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Number of siblings of a given Node in n-ary Tree


Reading Time - 9 mins


Difficulty Level Easy

Problem Statement

The problem “Number of siblings of a given Node in n-ary Tree” states that you are given an n-ary Tree and a target node. Find the number of siblings of the target node. Assume that node is always present in the tree and the first node is the root of the tree.

Example

Input

Number of siblings of a given Node in n-ary Tree

node = 10
node = 11

3
1

Explanation
Siblings of 10 are {41, 6, 32}
Siblings of 11 are {9}

Algorithm

Siblings of a node are the nodes present at the same level as the given node, or in other words, siblings of a node are one less than the number of children of its parent.

Consider the tree in above example, and let the node be 10
Parent of 10 = 51
Children of 51 are {10, 41, 32, 6}
Siblings of 10 are children of its parent except 10, that is, siblings of 10 are {41, 32, 6}

Important Point: The number of siblings of the root is 0. Because there is no parent of root.

The idea to find the number of siblings of a node is to do a BFS on the given tree, if a node’s children is the same as the given node, return (number of children of that node – 1).

  1. If the given node is equals to the root or root is null, return 0.
  2. Create a queue of nodes for BFS and push the root to the queue.
  3. While the queue is not empty repeat step 4.
  4. Remove an element from the queue, traverse through all the children of the current element, if any of its children is equals to the given node, return (number of children of current node – 1), else push the children to the queue.
  5. If there is no node matching the given node, return -1.
READ  Construct Binary Tree from Given Inorder and Preorder Traversals

Code

Java Code to find Number of siblings of a given Node in n-ary Tree

import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;

class NumberOfSiblingsOfAGivenNodeInNAryTree {
    // class representing node of n-ary tree
    static class Node {
        
        ArrayList<Node> child;
        int data;
        public Node(int data) {
            this.data = data;
            this.child = new ArrayList<>();
        }
    }

    private static int siblings(Node root, int target) {
        // if the given node is equals to the root or root is null, return 0
        if (root == null || root.data == target) {
            return 0;
        }

        // create a queue of nodes
        Queue<Node> queue = new LinkedList<>();
        // push the root to queue
        queue.add(root);

        // do a BFS of the tree
        while (!queue.isEmpty()) {
            // remove one element from the queue
            Node curr = queue.poll();
            // traverse its children
            for (int i = 0; i < curr.child.size(); i++) {
                // current child
                Node currChild = curr.child.get(i);
                // if current child is the target, return (parent's children count - 1)
                if (currChild.data == target) {
                    return (curr.child.size() - 1);
                }
                // add the child to the queue
                queue.add(currChild);
            }
        }

        // if there is no match, return -1
        return -1;
    }

    public static void main(String[] args) {
        // Example n-ary tree
        Node root = new Node(51);
        // children of 51
        root.child.add(new Node(10));
        root.child.add(new Node(41));
        root.child.add(new Node(6));
        root.child.add(new Node(32));
        // children of 10
        root.child.get(0).child.add(new Node(53));
        // children of 41
        root.child.get(1).child.add(new Node(95));
        // children of 6
        root.child.get(2).child.add(new Node(28));
        // children of 32
        root.child.get(3).child.add(new Node(9));
        root.child.get(3).child.add(new Node(11));
        // children of 53
        root.child.get(0).child.get(0).child.add(new Node(5));
        root.child.get(0).child.get(0).child.add(new Node(7));
        // children of 11
        root.child.get(3).child.get(1).child.add(new Node(3));
        root.child.get(3).child.get(1).child.add(new Node(8));

        System.out.println(siblings(root, 10));
        System.out.println(siblings(root, 11));
    }
}
3
1

C++ Code to find Number of siblings of a given Node in n-ary Tree

#include <bits/stdc++.h> 
using namespace std; 

// class representing node of a n-ary tree
class Node {
    public:
    int data;
    vector<Node*> child;
    
    Node(int d) {
        data = d;
    }
};

int siblings(Node *root, int target) {
    // if the given node is equals to the root or root is null, return 0
    if (root == NULL || root->data == target) {
        return 0;
    }
    
    // create a queue of nodes
    queue<Node*> q;
    // push the root to queue
    q.push(root);
    
    // do a BFS of the tree
    while (!q.empty()) {
        // remove one element from the queue
        Node *curr = q.front();
        q.pop();
        // traverse its children
        for (int i = 0; i < curr->child.size(); i++) {
            // current child
            Node *currChild = curr->child[i];
            // if current child is the target, return (parent's children count - 1)
            if (currChild->data == target) {
                return (curr->child.size() - 1);
            }
            // add the child to the queue
            q.push(curr->child[i]);
        }
    }
    
    // if there is no match, return -1
    return -1;
}

int main() {
    // Example n-ary tree
    Node *root = new Node(51);
    // children of 51
    root->child.push_back(new Node(10));
    root->child.push_back(new Node(41));
    root->child.push_back(new Node(6));
    root->child.push_back(new Node(32));
    // children of 10
    root->child[0]->child.push_back(new Node(53));
    // children of 41
    root->child[1]->child.push_back(new Node(95));
    // children of 6
    root->child[2]->child.push_back(new Node(28));
    // children of 32
    root->child[3]->child.push_back(new Node(9));
    root->child[3]->child.push_back(new Node(11));
    // children of 53
    root->child[0]->child[0]->child.push_back(new Node(5));
    root->child[0]->child[0]->child.push_back(new Node(7));
    // children of 11
    root->child[3]->child[1]->child.push_back(new Node(3));
    root->child[3]->child[1]->child.push_back(new Node(8));

    cout<<siblings(root, 10)<<endl;
    cout<<siblings(root, 11)<<endl;
    
    return 0;
}
3
1

Complexity Analysis

Time Complexity

O(N), because we have done BFS for tree. We have just traversed over all the nodes which made the algorithm to run in linear time.

READ  Construct BST from its given Level Order Traversal

Space Complexity

O(N), using a queue for BFS has cost us linear space. Thus the space complexity of the algorithm is O(N).

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