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Divide and conquer sorting algorithm
sorted). Repeatedly merge sublists to produce new sorted sublists until there is only one sublist remaining. This will be the sorted list. Merge sort
Merge_sort
Sorting algorithm
Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually
Bucket_sort
Array data structure
A sorted array is an array data structure in which each element is sorted in numerical, alphabetical, or some other order, and placed at equally spaced
Sorted_array
Sorting algorithm using the heap data structure
now-sorted end of the array), the order of the partitions has been reversed, and the larger partition at the beginning of the array may be sorted in the
Heapsort
Algorithm that arranges lists in order
being sorted by a relatively small key field, is to create an index into the array and then sort the index, rather than the entire array. (A sorted version
Sorting_algorithm
Sorting algorithm
print("Unsorted array:", random_array) sorted_arr = bogo_sort(random_array) print("Sorted array:", sorted_arr) This code creates a random array - random_array - in
Bogosort
Sorting algorithm
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient
Insertion_sort
Search algorithm finding the position of a target value within a sorted array
position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half
Binary_search
Divide and conquer sorting algorithm
partition-exchange sort. The sub-arrays are then sorted recursively. This can be done in-place, requiring small additional amounts of memory to perform the sorting. Quicksort
Quicksort
Sorting algorithm
item into its sorted position in the output array. The relative order of items with equal keys is preserved here; i.e., this is a stable sort. Because the
Counting_sort
Efficient sorting algorithm that combines insert and merge operations
their first sorted position within the array. This process repeats for each level of the outer bottom-up merge sort, at which point the array will have
Block_sort
Non-comparative lexicographical sorting algorithm
For this reason, radix sort has also been called bucket sort and digital sort. Radix sort can be applied to data that can be sorted lexicographically, be
Radix_sort
Data structure for a string
In computer science, a suffix array is a sorted array of all suffixes of a string. It is a data structure used in, among others, full-text indices, data-compression
Suffix_array
Simple sorting algorithm using comparisons
graphics, bubble sort is popular for its capability to detect a very small error (like a swap of just two elements) in almost-sorted arrays and fix it with
Bubble_sort
Method of searching a sorted array
computer science, the Fibonacci search technique is a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations
Fibonacci_search_technique
Hybrid sorting algorithm
highly structured arrays (arrays that are composed of a small number of sorted subarrays) and introsort otherwise to sort arrays of ints, longs, floats and
Introsort
Sorting algorithm
sort in that it runs much more efficiently if the array is already sorted or "close to sorted." While selection sort is preferable to insertion sort in
Selection_sort
Sorting algorithm
then performance can be strictly better. In fact, when the input array is already sorted, all values form a single pile and both phases run in O(n) time
Patience_sorting
Type of data structure
compared to tree-based data structures (compare a sorted array to a search tree). One or more large arrays are sometimes used to emulate in-program dynamic
Array_(data_structure)
Type of parallel computing architecture of tightly coupled nodes
up"), resulting in the stream of elements coming out sorted in ascending order. Sorting input arrays of larger size (N > P) than the number of processing
Systolic_array
Relaxed variant of the sorting problem
in a partially sorted list, for every index i from 1 to k, the i-th element is in the same place as it would be in the fully sorted list: element i of
Partial_sorting
Action of arranging objects into order
with the value in the first position. Repeat until array is sorted. Quick sort: Partition the array into two segments. In the first segment, all elements
Sorting
Type of computer science algorithm
example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort
In-place_algorithm
a form of bucket and radix sort. Once a ProxmapSort is complete, ProxmapSearch can be used to find keys in the sorted array in O ( 1 ) {\displaystyle O(1)}
Proxmap_sort
Sorting algorithm in computer science
interpolation sort, interpolation tag sort runs in linear time O ( n ) {\displaystyle O(n)} when the values in the array to be sorted are evenly distributed
Interpolation_sort
Sorting algorithm which uses multiple comparison intervals
holds: after h2-sorting of any h1-sorted array, the array remains h1-sorted. Every h1-sorted and h2-sorted array is also (a1h1+a2h2)-sorted, for any nonnegative
Shellsort
Hybrid sorting algorithm based on insertion sort and merge sort
