Given a tree of N nodes and N-1 edges. The task is to print the DFS of the subtree of a given node for multiple queries. The DFS must include the given node as the root of the subtree.
In the above tree, if 1 is given as the node, then the DFS of subtree will be 1 2 4 6 7 5 3.
If 2 is given as the node, then the DFS of the subtree will be 2 4 6 7 5..
- Add the edges between the nodes in an adjacency list.
- Call DFS function to generate the DFS of the complete tree.
- Use a under array to store the height of the subtree under the given node including the node.
- In the DFS function, keep incrementing the size of subtree on every recursive call.
- Mark the node index in the DFS of complete using hashing.
- The DFS of a subtree of a node will always be a contigous subarray starting from the node(say index ind) to (ind+height of subtree).
- Get the index of node which has been stored using hashing and print the nodes from original DFS till index = ind + heigth of subtree which has been stored in under[node].
Below is the implementation of the above approach.
Time Complexity: O( N + M ), where N is the number of nodes and M is the number of edges for pre-calculation and O(N) for queries in worst case.
Auxiliary Space: O(N)
- Queries for M-th node in the DFS of subtree
- Subtree of all nodes in a tree using DFS
- Subtree with given sum in a Binary Tree
- Find largest subtree sum in a tree
- Euler Tour | Subtree Sum using Segment Tree
- Find the largest BST subtree in a given Binary Tree | Set 1
- Number of leaf nodes in the subtree of every node of an n-ary tree
- Convert a Binary Tree such that every node stores the sum of all nodes in its right subtree
- Change a Binary Tree so that every node stores sum of all nodes in left subtree
- Check if a binary tree is subtree of another binary tree | Set 2
- Check if a binary tree is subtree of another binary tree | Set 1
- Perform the given queries on the rooted tree
- Queries to find distance between two nodes of a Binary tree
- Binary Indexed Tree : Range Updates and Point Queries
- Queries to find distance between two nodes of a Binary tree - O(logn) method