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Computer memory needed by an algorithm
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a
Space_complexity
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Notion in combinatorial game theory
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position)
Game_complexity
Set of problems in computational complexity theory
particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory)
Complexity_class
Feature of systems that defy description
Kolmogorov complexity are studied: the uniform complexity, prefix complexity, monotone complexity, time-bounded Kolmogorov complexity, and space-bounded
Complexity
Amount of resources to perform an algorithm
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus
Computational_complexity
Algorithm to search the nodes of a graph
determine which vertices have already been added to the queue, the space complexity can be expressed as O ( | V | ) {\displaystyle O(|V|)} , where | V
Breadth-first_search
Algorithm used for pathfinding and graph traversal
major practical drawback is its O ( b d ) {\displaystyle O(b^{d})} space complexity where d is the depth of the shallowest solution (the length of the
A*_search_algorithm
Type of computer science algorithm
that space complexity also has varied choices in whether or not to count the index lengths as part of the space used. Often, the space complexity is given
In-place_algorithm
Tree searching strategy
This means that the time complexity of iterative deepening is still O ( b d ) {\displaystyle O(b^{d})} . The space complexity of IDDFS is O ( d ) {\displaystyle
Iterative deepening depth-first search
Iterative_deepening_depth-first_search
Measurement of computational complexity
With respect to computational resources, asymptotic time complexity and asymptotic space complexity of computational algorithms and programs are commonly
Asymptotic computational complexity
Asymptotic_computational_complexity
1977 scholarly article by Donald Knuth
("space complexity" of the song) or even less. Knuth writes that "our ancient ancestors invented the concept of refrain" to reduce the space complexity
The_Complexity_of_Songs
Divide and conquer sorting algorithm
i\right)=O(n\log n).} The space used by quicksort depends on the version used. The in-place version of quicksort has a space complexity of O(log n), even in
Quicksort
Data structure for storing non-overlapping sets
Bernard A. Galler and Michael J. Fischer in 1964. In 1973, their time complexity was bounded to O ( log ∗ ( n ) ) {\displaystyle O(\log ^{*}(n))} , the
Disjoint-set_data_structure
Set of all possible values of a system
the goal states. A state space has some common properties: complexity, where branching factor is important structure of the space, see also graph theory:
State space (computer science)
State_space_(computer_science)
Measure of the structural complexity of a software program
Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent
Cyclomatic_complexity
Search tree data structure
for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may
Trie
Subroutine call performed as final action of a procedure
pure tail call is defined primarily by its space complexity: a pure tail call occurs when the stack space is strictly bounded during recursion. By guaranteeing
Tail_call
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Search algorithm finding the position of a target value within a sorted array
memory locations, regardless of the size of the array. Therefore, the space complexity of binary search is O ( 1 ) {\displaystyle O(1)} in the word RAM model
Binary_search
Algorithm to search the nodes of a graph
all) but the space complexity of this variant of DFS is only proportional to the depth limit, and as a result, is much smaller than the space needed for
Depth-first_search
On linear-time algorithms for graph logic
time complexity of an algorithm that recognizes an MSO property on bounded-treewidth graphs, it is also possible to analyze the space complexity of such
Courcelle's_theorem
Algorithm for visible surface determination in 3D graphics
number of pixels to be filled. The painter's algorithm's worst-case space-complexity is O(n+m), where n is the number of polygons and m is the number of
Painter's_algorithm
Geometric space with four dimensions
complicated shapes that the full richness and geometric complexity of 4D spaces emerge. A hint of that complexity can be seen in the accompanying 2D animation of
Four-dimensional_space
Method for finding loopless paths
improve the performance of the algorithm, but not the complexity. One method to slightly decrease complexity is to skip the nodes where there are non-existent
Yen's_algorithm
Data structures used in spatial indexing
