Given a tree with N nodes, and two integers K and V. The task is to find the Kth node in the DFS traversal of the vertex V.
Consider the below Tree:
DFS of node number 1 is [1, 2, 3, 5, 6, 8, 7, 9, 4].
DFS of node number 3 is [3, 5, 6, 8, 7, 9]
DFS of node number 7 is [7, 9]
DFS of node number 9 is .
Print “-1” if the numbers in the DFS of vertex V are less than K.
Input : Tree: Shown in above image, V = 3, K = 4 Output : 8 Input : Tree: Shown in above image, V = 7, K = 3 Output : -1
Approach : Let’s construct a vector : to store the DFS traversal of the complete tree from vertex 1. Let tinv be the position of the vertex V in the vector p (the size of the vector p in moment we call DFS from the vertex V) and toutv be the position of the first vertex pushed to the vector after leaving the subtree of vertex V (the size of the vector p in moment when we return from DFS from the vertex V). Then it is obvious that the subtree of the vertex V lies in the interval [tinv, toutv).
So, to find the Kth node in the DFS of the subtree of node V, we will have to return the Kth node in the interval [tinv, toutv).
Below is the implementation of the above approach:
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- Find n-th node in Preorder traversal of a Binary Tree
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- Find Leftmost and Rightmost node of BST from its given preorder traversal
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Improved By : mohit kumar 29