Searching Algorithms Questions Medium
The time complexity of searching in a segment tree is O(log n), where n is the number of elements in the input array.
Segment tree is a data structure that is used to efficiently answer range queries on an array. It divides the array into smaller segments and stores the precomputed information about each segment in a tree-like structure. This allows for efficient querying of ranges in the array.
During a search operation in a segment tree, we start from the root of the tree and recursively traverse down the tree based on the range we are interested in. At each level of the tree, we compare the range of the current node with the target range we are searching for. If the ranges do not overlap, we can skip that subtree and move to the next level. If the ranges overlap partially or completely, we continue traversing down the tree to find the relevant segments.
Since the height of a balanced binary tree is log n, where n is the number of elements in the input array, the time complexity of searching in a segment tree is O(log n). This is because at each level of the tree, we only need to visit a constant number of nodes (2 in the case of a binary tree) to determine the relevant segments for the given range. Therefore, the search operation in a segment tree has a logarithmic time complexity.