# Find parent of given node in a Binary Tree with given postorder traversal

Given two integers N and K where N denotes the height of a binary tree, the task is to find the parent of the node with value K in a binary tree whose postorder traversal is first natural numbers For N = 3, the Tree will be -

7
/   \
3     6
/   \  /  \
1     2 4   5



Examples:

Input: N = 4, K = 5
Output:
Explanation:
Parent of the node 5 is 6. As shown in the tree above.
Input: N = 5, K = 3
Output:
Explanation:
Parent of the node 3 is 7. As shown in the tree above.

Naive Approach: A simple approach is to build the tree according to the following pattern and then traverse the whole tree to find the parent of a given node.
Efficient Approach: The idea is to use a binary search to find the parent of the node. As we know the binary Tree of Height N has nodes. Therefore, the search space for the binary search will be 1 to Now each node has children value either or Therefore, parents of such nodes can be found easily.
Below is the implementation of the above approach:

## C++

 // C++ implementation to find the // parent of the given node K in // a binary tree whose post-order // traversal is N natural numbers   #include  using namespace std;   // Function to find the parent // of the given node int findParent(int height, int node) {     int start = 1;     int end = pow(2, height) - 1;       // Condition to check whether     // the given node is a root node.     // if it is then return -1 because     // root node has no parent     if (end == node)         return -1;       // Loop till we found     // the given node     while (node >= 1) {         end = end - 1;           // Finding the middle node of the         // tree because at every level         // tree parent is         // divided into two halves         int mid = start                   + (end - start)                         / 2;           // if the node is found return         // the parent always the child         // nodes of every node         // is node/2 or (node-1)         if (mid == node || end == node) {             return (end + 1);         }           // if the node to be found         // is greater than the mid         // search for left subtree else         // search in right subtree         else if (node < mid) {             end = mid;         }         else {             start = mid;         }     } }   // Driver Code int main() {     int height = 4;     int node = 6;       int k = findParent(height, node);     cout << k;       return 0; }

## Java

 // Java implementation to find the // parent of the given node K in // a binary tree whose post-order // traversal is N natural numbers import java.util.*; class GFG{   // Function to find the parent // of the given node static int findParent(int height,                        int node) {   int start = 1;   int end = (int)Math.pow(2, height) - 1;     // Condition to check whether   // the given node is a root node.   // if it is then return -1 because   // root node has no parent   if (end == node)     return -1;     // Loop till we found   // the given node   while (node >= 1)    {     end = end - 1;       // Finding the middle node of the     // tree because at every level     // tree parent is     // divided into two halves     int mid = start + (end - start) / 2;       // if the node is found return     // the parent always the child     // nodes of every node     // is node*/2 or (node-1)     if (mid == node || end == node)      {       return (end + 1);     }       // if the node to be found     // is greater than the mid     // search for left subtree else     // search in right subtree     else if (node < mid)      {       end = mid;     }     else     {       start = mid;     }   }   return -1; }   // Driver Code public static void main(String[] args) {   int height = 4;   int node = 6;   int k = findParent(height, node);   System.out.print(k); } }   // This code is contributed by gauravrajput1

## Python

 # Python implementation to find the # parent of the given node   import math    # Function to find the parent  # of the given node def findParent(height, node):       start = 1     end = pow(2, height) - 1       # Check whether the given node      # is a root node.if it is then      # return -1 because root      # node has no parent     if (end == node):         return -1       # Loop till we found      # the given node     while(node >= 1):           end = end - 1           # Find the middle node of the          # tree because at every level          # tree parent is divided          # into two halves         mid = start + (end - start)//2           # if the node is found          # return the parent         # always the child nodes of every         # node is node / 2 or (node-1)          if(mid == node or end == node):             return (end + 1)                   # if the node to be found is greater         # than the mid search for left         # subtree else search in right subtree         elif (node < mid):             end = mid           else:             start = mid   # Driver code if __name__ == "__main__":     height = 4     node = 6           # Function Call     k = findParent(height, node)     print(k)

Output:

7



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