variant of the R-tree is worst-case optimal, but due to its increased complexity it has remained confined to theoretical study and has not received much
R-tree
Probabilistic data structure
{O}}(\log n)} average complexity for search as well as O ( log n ) {\displaystyle {\mathcal {O}}(\log n)} average complexity for insertion within an
Skip_list
Parsing technique
the number and contents of each stack, thereby reducing the time and space complexity of the parser. This leads to an algorithm known as Generalized LL parsing
Top-down_parsing
Topics referred to by the same term
the time/space complexity of a particular problem in terms of all algorithms that solve it with computational resources (i.e., time or space) bounded
Algorithmic_complexity
Associative array for storing key–value pairs
probing sequence. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the
Hash_table
Data structure
the key, the system concludes that the key doesn't exist. Point lookup complexity is O ( L ) {\displaystyle O(L)} without Bloom filters, as each level must
Log-structured_merge-tree
Solution of the traveling salesman problem
{\displaystyle S} , raising space requirements by only a constant factor. The Held–Karp algorithm has exponential time complexity Θ ( 2 n n 2 ) {\displaystyle
Held–Karp_algorithm
Measures of how efficiently algorithms use resources
when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)). Heapsort has O(n) time when all elements
Best,_worst_and_average_case
On finding a repeating loop in a sequence
not be specified as a table of values. Such a table implies O(|S|) space complexity, and if that is permissible, building a predecessor array (associative
Cycle_detection
Self-balancing binary search tree data structure
hashcodes, a red–black tree is used. This results in the improvement of time complexity of searching such an element from O ( m ) {\displaystyle O(m)} to O (
Red–black_tree
Algorithm trading more space for lower time
where the time complexity of a problem can be reduced significantly by using more memory. Time/memory/data tradeoff attack which uses the space–time tradeoff
Space–time_tradeoff
Class of computational complexity
computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space. If we
PSPACE
Multidimensional search tree for points in k dimensional space
(short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional is that which concerns
K-d_tree
Data structure
is n k m a x = b h − 1 {\displaystyle n_{\mathrm {kmax} }=b^{h}-1} The space required to store the tree is O ( n ) {\displaystyle O(n)} Inserting a record
B+_tree
Divide and conquer sorting algorithm
since the space complexity for quicksort is O(log n), it helps in utilizing cache locality better than merge sort (with space complexity O(n)). On the
Merge_sort
Data structure used for indexing spatial information
{\displaystyle M} objects and has little impact on the total complexity. The total insert complexity is still comparable to the R-tree: reinsertions affect
R*-tree
Data structure in computer science
children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional
Octree
Complexity class (logarithmic space)
In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved
L_(complexity)
Tree-based computer data structure
some spaces. Instead of densely packing all the records in a block, the block can have some free space to allow for subsequent insertions. Those spaces would
B-tree
Rooted binary tree data structure
node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is linear with respect to the
Binary_search_tree
Study of resources used by an algorithm
the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient
Analysis_of_algorithms
String searching algorithm
O(km)} space, assuming a finite alphabet of length k. The C and Java implementations below have a O ( k ) {\displaystyle O(k)} space complexity (make_delta1
Boyer–Moore string-search algorithm
Boyer–Moore_string-search_algorithm
Indian computer scientist
includes publications in proof complexity, algebraic circuit complexity, small-space complexity classes, parameterized complexity, and algorithms for planar
Meena_Mahajan
Variant of heap data structure
worst-case time complexity of O(log n). For a random heap, and for repeated insertions, the insertion operation has an average-case complexity of O(1). The
Binary_heap
Software for sequence alignment
“MUSCLE: a multiple sequence alignment method with reduced time and space complexity” has been cited over 9,936 times. In late 2021, Edgar released Muscle5
MUSCLE_(alignment_software)
Algorithm for finding important nodes in a graph
algorithm improves on the space complexity of naive algorithms, which typically require O ( | V | 2 ) {\displaystyle O(|V|^{2})} space. Brandes' algorithm only
