What is the space complexity of a recursive binary tree traversal?
Practice Questions
Q1
What is the space complexity of a recursive binary tree traversal?
O(1)
O(n)
O(log n)
O(n^2)
Questions & Step-by-Step Solutions
What is the space complexity of a recursive binary tree traversal?
Step 1: Understand what a binary tree is. A binary tree is a data structure where each node has at most two children, referred to as the left child and the right child.
Step 2: Know what a recursive traversal means. A recursive traversal is a method of visiting each node in the tree using a function that calls itself.
Step 3: Identify the types of recursive traversals. Common types include in-order, pre-order, and post-order traversals.
Step 4: Recognize that each time a function calls itself, it adds a new layer to the call stack. The call stack is a structure that keeps track of function calls.
Step 5: Determine how deep the recursion can go. In the worst case, if the tree is unbalanced (like a linked list), the depth can be equal to the number of nodes, n.
Step 6: Conclude that the maximum depth of the call stack during the traversal is O(n) in the worst case, which means the space used by the call stack is O(n).
Step 7: Therefore, the space complexity of a recursive binary tree traversal is O(n) due to the call stack.