n)} comparisons to sort an array of n {\displaystyle n} elements. In the best case, which occurs when the input is already sorted, it runs in linear time
Timsort
Probabilistic data structure
of a sorted array (for searching) while maintaining a linked list-like structure that allows insertion, which is not possible with a static array. Fast
Skip_list
Sequence merge algorithm in computer science
sorted lists and merging them into a single sorted list. These merge algorithms generally refer to merge algorithms that take in a number of sorted lists
K-way_merge_algorithm
Comparison sorting algorithm
original array. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result
Cycle_sort
Topics referred to by the same term
mode Structured analysis, a software engineering technique Suffix array, a sorted array of all suffixes of a string System administrator System architecture
SA
Computational problem about sorting
values not yet sorted, and entries from k + 1 to the end of the array are values greater than mid. procedure three-way-partition(A : array of values, mid :
Dutch_national_flag_problem
Sorting algorithm
one pass of cocktail sort to become sorted, but if using an ascending bubble sort would take four passes. However one cocktail sort pass should be counted
Cocktail_shaker_sort
Method for finding kth smallest value
algorithms may be possible; as an extreme case, selection in an already-sorted array takes time O ( 1 ) {\displaystyle O(1)} . An algorithm for the selection
Selection_algorithm
Programming idiom for efficiently sorting a list by a computed key
anonymous array) used for the sorting, producing the items of the original list in the sorted order (sorted list of [item, value] ⇒ sorted list of item)
Schwartzian_transform
Describes approximate behavior of a function
search in a sorted array of uniformly distributed values O ( log n ) {\displaystyle O(\log n)} logarithmic Finding an item in a sorted array with a binary
Big_O_notation
perform an input or output operation. insertion sort A simple sorting algorithm that builds the final sorted array (or list) one item at a time. instruction
Glossary_of_computer_science
Data organization and storage formats
Lookup table Matrix Parallel array Sorted array Sparse matrix Iliffe vector Variable-length array Doubly linked list Array list Linked list also known
List_of_data_structures
list is sorted, and we have a reference to some node containing y, then we may find x in O(d) time by starting our search from y. In a sorted array A, one
Finger_search
Parallel sorting algorithm
describes the sorting process. In the code, a is the array to be sorted, low is the index of the first item in the sub-array to be sorted, k and count
Bitonic_sorter
Sorting algorithm
pigeonhole algorithm works as follows: Given an array of values to be sorted, set up an auxiliary array of initially empty "pigeonholes" (analogous to
Pigeonhole_sort
Measures of how efficiently algorithms use resources
the (j + 1)th element to be inserted on the average with half the already sorted sub-list, so tj = j/2. Working out the resulting average-case running time
Best,_worst_and_average_case
Estimate of time taken for running an algorithm
binary search in a sorted array. Algorithms that search for local structure in the input, for example finding a local minimum in a 1-D array (can be solved
Time_complexity
S_{k}} . It is a lexicographically sorted array of all suffixes of each string in the set S {\displaystyle S} . In the array, each suffix is represented by
Generalized_suffix_array
Categorization among data structures
not per record). A less trivial example is representing a sorted list by a sorted array, which allows search in logarithmic time by binary search. Contrast
Implicit_data_structure
Comparison-based sorting algorithm
array. Each extraction shrinks the prefix and adds the extracted element to a growing sorted suffix. When the prefix has shrunk to nothing, the array
Smoothsort
Algorithm for computing convex hulls in a set of points
point. The algorithm proceeds by considering each of the points in the sorted array in sequence. For each point, it is first determined whether traveling
Graham_scan
Algorithm that combines multiple sorted lists into one
sorted. The sorted partitions are then merged to produce larger, sorted, partitions, until 1 partition, the sorted array, is left. Merging two sorted
Merge_algorithm
Data structure representing a graph
the neighbours of this vertex. If the neighbours are represented as a sorted array, binary search may be used instead, taking time proportional to the logarithm
Adjacency_list
Computer file format
timer() sortedArray = SortVBSArray(split(myData,",")) endtime=timer() jscriptTime = round(endtime-starttime,2) wscript.echo "JScript sorted in " & jscriptTime
Windows_Script_File
1995 and 2007". Array if the key values span a moderately compact interval. Priority-sorted list; see linear search Key-sorted array; see binary search
Search_data_structure
Node ordering for directed acyclic graphs
beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node): L ← Empty list that will contain the sorted nodes while exists nodes
