# Search algorithm

In computer science, a search algorithm, broadly speaking, is an algorithm that takes a problem as input and returns a solution to the problem, usually after evaluating a number of possible solutions. Most of the algorithms studied by computer scientists that solve problems are kinds of search algorithms. The set of all possible solutions to a problem is called the search space. Brute-force search or "naïve"/uninformed search algorithms use the simplest, most intuitive method of searching through the search space, whereas informed search algorithms use heuristics to apply knowledge about the structure of the search space to try to reduce the amount of time spent searching.

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## Uninformed search

An uninformed search algorithm is one that does not take into account the specific nature of the problem. As such, they can be implemented in general, and then the same implementation can be used in a wide range of problems thanks to abstraction. The drawback is that most search spaces are extremely large, and an uninformed search (especially of a tree) will only take a reasonable amount of time for small examples. As such, to speed up the process, sometimes only an informed search will do.

### List search

List search algorithms are perhaps the most basic kind of search algorithm. The goal is to find one element of a set by some key (perhaps containing other information related to the key). As this is a common problem in computer science, the computational complexity of these algorithms has been well studied. The simplest such algorithm is linear search, which simply examines each element of the list in order. It has expensive O(n) running time, where n is the number of items in the list, but can be used directly on any unprocessed list. A more sophisticated list search algorithm is binary search; it runs in O(log n) time. This is significantly better than linear search for large lists of data, but it requires that the list be sorted before searching (see sort algorithm) and also be random access. Interpolation search is better than binary search for very large sorted lists with fairly even distributions. Grover's algorithm is a quantum algorithm that offers quadratic speedup over the classical linear search for unsorted lists.

Hash tables are also used for list search, requiring only constant time for search in the average case, but more space overhead and terrible O(n) worst-case search time. Another search based on specialized data structures uses self-balancing binary search trees and requires O(log n) time to search; these can be seen as extending the main ideas of binary search to allow fast insertion and removal. See associative array for more discussion of list search data structures.

Most list search algorithms, such as linear search, binary search, and self-balancing binary search trees, can be extended with little additional cost to find all values less than or greater than a given key, an operation called range search. The glaring exception is hash tables, which cannot perform such a search efficiently.

### Tree search

Tree search algorithms are the heart of searching techniques. These search nodes of trees, whether that tree is explicit or implicit (generated on the go). The basic principle is that a node is taken from a data structure, its successors examined and added to the data structure. By manipulating the data structure, the tree is explored in different orders for instance level by level (Breadth-first search) or reaching a leaf node first and backtracking (Depth-first search). Other examples of tree-searches include Iterative-deepening search, Depth-limited search, Bidirectional search and Uniform-cost search.

### Graph search

Many of the problems in graph theory can be solved using search algorithms, such as Dijkstra's algorithm, Kruskal's algorithm, the nearest neighbour algorithm, and Prim's algorithm. These can be seen as extensions of the tree-search algorithms.

## Informed search

In an informed search, a heuristic that is specific to the problem is used as a guide. A good heuristic will make an informed search dramatically out-perform any uninformed search.

There are few prominent informed list-search algorithms. A possible member of that category is a hash table with a hashing function that is a heuristic based on the problem at hand. Most informed search algorithms explore trees. These include Best-first search, and A*. Like the uninformed algorithms, they can be extended to work for graphs as well.

## Adversarial search

In games such as chess, there is a game tree of all possible moves by both players and the resulting board configurations, and we can search this tree to find an effective playing strategy. This type of problem has the unique characteristic that we must account for any possible move our opponent might make. To account for this, game-playing computer programs, as well as other forms of artificial intelligence like machine planning, often use search algorithms like the minimax algorithm, search tree pruning, and alpha-beta pruning.

## Constraint satisfaction

This is a type of search which solves constraint satisfaction problems where, rather than looking for a path, the solution is simply a set of values assigned to a set of variables. Because the variables can be processed in any order, the usual tree search algorithms are too inefficient. Methods of solving constraint problems include combinatorial search and backtracking, both of which take advantage of the freedom associated with constraint problems.

## Related articles

• No-Free-Lunch theorems relate the generality of search algorithms to the need for domain knowledge.
• Secretary problem is an online (ie sequentially presented) search problem with imperfect information, and a statistically optimal strategy.
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