Print path from a node to root of given Complete Binary Tree

Given an integer N, the task is to find the path from the N^th node to the root of a Binary Tree of the following form:

• The Binary Tree is a Complete Binary Tree up to the level of the N^th node.
• The nodes are numbered 1 to N, starting from the root as 1.
• The structure of the Tree is as follows: 
   

               1
           /       \
          2         3
       /    \    /   \
      4     5    6    7
      ................
   /    \ ............
 N - 1  N ............

Examples:

Input: N = 7
Output: 7 3 1
Explanation: The path from the node 7 to root is 7 -> 3 -> 1.

Input: N = 11
Output: 11 5 2 1
Explanation: The path from node 11 to root is 11 -> 5 -> 2 -> 1.

Naive Approach: The simplest approach to solve the problem is to perform DFS from the given node until the root node is encountered and print the path.

Time Complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the structure of the given Binary Tree. It can be observed that for every N, its parent node will be N / 2. Therefore, repeatedly print the current value of N and update N to N / 2 until N is equal to 1, i.e. root node is reached. 

Below is the implementation of the above approach:

// C++ program for the above approach

#include <iostream>
using namespace std;

// Function to print the path
// from node to root
void path_to_root(int node)
{
    // Iterate until root is reached
    while (node >= 1) {

        // Print the value of
        // the current node
        cout << node << ' ';

        // Move to parent of
        // the current node
        node /= 2;
    }
}

// Driver Code
int main()
{
    int N = 7;
    path_to_root(N);

    return 0;
}

// Java program for the above approach
import java.util.*;
 
class GFG{

// Function to print the path
// from node to root
static void path_to_root(int node)
{
    
    // Iterate until root is reached
    while (node >= 1) 
    {
        
        // Print the value of
        // the current node
        System.out.print(node + " ");

        // Move to parent of
        // the current node
        node /= 2;
    }
}

// Driver Code
public static void main(String[] args)
{
    int N = 7;
    
    path_to_root(N);
}
}

// This code is contributed by shivanisinghss2110

# Python3 program for the above approach

# Function to print the path
# from node to root
def path_to_root(node):
    
    # Iterate until root is reached
    while (node >= 1):

        # Print the value of
        # the current node
        print(node, end = " ")

        # Move to parent of
        # the current node
        node //= 2

# Driver Code
if __name__ == '__main__':

    N = 7

    path_to_root(N)

# This code is contributed by mohit kumar 29

// C# program for the above approach
using System;
class GFG
{

// Function to print the path
// from node to root
static void path_to_root(int node)
{
    
    // Iterate until root is reached
    while (node >= 1) 
    {
        
        // Print the value of
        // the current node
        Console.Write(node + " ");

        // Move to parent of
        // the current node
        node /= 2;
    }
}

// Driver Code
public static void Main(String[] args)
{
    int N = 7;    
    path_to_root(N);
}
}

// This code is contributed by shivanisinghss2110

<script>

// Javascript program for the above approach

// Function to print the path
// from node to root
function path_to_root(node)
{
    
    // Iterate until root is reached
    while (node >= 1) 
    {
        
        // Print the value of
        // the current node
        document.write(node + " ");

        // Move to parent of
        // the current node
        node = parseInt(node / 2, 10);
    }
}

// Driver code
let N = 7;

path_to_root(N);

// This code is contributed by divyeshrabadiya07

</script>

7 3 1

Time Complexity: O(log₂(N))
Auxiliary Space: O(1)