Topological_sorting
Group of standard library class templates
(stores a sorted set of unique keys) with vector as the default underlying container. std::flat_map<K, V> implements a "flat map" (stores a sorted set of
Sequence_container_(C++)
Data structure holding key/value pairs
In computer science, an associative array, key-value store, map, symbol table, or dictionary is an abstract data type that stores a collection of key/value
Associative_array
Abstract data type in computer science
suggest a sorting method: insert all the elements to be sorted into a priority queue, and sequentially remove them; they will come out in sorted order. This
Priority_queue
Implementation of an associative array
the value/pointer array. The bitmap fits within a typical CPU cache line, and random access only loads one cache line from the sorted list, so for reading
Judy_array
Type of randomized algorithm
i- 1] and A[i + 1 : n]. # Combine the responses in order to obtain a sorted array. A simple example is randomized quicksort, where the pivot is chosen
Las_Vegas_algorithm
Algorithm for searching sorted, infinite lists
given when the above result of the k-nested binary search is used on a sorted array. Using this, the number of comparisons done during a search is log (d)
Exponential_search
Comparison-based sorting algorithm
will be sorted. Below is a C/C++ implementation that builds up a Max-Heap and sorts the array after the heap is built. /* A C/C++ sample heap sort code that
Adaptive_heap_sort
Auxiliary data structure to the suffix array in computer science
are sorted lexicographically. Consider the string S = banana$ {\displaystyle S={\textrm {banana\$}}} : and its corresponding sorted suffix array A {\displaystyle
LCP_array
Sorting algorithm
many comparisons as insertion sort and has the same asymptotic run time characteristics. Gnome sort works by building a sorted list one element at a time
Gnome_sort
Algorithm for finding a zero of a function
to be confused with the binary search algorithm of searching a finite sorted array. Burden & Faires 2016, p. 51 "Interval Halving (Bisection)". Archived
Bisection_method
Computer science data structure
merge many already-sorted input streams into a single sorted output stream. Examples of the need for merging include external sorting and streaming results
Heap_(data_structure)
treated as a single key-value store. One variation of the LSM-Tree is the Sorted Array Merge Tree or SAMT. In this variation, a SAMT's component trees are called
Quotient_filter
sort. The input to these algorithms consists of two sorted arrays of numbers; the desired output is the same set of numbers in a single sorted array.
All_nearest_smaller_values
Data structure that always preserves the previous version of itself when it is modified
If the node has no parent—it's the root—it is added the new root to a sorted array of roots.) With this algorithm, given any time t, at most one modification
Persistent_data_structure
Problem in computational complexity theory
end The following example shows this algorithm's execution on a small sorted array. Current values of a are shown in red, values of b and c are shown in
3SUM
Inefficient recursive sorting algorithm
the array t = floor((j - i + 1) / 3) stoogesort(L, i, j-t) // Sort the first 2/3 of the array stoogesort(L, i+t, j) // Sort the last 2/3 of the array stoogesort(L
Stooge_sort
Data structure
and constructable by variants of the same algorithms. The suffix array, a sorted array of the starting positions of suffixes of the string, allowing substring
Substring_index
Searching algorithm
import std; using std::vector; /* arr[low, high) is sorted, search the data "key" in this array, if "key" is found, return the corresponding index (NOT
Interpolation_search
Type of sorting algorithm
out in sorted order. Its typical use is sorting elements online: after each insertion, the set of elements seen so far is available in sorted order. Tree
Tree_sort
Sorting algorithm
partitions the array into sub-intervals or buckets. The buckets are then sorted individually and then concatenated together. However, if the array is non-uniformly
Samplesort
Interval based sorting algorithm
combsort(array input) is gap := input.size // Initialize gap size shrink := 1.3 // Set the gap shrink factor sorted := false loop while sorted = false
Comb_sort
Property of an algorithm
is arranged; for example, some sorting algorithms perform poorly on data which is already sorted, or which is sorted in reverse order. In practice, there
Algorithmic_efficiency
Algorithm that employs a degree of randomness as part of its logic or procedure
algorithm require O(n2) time to sort n numbers for some well-defined class of degenerate inputs (such as an already sorted array), with the specific class of
Randomized_algorithm
Type of phased-array radar
active electronically scanned array (AESA) is a type of phased array antenna, which is a computer-controlled antenna array in which the beam of radio waves
Active electronically scanned array
Active_electronically_scanned_array
