What is the time complexity of searching for a value in a balanced binary search
Practice Questions
Q1
What is the time complexity of searching for a value 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 a value in a balanced binary search tree?
Step 1: Understand what a balanced binary search tree is. It is a type of data structure that keeps its elements in a sorted order and ensures that the tree remains balanced, meaning the height of the tree is kept as low as possible.
Step 2: Know that in a binary search tree, each node has at most two children. The left child contains values less than the parent node, and the right child contains values greater than the parent node.
Step 3: When searching for a value, you start at the root of the tree and compare the value you are looking for with the value of the current node.
Step 4: If the 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: Each time you move to a child node, you effectively reduce the number of nodes you need to search through by about half, because you are eliminating one side of the tree.
Step 6: The height of a balanced binary search tree is log(n), where n is the number of nodes in the tree. This is because a balanced tree grows logarithmically as you add more nodes.
Step 7: Since you may need to traverse from the root to a leaf node in the worst case, the time complexity for searching for a value in a balanced binary search tree is O(log n).
