Print path from root to all nodes in a Complete Binary Tree

Given a number N which is the total number of nodes in a complete binary tree where nodes are number from 1 to N sequentially level-wise. The task is to write a program to print paths from root to all of the nodes in the Complete Binary Tree.

For N = 3, the tree will be:

     1
  /     \
2        3 

For N = 7, the tree will be:

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

Examples:

Input : 7  
Output : 
1 
1 2 
1 2 4 
1 2 5 
1 3 
1 3 6 
1 3 7 

Input : 4 
Output :
1 
1 2 
1 2 4 
1 3 


Explanation :- Since, the given tree is a complete binary tree. For every node i we can calculate it’s left child as 2*i and right child as 2*i + 1.

The idea is to use a backtracking approach to print all paths. Maintain a vector to store paths, initially push the root node 1 to it, and before pushing the left and right childs print the current path stored in it and then call the function for the left and right childs as well.

Below is the complete implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to print path from root to all
// nodes in a complete binary tree.
  
#include <iostream>
#include <vector>
using namespace std;
  
// Funciton to print path of all the nodes
// nth node represent as given node
// kth node represents as left and right node
void printPath(vector<int> res, int nThNode, int kThNode)
{
    // base condition
    // if kth node value is greater
    // then nth node then its means
    // kth node is not valid so
    // we not store it into the res
    // simply we just return
    if (kThNode > nThNode)
        return;
  
    // Storing node into res
    res.push_back(kThNode);
  
    // Print the path from root to node
    for (int i = 0; i < res.size(); i++)
        cout << res[i] << " ";
    cout << "\n";
  
    // store left path of a tree
    // So for left we will go node(kThNode*2)
    printPath(res, nThNode, kThNode * 2);
  
    // right path of a tree
    // and for right we will go node(kThNode*2+1)
    printPath(res, nThNode, kThNode * 2 + 1);
}
  
// Function to print path from root to all of the nodes
void printPathToCoverAllNodeUtil(int nThNode)
{
    // res is for store the path
    // from root to particulate node
    vector<int> res;
  
    // Print path from root to all node.
    // third argument 1 because of we have
    // to consider root node is 1
    printPath(res, nThNode, 1);
}
  
// Driver Code
int main()
{
    // Given Node
    int nThNode = 7;
  
    // Print path from root to all node.
    printPathToCoverAllNodeUtil(nThNode);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to print path from root to all 
// nodes in a complete binary tree. 
import java.util.*;
  
class GFG
{
  
// Funciton to print path of all the nodes 
// nth node represent as given node 
// kth node represents as left and right node 
static void printPath(Vector<Integer> res,
                    int nThNode, int kThNode) 
    // base condition 
    // if kth node value is greater 
    // then nth node then its means 
    // kth node is not valid so 
    // we not store it into the res 
    // simply we just return 
    if (kThNode > nThNode) 
        return
  
    // Storing node into res 
    res.add(kThNode); 
  
    // Print the path from root to node 
    for (int i = 0; i < res.size(); i++) 
        System.out.print( res.get(i) + " "); 
    System.out.print( "\n"); 
  
    // store left path of a tree 
    // So for left we will go node(kThNode*2) 
    printPath(res, nThNode, kThNode * 2); 
  
    // right path of a tree 
    // and for right we will go node(kThNode*2+1) 
    printPath(res, nThNode, kThNode * 2 + 1); 
      
    res.remove(res.size()-1);
  
// Function to print path from root to all of the nodes 
static void printPathToCoverAllNodeUtil(int nThNode) 
    // res is for store the path 
    // from root to particulate node 
    Vector<Integer> res=new Vector<Integer>(); 
  
    // Print path from root to all node. 
    // third argument 1 because of we have 
    // to consider root node is 1 
    printPath(res, nThNode, 1); 
  
// Driver Code 
public static void main(String args[])
    // Given Node 
    int nThNode = 7
  
    // Print path from root to all node. 
    printPathToCoverAllNodeUtil(nThNode); 
}
}
  
// This code is contributed by Arnab Kundu

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to print path from root 
# to all nodes in a complete binary tree. 
  
