Print common nodes on path from root (or common ancestors)

2.5

Given a binary tree and two nodes, the task is to Print all the nodes that are common for 2 given nodes in a binary tree.

Examples:

Given binary tree is :
                     1
                  /    \
                2       3
              /   \     /  \
             4     5   6    7
            /        /  \
           8        9   10

Given nodes 9 and 7, so the common nodes are:-
1, 3

Asked in : Amazon

  1. Find the LCA of given two nodes.
  2. Print all ancestors of the LCA as done in this post, also print the LCA.

C/C++

// C++ Program to find common nodes for given two nodes
#include <iostream>
using namespace std;

// A Binary Tree Node
struct Node {
    struct Node* left, *right;
    int key;
};

// Utility function to create a new tree Node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return temp;
}

// Utility function to find the LCA of two given values
// n1 and n2.
struct Node* findLCA(struct Node* root, int n1, int n2)
{
    // Base case
    if (root == NULL)
        return NULL;

    // If either n1 or n2 matches with root's key,
    // report the presence by returning root (Note
    // that if a key is ancestor of other, then the
    // ancestor key becomes LCA
    if (root->key == n1 || root->key == n2)
        return root;

    // Look for keys in left and right subtrees
    Node* left_lca = findLCA(root->left, n1, n2);
    Node* right_lca = findLCA(root->right, n1, n2);

    // If both of the above calls return Non-NULL, then
    // one key  is present in once subtree and other is
    // present in other, So this node is the LCA
    if (left_lca && right_lca)
        return root;

    // Otherwise check if left subtree or right
    // subtree is LCA
    return (left_lca != NULL) ? left_lca : right_lca;
}

// Utility Function to print all ancestors of LCA
bool printAncestors(struct Node* root, int target)
{
    /* base cases */
    if (root == NULL)
        return false;

    if (root->key == target) {
        cout << root->key << " ";
        return true;
    }

    /* If target is present in either left or right
      subtree of this node, then print this node */
    if (printAncestors(root->left, target) ||
        printAncestors(root->right, target)) {
        cout << root->key << " ";
        return true;
    }

    /* Else return false */
    return false;
}

// Function to find nodes common to given two nodes
bool findCommonNodes(struct Node* root, int first,
                                       int second)
{
    struct Node* LCA = findLCA(root, first, second);
    if (LCA == NULL)
        return false;

    printAncestors(root, LCA->key);
}

// Driver program to test above functions
int main()
{
    // Let us create binary tree given in the above
    // example
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->left->left->left = newNode(8);
    root->right->left->left = newNode(9);
    root->right->left->right = newNode(10);

    if (findCommonNodes(root, 9, 7) == false)
        cout << "No Common nodes";

    return 0;
}

Java

// Java Program to find common nodes for given two nodes
import java.util.LinkedList;
 
// Class to represent Tree node 
class Node 
{
	int data;
	Node left, right;
 
	public Node(int item) 
	{
		data = item;
		left = null;
		right = null;
	}
}
 
// Class to count full nodes of Tree 
class BinaryTree 
{
    static Node root;
// Utility function to find the LCA of two given values
// n1 and n2.
static Node findLCA(Node root, int n1, int n2)
{
	// Base case
	if (root == null)
		return null;
 
	// If either n1 or n2 matches with root's key,
	// report the presence by returning root (Note
	// that if a key is ancestor of other, then the
	// ancestor key becomes LCA
	if (root.data == n1 || root.data == n2)
		return root;
 
	// Look for keys in left and right subtrees
	Node left_lca = findLCA(root.left, n1, n2);
	Node right_lca = findLCA(root.right, n1, n2);
 
	// If both of the above calls return Non-NULL, then
	// one key is present in once subtree and other is
	// present in other, So this node is the LCA
	if (left_lca!=null && right_lca!=null)
		return root;
 
	// Otherwise check if left subtree or right
	// subtree is LCA
	return (left_lca != null) ? left_lca : right_lca;
}
 
// Utility Function to print all ancestors of LCA
static boolean printAncestors(Node root, int target)
{
	/* base cases */
	if (root == null)
		return false;
 
	if (root.data == target) {
		System.out.print(root.data+ " ");
		return true;
	}
 
	/* If target is present in either left or right
	subtree of this node, then print this node */
	if (printAncestors(root.left, target) ||
		printAncestors(root.right, target)) {
		System.out.print(root.data+ " ");
		return true;
	}
 
	/* Else return false */
	return false;
}
 
// Function to find nodes common to given two nodes
static boolean findCommonNodes(Node root, int first,
									int second)
{
	Node LCA = findLCA(root, first, second);
	if (LCA == null)
		return false;
 
	printAncestors(root, LCA.data);
	return true;
}
 
// Driver program to test above functions
	public static void main(String args[]) 
	{
	/*Let us create Binary Tree shown in 
		above example */
 
		BinaryTree tree = new BinaryTree();
		tree.root = new Node(1);
		tree.root.left = new Node(2);
		tree.root.right = new Node(3);
		tree.root.left.left = new Node(4);
		tree.root.left.right = new Node(5);
		tree.root.right.left = new Node(6);
		tree.root.right.right = new Node(7);
		tree.root.left.left.left = new Node(8);
		tree.root.right.left.left = new Node(9);
		tree.root.right.left.right = new Node(10);
 
   if (findCommonNodes(root, 9, 7) == false)
	System.out.println("No Common nodes");
 
	}
}

// This code is contributed by Mr Somesh Awasthi


Output:

3 1

This article is contributed by Sahil Chhabra. 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.

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