Print Ancestors of a given node in Binary Tree

Given a Binary Tree and a key, write a function that prints all the ancestors of the key in the given binary tree. 

For example, if the given tree is following Binary Tree and the key is 7, then your function should print 4, 2, and 1.

              1
            /   \
          2      3
        /  \
      4     5
     /
    7

Thanks to Mike, Sambasiva and wgpshashank for their contribution.

C++

// C++ program to print ancestors of given node
#include<bits/stdc++.h>

using namespace std;

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
   int data;
   struct node* left;
   struct node* right;
};

/* If target is present in tree, then prints the ancestors
   and returns true, otherwise returns false. */
bool printAncestors(struct node *root, int target)
{
  /* base cases */
  if (root == NULL)
     return false;

  if (root->data == target)
     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->data << " ";
    return true;
  }

  /* Else return false */
  return false;
}

/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newnode(int data)
{
  struct node* node = (struct node*)
                       malloc(sizeof(struct node));
  node->data = data;
  node->left = NULL;
  node->right = NULL;

  return(node);
}

/* Driver program to test above functions*/
int main()
{

  /* Construct the following binary tree
              1
            /   \
          2      3
        /  \
      4     5
     /
    7
  */
  struct node *root = newnode(1);
  root->left        = newnode(2);
  root->right       = newnode(3);
  root->left->left  = newnode(4);
  root->left->right = newnode(5);
  root->left->left->left  = newnode(7);

  printAncestors(root, 7);

  getchar();
  return 0;
}

Java

// Java program to print ancestors of given node

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
class Node
{
    int data;
    Node left, right, nextRight;

    Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}

class BinaryTree
{
    Node root;

    /* If target is present in tree, then prints the ancestors
       and returns true, otherwise returns false. */
    boolean printAncestors(Node node, int target)
    {
         /* base cases */
        if (node == null)
            return false;

        if (node.data == target)
            return true;

        /* If target is present in either left or right subtree
           of this node, then print this node */
        if (printAncestors(node.left, target)
                || printAncestors(node.right, target))
        {
            System.out.print(node.data + " ");
            return true;
        }

        /* Else return false */
        return false;
    }

    /* Driver program to test above functions */
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();

        /* Construct the following binary tree
                  1
                /   \
               2     3
              /  \
             4    5
            /
           7
        */
        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.left.left.left = new Node(7);

        tree.printAncestors(tree.root, 7);

    }
}

// This code has been contributed by Mayank Jaiswal

Python3

# Python program to print ancestors of given node in
# binary tree

# A Binary Tree node
class Node:

    # Constructor to create a new node
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# If target is present in tree, then prints the ancestors
# and returns true, otherwise returns false
def printAncestors(root, target):

    # Base case
    if root == None:
        return False

    if root.data == target:
        return True

    # If target is present in either left or right subtree
    # of this node, then print this node
    if (printAncestors(root.left, target) or
        printAncestors(root.right, target)):
        print(root.data,end=' ')
        return True

    # Else return False
    return False

# Driver program to test above function
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.left.left.left = Node(7)

printAncestors(root, 7)

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

using System;

// C# program to print ancestors of given node

/* A binary tree node has data, pointer to left child
and a pointer to right child */
public class Node
{
    public int data;
    public Node left, right, nextRight;

    public Node(int item)
    {
        data = item;
        left = right = nextRight = null;
    }
}

public class BinaryTree
{
    public Node root;

    /* If target is present in tree, then prints the ancestors
    and returns true, otherwise returns false. */
    public virtual bool printAncestors(Node node, int target)
    {
        /* base cases */
        if (node == null)
        {
            return false;
        }

        if (node.data == target)
        {
            return true;
        }

        /* If target is present in either left or right subtree
        of this node, then print this node */
        if (printAncestors(node.left, target)
        || printAncestors(node.right, target))
        {
            Console.Write(node.data + " ");
            return true;
        }

        /* Else return false */
        return false;
    }

    /* Driver program to test above functions */
    public static void Main(string[] args)
    {
        BinaryTree tree = new BinaryTree();

        /* Construct the following binary tree
                1
                / \
            2     3
            / \
            4 5
            /
        7
        */
        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.left.left.left = new Node(7);

        tree.printAncestors(tree.root, 7);

