What is the time complexity of searching for an element in a binary search tree
Practice Questions
Q1
What is the time complexity of searching for an element in a binary search tree (BST) in the worst case?
O(log n)
O(n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of searching for an element in a binary search tree (BST) in the worst case?
Step 1: Understand what a binary search tree (BST) is. A BST is a data structure where each node has a value, and the left child has a smaller value while the right child has a larger value.
Step 2: Know that searching for an element in a BST involves comparing the target value with the values of the nodes, starting from the root.
Step 3: In a balanced BST, the height is log(n), where n is the number of nodes. This means searching takes O(log n) time.
Step 4: In the worst case, the BST can become unbalanced, where all nodes are in a straight line (like a linked list). This happens when each node only has one child.
Step 5: In this unbalanced case, the height of the tree becomes n (the number of nodes), making the search time O(n).
Step 6: Therefore, the worst-case time complexity for searching in a binary search tree is O(n).
