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 contiguous 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 + height of subtree which has been stored in under[node].
Below is the implementation of the above approach.
The DFS of subtree 2: 2 4 6 7 5 The DFS of subtree 4: 4 6 7
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 the worst case.
Auxiliary Space: O(N)
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