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When many values have to be searched in the same list, it often pays to pre-process the list in order to use a faster method. For example, one may sort the list and use binary search, or build an efficient search data structure from it. Should the content of the list change frequently, repeated re-organization may be more trouble than it is worth.
For example, the key may be a geographic position (latitude and longitude) on the Earth. In that case, common kinds of queries are "find the record with a key closest to a given point v ", or "find all items whose key lies at a given distance from v ", or "find all items within a specified region R of the space".
In quicksort, we recursively sort both branches, leading to best-case () time. However, when doing selection, we already know which partition our desired element lies in, since the pivot is in its final sorted position, with all those preceding it in an unsorted order and all those following it in an unsorted order.
Linear search: locates an item in an unsorted sequence; Selection algorithm: finds the kth largest item in a sequence; Ternary search: a technique for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa; Sorted lists. Binary search algorithm: locates an item in a sorted sequence
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
When they are sorted with a non-stable sort, the 5s may end up in the opposite order in the sorted output. Stable sort algorithms sort equal elements in the same order that they appear in the input. For example, in the card sorting example to the right, the cards are being sorted by their rank, and their suit is being ignored.
If the search set decreases exponentially quickly in size (by a fixed proportion), this yields a geometric series times the () factor of a single step, and thus linear overall time. However, if the search set decreases slowly in size, such as linearly (by a fixed number of elements, in the worst case only reducing by one element each time ...
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.