1
The list	n	n	1	1
Hash table	–	n	n	n	In the case of a full hash function, order one.
Binary search tree	n	n	n	n	In the balanced tree case, it’s order log of n.
B tree	log(n)	log(n)	log(n)	log(n)
Red and black tree	log(n)	log(n)	log(n)	log(n)
AVL tree	log(n)	log(n)	log(n)	log(n)
Bloom filter	–	1	1	–	There is a probability of misjudgment (misjudgment of existence)

The name of the	The optimal	On average,	The worst	memory	stable	note
Bubble sort	n	n^2	n^2	1	Yes
Insertion sort	n	n^2	n^2	1	Yes
Selection sort	n^2	n^2	n^2	1	No
Heap sort	n log(n)	n log(n)	n log(n)	1	No
Merge sort	n log(n)	n log(n)	n log(n)	n	Yes
Quick sort	n log(n)	n log(n)	n^2	log(n)	No	In the in-place version, memory complexity is usually order log(n).
Hill sorting	n log(n)	Dependent on gap sequence	n (log(n))^2	1	No
Count sorting	n + r	n + r	n + r	n + r	Yes	R – The largest number in the array
Radix sort	n * k	n * k	n * k	n + k	Yes	K – The ascending order of the longest key