Brandes'_algorithm
Tree data structure that partitions a 2D area
analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated
Quadtree
Property of an algorithm
minimize resource usage. However, different resources such as time and space complexity cannot be compared directly, so which of two algorithms is considered
Algorithmic_efficiency
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(complexity)
Field in logic and theoretical computer science
complexity theory, efficiency can be measured by how many steps are required (time complexity), how much working space is required (space complexity)
Proof_complexity
Algorithmic complexity class
machine in polynomial space. EXPTIME relates to the other basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME
EXPTIME
Method of analyzing the amortized complexity of a data structure
In computational complexity theory, the potential method is a method used to analyze the amortized time and space complexity of a data structure, a measure
Potential_method
Finding an optimal algorithm for playing chess
solved at least weakly. Calculated estimates of game-tree complexity and state-space complexity of chess exist which provide a bird's eye view of the computational
Solving_chess
Data structure for processing palindromes
single string can be done with O ( n ∗ i ) {\displaystyle O(n*i)} additional space where i {\displaystyle i} is the number of strings being compared. This
Palindrome_tree
Maximal subgraph whose vertices can reach each other
change. In computational complexity theory, connected components have been used to study algorithms with limited space complexity, and sublinear time algorithms
Component_(graph_theory)
Algorithm for the kth smallest element in an array
the side with the element it is searching for. This reduces the average complexity from O ( n log n ) {\displaystyle O(n\log n)} to O ( n ) {\displaystyle
Quickselect
Relation between deterministic and nondeterministic space complexity
computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity
Savitch's_theorem
Both deterministic and nondeterministic machines can solve more problems given more space
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines
Space_hierarchy_theorem
Board game from Madagascar
game-tree complexity and state-space complexity can be computed. Fanorona has a game-tree complexity of ~1046 and a state-space complexity of ~1021. In
Fanorona
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
Logarithmic-space (RL), sometimes called RLP (Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems
RL_(complexity)
Array data structure
look up elements quickly, e.g. as a set or multiset data structure. This complexity for lookups is the same as for self-balancing binary search trees. In
Sorted_array
Data structure for priority queue operations
array-based heaps. Here are time complexities of various heap data structures. The abbreviation am. indicates that the given complexity is amortized, otherwise
Fibonacci_heap
Method for aligning biological sequences
Since the algorithm fills an n × m {\displaystyle n\times m} table the space complexity is O ( m n ) . {\displaystyle O(mn).} The original purpose of the algorithm
Needleman–Wunsch_algorithm
Sorting algorithm
efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each element in the input is no more than k places away
Insertion_sort
Non-comparative lexicographical sorting algorithm
optimal complexity O(log(n)) are those of the Three Hungarians and Richard Cole and Batcher's bitonic merge sort has an algorithmic complexity of O(log2(n))
Radix_sort
Sorting algorithm
{badsort}}(L,0)={\texttt {bubblesort}}(L)} . Therefore, badsort's time complexity is O ( n 2 ) {\displaystyle O(n^{2})} if k = 0 {\displaystyle k=0} . However
Bogosort
fact that L {\displaystyle L} will probably not exceed 6 reduces the space complexity to O ( R F ) {\displaystyle O(RF)} . The entire algorithm runs in O
Teknomo–Fernandez_algorithm
Algorithm for finding sub-text location(s) inside a given sentence in Big O(n) time
(only needed when all word occurrences are searched) The time (and space) complexity of the table algorithm is O ( k ) {\displaystyle O(k)} , where k {\displaystyle
Knuth–Morris–Pratt_algorithm
Abstract strategy board game
the state-space complexity of Connect(19,19,6,2,1) is 10172, about the same as that in Go or Gomoku. If a larger board is used, the complexity is much higher
Connect6
Time used by a computer
Algorithms are more commonly compared using measures of time complexity and space complexity. Typically, the CPU time used by a program is measured by the
CPU_time
Self-adjusting binary search tree