Sorting algorithm
Library sort or gapped insertion sort is a sorting algorithm that uses an insertion sort, but with gaps in the array to accelerate subsequent insertions
Library_sort
Exponent of a power of two
O(log n) or O(n log n) are: Average time quicksort and other comparison sort algorithms Searching in balanced binary search trees Exponentiation by squaring
Binary_logarithm
Humorous sorting algorithm
end_idx - 1) // (2) Sort the first half, recursively. (1.1) Sort the second half, recursively. (1.2) Find the maximum of the whole array by comparing the
Slowsort
Topics referred to by the same term
chemical entity (e.g.: A + B–C → B–A–C) Insertion sort, a simple computer algorithm for sorting arrays Local insertion, in broadcasting Insertion of a character
Insertion
{\displaystyle |S|>|C|} , then starting from the smallest element in the sorted array, sequentially insert each element of S {\displaystyle S} into C {\displaystyle
Shadow_heap
Array sorting algorithm
Cubesort is a parallel sorting algorithm that builds a self-balancing multi-dimensional array from the keys to be sorted. As the axes are of similar length
Cubesort
Type of sorting algorithm that works by comparing pairs of elements
already close to sorted, according to some measure of sortedness, the number of comparisons required to sort it can be smaller. An adaptive sort takes advantage
Comparison_sort
In-place, comparison-based sorting algorithm
result LULURR consists of two arrays of the necessary form (a sorted part adjacent to an unsorted part) and are sorted recursively. Leapfrogging samplesort
Proportion_extend_sort
Binary search variation with simplified midpoint calculation
binary search that uses a specific permutation of keys in an array instead of the sorted order used by regular binary search. Multiplicative binary search
Multiplicative_binary_search
Use of functions that call themselves
sorted array for a single element by cutting the array in half with each recursive pass. The trick is to pick a midpoint near the center of the array
Recursion_(computer_science)
Sorting algorithms which exploit existing order in its input
into an array of previously sorted items. Pseudo-code for the insertion sort algorithm follows (array X is zero-based): procedure Insertion Sort (X): for
Adaptive_sort
Computer programming operation
is a sorting operation such as: I = array_sort(A); % Obtain a list of sort indices B = A[I]; % B is the sorted version of A C = A[array_sort(A)]; %
Array_slicing
a sorted array. With this structure, one can use binary search to find the point closest to the start of a query interval, and then scan the array from
Range_reporting
Algorithm used in data compression
Burrows–Wheeler matrix) whose rows are the circular shifts of the input text, sorted in lexicographic order, then taking the final column of that matrix. To
Burrows–Wheeler_transform
Type of antenna
A passive electronically scanned array (PESA), also known as passive phased array, is an antenna in which the beam of radio waves can be electronically
Passive electronically scanned array
Passive_electronically_scanned_array
Tree containing all suffixes of a given text
implementations with efficient running time properties use hash maps, sorted or unsorted arrays (with array doubling), or balanced search trees. We are interested in:
Suffix_tree
Digital circuit
is Branch Prediction? (first answer, Answer 35214) Why is processing a sorted array faster than processing an unsorted array?". Stack Overflow: Java.
Branch_predictor
Variant of radix sort
flag sort comes by analogy with the Dutch national flag problem in the last step: efficiently partition the array into many "stripes". Sorting algorithms
American_flag_sort
Surface-mount packaging that uses an array of solder balls
A ball grid array (BGA) is a type of surface-mount packaging (a chip carrier) used for integrated circuits. BGA packages are used to permanently mount
Ball_grid_array
Feature detection algorithm in computer vision
standard SIFT descriptor, by setting each histogram bin to its rank in a sorted array of bins. The Euclidean distance between SIFT-Rank descriptors is invariant
Scale-invariant feature transform
Scale-invariant_feature_transform
Function for sorting in C++ standard library
object std::less), which may be overloaded in C++. This code sample sorts a given array of integers (in ascending order) and prints it out. import std; int
Sort_(C++)
Sorting algorithm
to merge sort in that some number of subarrays are recursively sorted, after which a merging step combines the subarrays into one sorted array. Merging
Funnelsort
Sorting algorithm
oddEvenSort(list) { function swap(list, i, j) { var temp = list[i]; list[i] = list[j]; list[j] = temp; } var sorted = false; while (!sorted) { sorted = true;
Odd–even_sort
Arrangement of chemical sensors
A chemical sensor array is a sensor architecture with multiple sensor components that create a pattern for analyte detection from the additive responses
Chemical_sensor_array
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