Time complexity of various sorting algorithms

Comparison of various sorting algorithms

Various common sorting algorithms
Category	Sorting methods	Complexity of Time			Complexity of space	Stability	Complexity	Characteristics
		Best	Average	Worst	Secondary storage		Simple
Insert Sort	Insert directly	O (N)	O (N2)	O (N2)	O (1)	Stability	Simple
	Hill sort	O (N)	O (N1.3)	O (N2)	O (1)	Not stable	Complex
Choose Sort	Direct selection	O (N)	O (N2)	O (N2)	O (1)	Not stable
	Heap Sort	O (N*LOG2N)	O (N*LOG2N)	O (N*LOG2N)	O (1)	Not stable	Complex
interchange sort	bubble sort	o (N)	o (N2)	o (N2)	o (+)	stable	simple	1, bubble sort is a time-to-space sorting method, N-hour good 2, the worst case is the order of the sequence into reverse, or the order of the inverse of the sequence, the worst time complexity O (n^2) just to indicate the number of times its operations 3 The best case scenario is that the data is inherently ordered and the complexity is O (n)
	quick sort	o (n*log2n)	o (n*log2n)	o (N2)	Span style= "color: #0000ff;" >o (log2n) ~o (n)	unstable	complex	1, n good, fast sorting compared to occupy memory, memory increases with the increase of N, but it is an efficient and highly unstable sorting algorithm. 2, after dividing one side is a, side is n-1, the time complexity of this extreme situation is O (n^2) 3, the best case is to evenly divide the sequence every time, O (n*log2n)
merge sort		o (n*log2n)	Span style= "color: #0000ff;" >o (n*log2n)	o (n*log2n)	o (n)	stable	complex	1, n good, merge compared to occupy memory, memory increases with the increase of N, but it is a high efficiency and stable sorting algorithm.
Base sort		O (d (r+n))	O (d (r+n))	O (d (r+n))	O (Rd+n)	Stability	Complex
Note: R for the keyword cardinality, d for length, N for the number of keywords

Note:

1, merge sort each recursive will use a secondary table, the length of the table to be sorted the same length, although the number of recursion is O (log2n), but each recursion will release the occupied secondary space,

2, the rapid sorting space complexity is only in the usual case O (log2n), if the worst case, it is clear that the O (n) space. Of course, the spatial complexity can be reduced to O (log2n) by randomization of the pivot selection.

Related concepts:

1. Complexity of Time

Time complexity can be thought of as the total number of operations on the sorted data. Reflects the regularity of the number of operations when n changes.

Common time complexities are: constant order O (1), Logarithmic order O (log2n), linear order O (n), linear logarithmic order O (nlog2n), square order O (N2)

Time complexity O (1): The number of statements executed in the algorithm is a constant, the time complexity is O (1),

2. Complexity of space

Spatial complexity is a measure of the amount of storage space required for an algorithm to execute within a computer, and it is also a function of problem size n

Space complexity O (1): When the spatial complexity of an algorithm is a constant, i.e. it is not changed with the size of the data volume n being processed, it can be represented as O (1)

Space complexity O (log2n): When the spatial complexity of an algorithm is proportional to the logarithm of the base 2 N, it can be represented as O (log2n)

Ax=n, then X=logan,

Space complexity O (n): When the spatial complexity of an algorithm is linearly proportional to n, it can be represented as 0 (n).

Time complexity of various sorting algorithms