insertions and deletions, and the find operation, therefore, has linear time complexity. #include <functional> #ifndef SPLAY_TREE #define SPLAY_TREE template<typename
Splay_tree
Computer science metric of string similarity
time complexity of Θ(mn) where m and n are the lengths of the strings. When the full dynamic programming table is constructed, its space complexity is also
Edit_distance
Class of algorithms which use a moving line to solve geometrical problems
intersections among any N segments in the plane in time complexity of O((N + K) log N) and space complexity of O(N). Since then, this approach has been used
Sweep_line_algorithm
Hybrid sorting algorithm based on insertion sort and merge sort
Peter McIlroy's 1993 paper "Optimistic Sorting and Information Theoretic Complexity". Timsort was designed to take advantage of runs of consecutive ordered
Timsort
Ordered tree data structure
time O ( log d − 1 n + k ) {\displaystyle O(\log ^{d-1}n+k)} and space complexity O ( n ( log n log log n ) d − 1 ) {\displaystyle O\left(n\left({\frac
Range_tree
Random search tree data structure
for intersection is similar, but requires the join helper routine. The complexity of each of union, intersection and difference is O(m log n/m) for treaps
Treap
Memory space for a deterministic Turing machine
In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine
DSPACE
Tree data structure
metric space R requires O(|R|) space, during the construction and during the execution of the Find algorithm. Tables below show time complexity estimates
Compressed_cover_tree
Graph algorithm
it is on the stack, and performing this test by examining the flag. Space Complexity: The Tarjan procedure requires two words of supplementary data per
Tarjan's strongly connected components algorithm
Tarjan's_strongly_connected_components_algorithm
Sorting algorithm
can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space O(k). If each item
Counting_sort
Measure of algorithmic complexity
theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer
Kolmogorov_complexity
System composed of many interacting components
complexity in 1961, citing Dr. Weaver's 1948 essay. As an example, she explains how an abundance of factors interplay into how various urban spaces lead
Complex_system
Simple sorting algorithm using comparisons
who coined its current name. Bubble sort has a worst-case and average complexity of O ( n 2 ) {\displaystyle O(n^{2})} , where n {\displaystyle n} is the
Bubble_sort
Algorithm that arranges lists in order
of merge sort uses O(n) additional space, and simple implementation of quicksort has O(n2) worst-case complexity. These problems can be solved or ameliorated
Sorting_algorithm
Standard for the encryption of electronic data
paper in 2015 later improved the space complexity to 256 bits, which is 9007 terabytes (while still keeping a time complexity of approximately 2126). According
Advanced_Encryption_Standard
Sorting algorithm
sort is an in-place comparison sorting algorithm. It has a O(n2) time complexity, which makes it inefficient on large lists, and generally performs worse
Selection_sort
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete
Cook–Levin_theorem
Algorithm to parse a syntax with infix notation to postfix notation
the operator stack onto the output queue To analyze the running time complexity of this algorithm, one has only to note that each token will be read once
Shunting_yard_algorithm
Self-balancing binary search tree data structure
is a variant of the red–black tree and guarantees the same asymptotic complexity for operations, but is designed to be easier to implement. A left-leaning
Left-leaning_red–black_tree
Computer science award
1137/S0097539796307698 Alon, Noga; Matias, Yossi; Szegedy, Mario (1999), "The space complexity of approximating the frequency moments" (PDF), Journal of Computer
Gödel_Prize
Ancient algorithm for generating prime numbers
+1)^{2}>(k+1)\Delta } . If Δ is chosen to be √n, the space complexity of the algorithm is O(√n), while the time complexity is the same as that of the regular sieve
Sieve_of_Eratosthenes
Type of computational algorithm
computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually
Log-space_reduction
Algorithm for finding the shortest paths in graphs
found, and therefore there are no negative cycles. In that case, the complexity of the algorithm is reduced from O ( | V | ⋅ | E | ) {\displaystyle O(|V|\cdot
Bellman–Ford_algorithm
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
SPACE COMPLEXITY
SPACE COMPLEXITY
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Space; Sky
Boy/Male
Hindu
Space
Girl/Female
Indian, Japanese, Tamil
Space; Star
Male
English
English surname transferred to forename use, derived from the French personal name Pascal, PACE means "Passover; Easter."
