What is the time complexity of searching for an element in a balanced binary sea
Practice Questions
Q1
What is the time complexity of searching for an element in a balanced binary search tree?
O(n)
O(log n)
O(n log n)
O(1)
Questions & Step-by-Step Solutions
What is the time complexity of searching for an element in a balanced binary search tree?
Step 1: Understand what a balanced binary search tree is. It is a tree structure where each node has at most two children, and the tree is balanced, meaning the height is kept low.
Step 2: Know that in a binary search tree, for any given node, all values in the left subtree are less than the node's value, and all values in the right subtree are greater.
Step 3: When searching for an element, you start at the root of the tree and compare the target value with the value of the current node.
Step 4: If the target value is less than the current node's value, you move to the left child; if it is greater, you move to the right child.
Step 5: Repeat this process until you find the target value or reach a leaf node (a node with no children).
Step 6: In a balanced binary search tree, the height of the tree is approximately log base 2 of the number of nodes (n), which means you will make at most log n comparisons to find the element.
Step 7: Therefore, the time complexity for searching for an element in a balanced binary search tree is O(log n).