# Function to print path of all the nodes 
# nth node represent as given node kth
# node represents as left and right node 
def printPath(res, nThNode, kThNode): 
  
    # base condition 
    # if kth node value is greater 
    # then nth node then its means 
    # kth node is not valid so 
    # we not store it into the res 
    # simply we just return 
    if kThNode > nThNode: 
        return
  
    # Storing node into res 
    res.append(kThNode) 
  
    # Print the path from root to node 
    for i in range(0, len(res)): 
        print(res[i], end = " "
    print() 
  
    # store left path of a tree 
    # So for left we will go node(kThNode*2) 
    printPath(res[:], nThNode, kThNode * 2
  
    # right path of a tree 
    # and for right we will go node(kThNode*2+1) 
    printPath(res[:], nThNode, kThNode * 2 + 1
  
# Function to print path from root 
# to all of the nodes 
def printPathToCoverAllNodeUtil(nThNode): 
  
    # res is for store the path 
    # from root to particulate node 
    res = []
  
    # Print path from root to all node. 
    # third argument 1 because of we have 
    # to consider root node is 1 
    printPath(res, nThNode, 1
  
# Driver Code 
if __name__ == "__main__"
  
    # Given Node 
    nThNode = 7
  
    # Print path from root to all node. 
    printPathToCoverAllNodeUtil(nThNode) 
  
# This code is contributed by Rituraj Jain

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to print path from root to all 
// nodes in a complete binary tree. 
using System;
using System.Collections.Generic; 
  
class GFG
{
  
// Funciton to print path of all the nodes 
// nth node represent as given node 
// kth node represents as left and right node 
static void printPath(List<int> res,
                    int nThNode, int kThNode) 
    // base condition 
    // if kth node value is greater 
    // then nth node then its means 
    // kth node is not valid so 
    // we not store it into the res 
    // simply we just return 
    if (kThNode > nThNode) 
        return
  
    // Storing node into res 
    res.Add(kThNode); 
  
    // Print the path from root to node 
    for (int i = 0; i < res.Count; i++) 
        Console.Write( res[i] + " "); 
    Console.Write( "\n"); 
  
    // store left path of a tree 
    // So for left we will go node(kThNode*2) 
    printPath(res, nThNode, kThNode * 2); 
  
    // right path of a tree 
    // and for right we will go node(kThNode*2+1) 
    printPath(res, nThNode, kThNode * 2 + 1); 
      
    res.RemoveAt(res.Count-1);
  
// Function to print path from root to all of the nodes 
static void printPathToCoverAllNodeUtil(int nThNode) 
    // res is for store the path 
    // from root to particulate node 
    List<int> res=new List<int>(); 
  
    // Print path from root to all node. 
    // third argument 1 because of we have 
    // to consider root node is 1 
    printPath(res, nThNode, 1); 
  
// Driver Code 
public static void Main(String []args)
    // Given Node 
    int nThNode = 7; 
  
    // Print path from root to all node. 
    printPathToCoverAllNodeUtil(nThNode); 
}
}
  
// This code contributed by Rajput-Ji

chevron_right


PHP

$nThNode)
return;

// Storing node into res
array_push($res, $kThNode);

// Print the path from root to node
for ($i = 0; $i < count($res); $i++) echo $res[$i] . " "; echo "\n"; // store left path of a tree // So for left we will go node(kThNode*2) printPath($res, $nThNode, $kThNode * 2); // right path of a tree // and for right we will go node(kThNode*2+1) printPath($res, $nThNode, $kThNode * 2 + 1); } // Function to print path // from root to all of the nodes function printPathToCoverAllNodeUtil($nThNode) { // res is for store the path // from root to particulate node $res = array(); // Print path from root to all node. // third argument 1 because of we have // to consider root node is 1 printPath($res, $nThNode, 1); } // Driver Code // Given Node $nThNode = 7; // Print path from root to all node. printPathToCoverAllNodeUtil($nThNode); // This code is contributed by mits ?>

Output:

1 
1 2 
1 2 4 
1 2 5 
1 3 
1 3 6 
1 3 7


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.