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A segment tree, also known as a interval tree, is a data structure that is used to efficiently answer range queries on an array or a list. It is particularly useful when there is a need to perform operations such as finding the sum, minimum, maximum, or any other associative operation over a specific range of elements in the array.
The segment tree is built by recursively dividing the array into smaller segments or intervals. Each node in the tree represents an interval and stores the result of the operation performed on that interval. The root node represents the entire array, and its children represent the two halves of the array. The process continues until each leaf node represents a single element of the array.
To build the segment tree, the array is divided into two halves, and the left and right children of the current node are recursively built using the corresponding halves. The operation performed on each node is determined by the specific range query requirement. For example, if the operation is to find the sum of elements in a range, each node would store the sum of its left and right children.
Once the segment tree is built, range queries can be efficiently answered by traversing the tree. When a query is made for a specific range, the tree is traversed recursively, and the results from the relevant intervals are combined to provide the final result.
The segment tree has a time complexity of O(log n) for both construction and query operations, where n is the number of elements in the array. This makes it a powerful data structure for solving problems that involve range queries efficiently.