Boy/Male
Tamil
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Space
Antrix | அஂதà¯à®°à¯€à®•à¯à®·
Surname or Lastname
English
English : from a vernacular short form of the Latin personal name Paschalis (see Pascal, Italian Pasquale).nickname for a mild-mannered and peaceable person, from Middle English pace, pece ‘peace’, ‘concord’, ‘amity’ (via Anglo-Norman French from Latin pax, genitive pacis).Italian : from the medieval personal name Pace, used for both men and women, from the word pace ‘peace’ (see 1).
Boy/Male
Tamil
Antariksh | அஂதரிகà¯à®·
Space
Antariksh | அஂதரிகà¯à®·
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Limitless Space
Boy/Male
Hindu, Indian
Space; Outer Space; Sky
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Boy/Male
Hindu
Space
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Boy/Male
Hindu, Indian
Space; Sky
Girl/Female
Hindu, Indian, Marathi
Space; Sky
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Space; Universe
Boy/Male
Hindu
Space
Surname or Lastname
English and Irish
English and Irish : variant of Stacey.
Boy/Male
Tamil
Antareeksh | அஂதரீகà¯à®·
Space
Antareeksh | அஂதரீகà¯à®·
Girl/Female
Indian, Telugu
Space
SPACE COMPLEXITY
SPACE COMPLEXITY
Male
English
Anglicized form of Hebrew Yehoshafat, JEHOSHAFAT means "God has judged" or "whom God judges."
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from Shorrock Green in Lancashire, probably so named from Old English scora ‘bank’ + Äc ‘oak’.
Boy/Male
Indian
Variant of aditya: the Sun
Boy/Male
Indian, Punjabi, Sikh
Highest Gem
Girl/Female
Danish, German, Hebrew, Swedish
God Sees
Boy/Male
Tamil
Permanent, Eternal God, Lord Shiva
Boy/Male
Tamil
Kharadhwamsine | கராதà¯à®µà®¾à®®à¯à®¸à¯€à®¨à¯‡
Slayer of demon khara
Girl/Female
Indian
An Angel
Boy/Male
American, British, English, French
Of the Mountain
Boy/Male
Indian
Slave of the merciful
SPACE COMPLEXITY
SPACE COMPLEXITY
SPACE COMPLEXITY
SPACE COMPLEXITY
SPACE COMPLEXITY
n.
The right of bowling again at a full set of pins, after having knocked all the pins down in less than three bowls. If all the pins are knocked down in one bowl it is a double spare; in two bowls, a single spare.
n.
Manner of stepping or moving; gait; walk; as, the walk, trot, canter, gallop, and amble are paces of the horse; a swaggering pace; a quick pace.
n.
To arrange or adjust the spaces in or between; as, to space words, lines, or letters.
n.
Space.
n.
The distance or interval between words or letters in the lines, or between lines, as in books.
v. t.
Being over and above what is necessary, or what must be used or reserved; not wanted, or not used; superfluous; as, I have no spare time.
v. t.
To season with spice, or as with spice; to mix aromatic or pungent substances with; to flavor; to season; as, to spice wine; to spice one's words with wit.
n.
A quantity or portion of extension; distance from one thing to another; an interval between any two or more objects; as, the space between two stars or two hills; the sound was heard for the space of a mile.
imp. & p. p.
of Space
n.
Figuratively, that which enriches or alters the quality of a thing in a small degree, as spice alters the taste of food; that which gives zest or pungency; a slight flavoring; a relish; hence, a small quantity or admixture; a sprinkling; as, a spice of mischief.
n.
A small piece of metal cast lower than a face type, so as not to receive the ink in printing, -- used to separate words or letters.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
n.
One of that suit of cards each of which bears one or more figures resembling a spade.
adv.
With a quick pace; quick; fast; speedily.
v. t.
To dig with a spade; to pare off the sward of, as land, with a spade.
n.
One of the intervals, or open places, between the lines of the staff.
v. t.
To measure by steps or paces; as, to pace a piece of ground.
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
n.
To walk; to rove; to roam.
v. t.
To develop, guide, or control the pace or paces of; to teach the pace; to break in.