Skip to content
Related Articles

Related Articles

Improve Article

Burn the binary tree starting from the target node

  • Difficulty Level : Hard
  • Last Updated : 25 Sep, 2021

Given a binary tree and target node. By giving the fire to the target node and fire starts to spread in a complete tree. The task is to print the sequence of the burning nodes of a binary tree.
Rules for burning the nodes : 

  • Fire will spread constantly to the connected nodes only.
  • Every node takes the same time to burn.
  • A node burns only once.

Examples: 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Input : 
                       12
                     /     \
                   13       10
                          /     \
                       14       15
                      /   \     /  \
                     21   24   22   23
target node = 14

Output :
14
21, 24, 10
15, 12
22, 23, 13

Explanation : First node 14 burns then it gives fire to it's 
neighbors(21, 24, 10) and so on. This process continues until 
the whole tree burns.


Input :
                       12
                     /     \
                  19        82
                 /        /     \
               41       15       95
                 \     /         /  \
                  2   21        7   16
target node = 41

Output :
41
2, 19
12
82
15, 95
21, 7, 16

Approach : 
First search the target node in a binary tree recursively. After finding the target node print it and save its left child(if exist) and right child(if exist) in a queue. and return. Now, get the size of the queue and run while loop. Print elements in the queue.



Below is the implementation of the above approach : 

CPP




// C++ implementation to print the sequence
// of burning of nodes of a binary tree
#include <bits/stdc++.h>
using namespace std;
 
// A Tree node
struct Node {
    int key;
    struct Node *left, *right;
};
 
// Utility function to create a new node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}
 
// Utility function to print the sequence of burning nodes
int burnTreeUtil(Node* root, int target, queue<Node*>& q)
{
    // Base condition
    if (root == NULL) {
        return 0;
    }
 
    // Condition to check whether target
    // node is found or not in a tree
    if (root->key == target) {
        cout << root->key << endl;
        if (root->left != NULL) {
            q.push(root->left);
        }
        if (root->right != NULL) {
 
            q.push(root->right);
        }
 
        // Return statements to prevent
        // further function calls
        return 1;
    }
 
    int a = burnTreeUtil(root->left, target, q);
 
    if (a == 1) {
        int qsize = q.size();
 
        // Run while loop until size of queue
        // becomes zero
        while (qsize--) {
            Node* temp = q.front();
 
            // Printing of burning nodes
            cout << temp->key << " , ";
            q.pop();
 
            // Check if condition for left subtree
            if (temp->left != NULL)
                q.push(temp->left);
 
            // Check if condition for right subtree
            if (temp->right != NULL)
                q.push(temp->right);
        }
 
        if (root->right != NULL)
            q.push(root->right);
 
        cout << root->key << endl;
 
        // Return statement it prevents further
        // further function call
        return 1;
    }
 
    int b = burnTreeUtil(root->right, target, q);
 
    if (b == 1) {
        int qsize = q.size();
        // Run while loop until size of queue
        // becomes zero
 
        while (qsize--) {
            Node* temp = q.front();
 
            // Printing of burning nodes
            cout << temp->key << " , ";
            q.pop();
 
            // Check if condition for left subtree
            if (temp->left != NULL)
                q.push(temp->left);
 
            // Check if condition for left subtree
            if (temp->right != NULL)
                q.push(temp->right);
        }
 
        if (root->left != NULL)
            q.push(root->left);
 
        cout << root->key << endl;
 
        // Return statement it prevents further
        // further function call
        return 1;
    }
}
 
// Function will print the sequence of burning nodes
void burnTree(Node* root, int target)
{
    queue<Node*> q;
 
    // Function call
    burnTreeUtil(root, target, q);
 
    // While loop runs unless queue becomes empty
    while (!q.empty()) {
        int qSize = q.size();
        while (qSize > 0) {
            Node* temp = q.front();
 
            // Printing of burning nodes
            cout << temp->key;
            // Insert left child in a queue, if exist
            if (temp->left != NULL) {
                q.push(temp->left);
            }
            // Insert right child in a queue, if exist
            if (temp->right != NULL) {
                q.push(temp->right);
            }
 
            if (q.size() != 1)
                cout << " , ";
 
            q.pop();
            qSize--;
        }
        cout << endl;
    }
}
 
// Driver Code
int main()
{
    /*      10
           /  \
          12  13
              / \
             14 15
            / \ / \
          21 22 23 24
 
        Let us create Binary Tree as shown
        above */
 
    Node* root = newNode(10);
    root->left = newNode(12);
    root->right = newNode(13);
 
    root->right->left = newNode(14);
    root->right->right = newNode(15);
 
    root->right->left->left = newNode(21);
    root->right->left->right = newNode(22);
    root->right->right->left = newNode(23);
    root->right->right->right = newNode(24);
    int targetNode = 14;
 
