What is the time complexity of a depth-first search (DFS) on a tree?
Practice Questions
Q1
What is the time complexity of a depth-first search (DFS) on a tree?
O(V)
O(E)
O(V + E)
O(n log n)
Questions & Step-by-Step Solutions
What is the time complexity of a depth-first search (DFS) on a tree?
Step 1: Understand what a tree is. A tree is a data structure that consists of nodes connected by edges, with one node as the root and no cycles.
Step 2: Know what depth-first search (DFS) is. DFS is a method for exploring all the nodes in a tree by going as deep as possible down one branch before backtracking.
Step 3: Realize that during DFS, each node (or vertex) in the tree is visited exactly once.
Step 4: Count the number of nodes in a tree. This is represented as V (for vertices).
Step 5: Since each node is visited once, the time taken to visit all nodes is proportional to the number of nodes, which is V.
Step 6: Conclude that the time complexity of DFS on a tree is O(V), where V is the number of vertices (nodes) in the tree.