    }
}

// This code is contributed by Shrikant13

Javascript

<script>

    // JavaScript program to print ancestors of given node

    class Node
    {
        constructor(item) {
              this.data = item;
            this.left = null;
            this.right = null;
            this.nextRight = null;
        }
    }

    let root;

    /* If target is present in tree, then prints the ancestors
       and returns true, otherwise returns false. */
    function printAncestors(node, target)
    {
         /* base cases */
        if (node == null)
            return false;

        if (node.data == target)
            return true;

        /* If target is present in either left or right subtree
           of this node, then print this node */
        if (printAncestors(node.left, target)
                || printAncestors(node.right, target))
        {
            document.write(node.data + " ");
            return true;
        }

        /* Else return false */
        return false;
    }

    /* Construct the following binary tree
                    1
                  /   \
                 2     3
                /  \
               4    5
              /
             7
          */
    root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.left.right = new Node(5);
    root.left.left.left = new Node(7);

    printAncestors(root, 7);

</script>

Output

4 2 1 

Time Complexity: O(n) where n is the number of nodes in the given Binary Tree.
Auxiliary Space: O(h) where h is the height of given Binary Tree

Another Approach :

An alternative approach to solving this problem is by using an iterative approach with a stack data structure.

1. We start by creating an empty stack to store the nodes.
2. We enter a while loop that continues until the current node is NULL and the stack is empty.
3. Inside the loop, we traverse the left subtree of the current node, pushing each encountered node onto the stack until we reach a leaf node or find the target node.
4. If we find the target node, we break out of the loop.
5. If the current node is NULL and the stack is not empty, it means we have finished processing the left subtree and need to backtrack to the parent nodes.
6. We check if the right child of the top node on the stack is NULL or if it has already been processed. If so, it indicates that we have finished processing that node        and its subtree.
7. In such cases, we print the top node’s data (which represents an ancestor) and pop it from the stack.
8. We continue this process until we find a node whose right child has not been processed.
9. Once we finish processing the left subtree and backtrack to the current node’s right child, we update the current node accordingly.
              a) If the stack is not empty, we set the current node to the right child of the top node on the stack.
              b) If the stack is empty, it means we have finished traversing the entire tree, and we set the current node to NULL.
10. Finally, if the stack is not empty, we print the contents of the stack, which represents the ancestors of the target node.
11. If the stack is empty, it means the target node was not found, and we return false.

This iterative approach simulates the recursive approach by using a stack to keep track of the nodes and their respective subtrees as we traverse the tree. It eliminates the need for recursive function calls and utilizes the stack to manage the backtracking process.

Both the recursive and iterative approaches achieve the same goal of finding and printing the ancestors of a given node in a binary tree.

C++

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

/* A binary tree node has data, pointer to left child
   and a pointer to right child */
struct node
{
   int data;
   struct node* left;
   struct node* right;
};

/* If target is present in tree, then prints the ancestors
   and returns true, otherwise returns false. */
bool printAncestors(struct node *root, int target)
{
    stack<node*> st;
    while (root || !st.empty()) {
        while (root && root->data != target) {
            st.push(root);
            root = root->left;
        }

        if (root && root->data == target)
            break;

        if (!st.empty() && st.top()->right == NULL) {
            root = st.top();
            st.pop();

            while (!st.empty() && st.top()->right == root) {
                root = st.top();
                st.pop();
            }
        }

        root = (!st.empty()) ? st.top()->right : NULL;
    }

    if (!st.empty()) {
        while (!st.empty()) {
            cout << st.top()->data << " ";
            st.pop();
        }
        return true;
    }

    return false;
}

/* Helper function that allocates a new node with the
   given data and NULL left and right pointers. */
struct node* newnode(int data)
{
  struct node* node = (struct node*)malloc(sizeof(struct node));
  node->data = data;
  node->left = NULL;
  node->right = NULL;

  return(node);
}

/* Driver program to test above functions*/
int main()
{
  /* Construct the following binary tree
              1
            /   \
          2      3
        /  \
      4     5
     /
    7
  */
  struct node *root = newnode(1);
  root->left = newnode(2);
  root->right = newnode(3);
  root->left->left = newnode(4);
  root->left->right = newnode(5);
  root->left->left->left = newnode(7);

  printAncestors(root, 7);

  return 0;
}

Output

4 2 1 

• Time Complexity: O(n) where n is the number of nodes in the given Binary Tree.
• Auxiliary Space: O(h) where h is the height of given Binary Tree