    // Function call
    burnTree(root, targetNode);
 
    return 0;
}

Java




import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
 
// Tree node class
 
class TreeNode
{
    int val;
    TreeNode left;
    TreeNode right;
    TreeNode() {}
    TreeNode(int val) { this.val = val; }
    TreeNode(int val, TreeNode left, TreeNode right)
    {
        this.val = val;
        this.left = left;
        this.right = right;
    }
}
 
class Solution {
   
     
    // function to print the sequence of burning nodes
    public static int search(TreeNode root,
                              int num,
                              Map<Integer,
                             Set<Integer> > levelOrderMap)
    {
        if (root != null)
        {
            // Condition to check whether target
            // node is found or not in a tree
            if (root.val == num)
            {
 
                levelOrderStoredInMap(root.left, 1,
                                      levelOrderMap);
                levelOrderStoredInMap(root.right, 1,
                                      levelOrderMap);
                // Return statements to prevent
                // further function calls
                return 1;
            }
            int k = search(root.left, num, levelOrderMap);
            if (k > 0)
            {
                // store root in map with k
                storeRootAtK(root, k, levelOrderMap);
                // store level order for other branch
                levelOrderStoredInMap(root.right, k + 1,
                                      levelOrderMap);
                return k + 1;
            }
            k = search(root.right, num, levelOrderMap);
            if (k > 0)
            {
                // store root in map with k
                storeRootAtK(root, k, levelOrderMap);
                // store level order for other branch
                levelOrderStoredInMap(root.left, k + 1,
                                      levelOrderMap);
                return k + 1;
            }
        }
        return -1; // Base condition
    }
 
    public static void levelOrderStoredInMap(
        TreeNode root, int k,
        Map<Integer, Set<Integer> > levelOrderMap)
    {
        if (root != null) {
            storeRootAtK(root, k, levelOrderMap);
            levelOrderStoredInMap(root.left, k + 1,
                                  levelOrderMap);
            levelOrderStoredInMap(root.right, k + 1,
                                  levelOrderMap);
        }
    }
 
    private static void
    storeRootAtK(TreeNode root, int k,
                 Map<Integer, Set<Integer> > levelOrderMap)
    {
        if (levelOrderMap.containsKey(k)) {
            levelOrderMap.get(k).add(root.val);
        }
        else {
            Set<Integer> set = new HashSet<>();
            set.add(root.val);
            levelOrderMap.put(k, set);
        }
    }
 
    // Driver Code
    public static void main(String[] args)
    {
 
        /*  12
           /  \
          13  10
              / \
             14 15
            / \ / \
          21 24 22 23
 
        Let us create Binary Tree as shown
        above */
        TreeNode root = new TreeNode(12);
        root.left = new TreeNode(13);
        root.right = new TreeNode(10);
        root.right.left = new TreeNode(14);
        root.right.right = new TreeNode(15);
        TreeNode left = root.right.left;
        TreeNode right = root.right.right;
        left.left = new TreeNode(21);
        left.right = new TreeNode(24);
        right.left = new TreeNode(22);
        right.right = new TreeNode(23);
 
        // Utility map to store the sequence of burning
        // nodes
        Map<Integer, Set<Integer> > levelOrderMap
            = new HashMap<>();
 
        // search node and store the level order from that
        // node in map
        search(root, 14, levelOrderMap);
 
        // will print the sequence of burning nodes
        System.out.println(14);
        for (Integer level : levelOrderMap.keySet())
        {
            for (Integer val : levelOrderMap.get(level))
            {
                System.out.print(val + " ");
            }
            System.out.println();
        }
    }
     
     
}
// This code is contributed by Niharika Sahai
Output
14
21 , 22 , 13
15 , 10
23 , 24 , 12

Output :

14
21 24 10 
12 15 
22 23 13 

Another Approach : Convert tree into undirected graph and print its level order traversal 

  • Build a undirected graph using Treenodes as vertices, and the parent-child relation as edges
  • Do BFS with source vertex as a target.

Java




import java.io.*;
import java.util.*;
 
public class GFG {
 
    /*package whatever //do not write package name here */
 
    static class TreeNode
    {
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode() {}
        TreeNode(int val) { this.val = val; }
        TreeNode(int val, TreeNode left, TreeNode right)
        {
            this.val = val;
            this.left = left;
            this.right = right;
        }
    }
     
     
     
    static  Map<TreeNode, List<TreeNode>> map = new HashMap<>();
        public static void main (String[] args) {
            TreeNode root = new TreeNode(12);
            root.left = new TreeNode(13);
            root.right = new TreeNode(10);
            root.right.left = new TreeNode(14);
            root.right.right = new TreeNode(15);
            TreeNode left = root.right.left;
            TreeNode right = root.right.right;
            left.left = new TreeNode(21);
            left.right = new TreeNode(24);
            right.left = new TreeNode(22);
            right.right = new TreeNode(23);
            // target Node value is 14
            burnTree(root,left);
          System.out.println();
        }
      private static void burnTree(TreeNode root, TreeNode target) {
             List<Integer> res = new ArrayList<Integer> ();
            if (root == null )
              return ;
            buildMap(root, null);
            if (!map.containsKey(target))
            { System.out.println("Target Not found");
              return;
            }
            Set<TreeNode> visited = new HashSet<TreeNode>();
        //BFS traversal
            Queue<TreeNode> q = new LinkedList<TreeNode>();
            q.add(target);
            visited.add(target);
            while (!q.isEmpty()) {
                int size = q.size();
                
                for (int i = 0; i < size; i++) {
                    TreeNode node = q.poll();
                    System.out.print(node.val+" ");
                    for (TreeNode next : map.get(node)) {
                        if (visited.contains(next))
                          continue;
                        visited.add(next);
                        q.add(next);
                    }
                }
                System.out.println();
                 
            }
       
      
    }
        // build undirected graph
      private  static void buildMap(TreeNode node, TreeNode parent) {
            if (node == null)
                return;
            if (!map.containsKey(node)) {
                
                map.put(node, new ArrayList<TreeNode>());
                if (parent != null)  { map.get(node).add(parent); map.get(parent).add(node) ; }
                buildMap(node.left, node);
                buildMap(node.right, node);
            }
        }   
 
 
}
Output
14 
10 21 24 
12 15 
13 22 23 

Output: 

14 
10 21 24 
12 15 
13 22 23  



My Personal Notes arrow_drop_up
Recommended Articles
Page :