Searching Algorithms Questions Medium
The time complexity of searching in a binary indexed tree (also known as a Fenwick tree) is O(log n), where n is the number of elements in the tree.
Binary indexed tree is a data structure that allows efficient querying and updating of prefix sums of an array. It achieves this by representing the array as a binary tree, where each node stores the sum of a range of elements. The tree is constructed in a way that allows for efficient updates and queries.
When searching in a binary indexed tree, we start from the root node and traverse down the tree based on the binary representation of the index we are searching for. At each level, we either move to the left or right child node, depending on whether the corresponding bit in the binary representation is 0 or 1.
Since the height of a binary indexed tree is log n, where n is the number of elements, the time complexity of searching is O(log n). This is because we need to traverse down the tree from the root to the leaf node, which takes at most log n steps.
Therefore, the time complexity of searching in a binary indexed tree is O(log n).