Searching Algorithms Questions Medium
The time complexity of searching in a van Emde Boas (vEB) tree is O(log log M), where M is the maximum number that can be stored in the tree.
The vEB tree is a data structure that provides efficient searching, insertion, and deletion operations. It is particularly useful when dealing with a large range of keys. The tree is recursively defined, with each node representing a cluster of elements.
During a search operation, the vEB tree follows a top-down approach. It starts by checking if the desired element is present in the summary structure, which is a smaller vEB tree representing the presence or absence of elements in the clusters. If the element is not found in the summary, the search continues in the appropriate cluster.
The time complexity of searching in a vEB tree is determined by the height of the tree, which is proportional to log M. At each level of the tree, the search operation takes O(1) time to check the summary structure and O(log log M) time to search within the cluster. Therefore, the overall time complexity of searching in a vEB tree is O(log log M).