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• Dynamic programming
  '''Dynamic programming''' (DP) is a technique for solving problems that involves compu ===Example: dynamic solution to Plentiful Paths===
  34 KB (6,107 words) - 14:38, 9 February 2016
• Floyd–Warshall algorithm
  ...test-paths matrix. If the distance from each vertex to itself is initially set as infinite, this matrix will also tell us the length of the shortest path Floyd–Warshall is one of the most well-known examples of a [[dynamic programming]] algorithm. It consists of a single looping structure containi
  7 KB (1,319 words) - 12:16, 25 April 2022
• Heavy-light decomposition
  ...st</code> variable holds. (If both final links to the LCA are light, it is set to the root of the tree, which is otherwise impossible, to indicate this.) ===Dynamic distance query===
  9 KB (1,665 words) - 12:40, 6 August 2015
• Segment tree
  ...rsive calls made on behalf of a non-leaf node return, that node's value is set to the minimum of the values stored at the children. Bottom-up construction Consider the set of selected nodes (marked in yellow in the illustration). It is possible, i
  21 KB (3,669 words) - 02:34, 6 April 2016
• Convex hull trick
  ...used to determine ''efficiently'', after preprocessing, which member of a set of linear functions in one variable attains an extremal value for a given v <p>Suppose that a large set of linear functions in the form <math>y = m_i x + b_i</math> is given along
  19 KB (3,419 words) - 02:24, 13 September 2023
• Big numbers
  ===Fixed-width versus dynamic-width bignums=== ...ssing digits as zeroes, but in any case it requires extra code. When using dynamic bignums the difference between the little-endian and big-endian representat
  13 KB (2,098 words) - 20:22, 28 June 2011
• Optimization
  ...y has to check whether something belongs to this set, we can represent the set using a [[hash table]] and thus perform this check in constant time rather ...element in the set greater than the given element, we can use an [[ordered set]] based on a [[balanced binary search tree]] or [[skip list]], rather than
  7 KB (1,155 words) - 01:34, 5 January 2012
• Shortest path
  ...]. Given a directed graph <math>G = (V,E)</math>, possibly weighted, and a set of pairs of vertices <math>\{(u_1,v_1), ..., (u_n,v_n)\}, u_i, v_i \in V</m ...t path'' problem, there is only one pair <math>(u,v)</math> in the problem set. In other words the shortest path is desired between a single pair of verti
  18 KB (3,150 words) - 07:09, 26 May 2011
• Longest common subsequence
  ...th> is achieved, then the problem may be solved in polynomial time using [[dynamic programming]]. ...want to show that this problem has the optimal substructure required for a dynamic solution. To do this, we first notice that our optimal solution either uses
  17 KB (2,927 words) - 05:07, 31 May 2011
• Longest increasing subsequence
  ...(finite) input sequence whose elements are taken from a partially ordered set. For example, consider the sequence [9,2,6,3,1,5,0,7]. An increasing subseq ==Dynamic programming solution==
  14 KB (2,315 words) - 11:10, 10 June 2018
• Disjoint sets
  ...find operations in succession on two elements that are located in the same set, then the same value is returned, whereas different values are returned if ...esentative of one of the two sets as the representative of the new, united set, or we pick a new element altogether to be the representative.
  13 KB (2,270 words) - 01:29, 11 December 2011
• Array
  ...paragraph), but may be any kind of object taken from a finite well-ordered set. (For example, the Pascal programming language allows the use of characters Now, suppose this array is indexed by members of some finite well-ordered set <math>I</math>. Define a bijection <math>f</math> between <math>I</math> an
  17 KB (2,904 words) - 03:08, 17 April 2012
• Graph theory
  ...ponents, all graphs have at least a set of vertices, <math>V</math>, and a set of edges, <math>E</math>. Each edge is a pair of vertices, say, <math>u</ma ...graph with loops will have to be considered a multiset instead of a plain set, as it contains two of the same vertex.
  25 KB (4,451 words) - 23:15, 19 October 2020
• Tree
  ...unction of the data stored in its children. Segment trees enable efficient dynamic computation of associative functions on segments of the array. ...BIT) or ''Fenwick tree'': Similar to a segment tree, but enables efficient dynamic computation of associative functions only on ''prefixes'' of the array. Nev
  17 KB (2,906 words) - 03:22, 12 December 2011
• Directed acyclic graph
  ..., '''B''', '''C''', ''etc''.). Each label corresponds to an element in our set. ...n <math>O(E+V)</math> time by topologically sorting first and then using [[dynamic programming]].
  6 KB (993 words) - 05:36, 18 March 2011
• Longest common substring
  ==Dynamic programming solution== [[Dynamic programming]] admits a solution with time and space polynomial in the lengt
  7 KB (1,242 words) - 04:49, 29 May 2011
• Algorithm
  ...e gene contains 3&times;10⁴ base pairs. Suppose that we wish to set up a web server that will allow biologists to search for genes in the human ...t with [[memoization]] or by converting them into '''[[Dynamic programming|dynamic algorithms]]''', such as the classic [[longest increasing subsequence]] alg
  10 KB (1,628 words) - 18:12, 28 June 2011
• Greedy algorithm
  ...ally the method of choice, because of its efficiency. Contrast this with [[dynamic programming]], which accounts for all possible choices at each step, whethe ...tem of currency is amenable to the greedy solution method. However, if the set of coins had values of 2, 3, and 4 cents, then the greedy algorithm would f
  3 KB (549 words) - 00:32, 14 January 2012
• Sliding range minimum query
  ...the [[balanced binary search tree]] that is probably used to implement the set.
  5 KB (938 words) - 21:33, 4 April 2021
• Range minimum query
  ...a contiguous subsequence of a list of items taken from a [[totally ordered set]] (usually numbers). This is one of the most extensively-studied problems i A single range minimum query is a set of indices <math>i < j</math> into an array <math>A</math>; the answer to t
  14 KB (2,606 words) - 16:46, 24 April 2014