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:
# Python3 program to find the Kth node in the
# DFS traversal of the subtree of given
# vertex V in a Tree
N = 100005
n = 10
tree = [for i in range(N)]
# To store the current index of vertex in DFS
currentIdx = 0
# To store the starting index and ending
# index of vertex in the DFS traversal array
startIdx = [0 for i in range(n)]
endIdx = [0 for i in range(n)]
# To store the DFS of vertex 1
p = [0 for i in range(n)]
# Function to add edge between two nodes
def Add_edge(u, v):
# Initialize the vectors
# Function to perform DFS of a vertex
# 1. stores the DFS of the vertex 1 in vector p,
# 2. store the start index of DFS of every vertex
# 3. store the end index of DFS of every vertex
def Dfs(ch, par):
p[currentIdx] = ch
# store staring index of node ch
startIdx[ch] = currentIdx
currentIdx += 1
for c in tree[ch]:
if (c != par):
# store ending index
endIdx[ch] = currentIdx – 1
# Function to find the Kth node in
# DFS of vertex V
def findNode(v, k):
k += startIdx[v] – 1
# check if kth number exits or not
if (k <= endIdx[v]): return p[k] return -1 # Driver code # number of nodes n = 9 # add edges Add_edge(1, 2) Add_edge(1, 3) Add_edge(1, 4) Add_edge(3, 5) Add_edge(3, 7) Add_edge(5, 6) Add_edge(5, 8) Add_edge(7, 9) intisalise() # store DFS of 1st node Dfs(1, 0) v, k = 3, 4 print(findNode(v, k)) # This code is contributed by mohit kumar [tabbyending]
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Improved By : mohit kumar 29