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51 lines
2.1 KiB
Markdown
51 lines
2.1 KiB
Markdown
# Segment Tree
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In computer science, a **segment tree** also known as a statistic tree
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is a tree data structure used for storing information about intervals,
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or segments. It allows querying which of the stored segments contain
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a given point. It is, in principle, a static structure; that is,
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it's a structure that cannot be modified once it's built. A similar
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data structure is the interval tree.
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A segment tree is a binary tree. The root of the tree represents the
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whole array. The two children of the root represent the
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first and second halves of the array. Similarly, the
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children of each node corresponds to the two halves of
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the array corresponding to the node.
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We build the tree bottom up, with the value of each node
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being the "minimum" (or any other function) of its children's values. This will
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take `O(n log n)` time. The number
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of operations done is the height of the tree, which
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is `O(log n)`. To do range queries, each node splits the
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query into two parts, one sub-query for each child.
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If a query contains the whole subarray of a node, we
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can use the precomputed value at the node. Using this
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optimisation, we can prove that only `O(log n)` minimum
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operations are done.
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## Application
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A segment tree is a data structure designed to perform
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certain array operations efficiently - especially those
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involving range queries.
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Applications of the segment tree are in the areas of computational geometry,
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and geographic information systems.
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Current implementation of Segment Tree implies that you may
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pass any binary (with two input params) function to it and
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thus you're able to do range query for variety of functions.
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In tests you may find examples of doing `min`, `max` and `sam` range
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queries on SegmentTree.
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## References
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- [Wikipedia](https://en.wikipedia.org/wiki/Segment_tree)
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- [YouTube](https://www.youtube.com/watch?v=ZBHKZF5w4YU&index=65&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
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- [GeeksForGeeks](https://www.geeksforgeeks.org/segment-tree-set-1-sum-of-given-range/)
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