Print the first shortest root to leaf path in a Binary Tree

Given a Binary Tree with distinct values, the task is to print the first smallest root to leaf path. We basically need to print the leftmost root to leaf path that has the minimum number of nodes.

Input:
          1
         /  \
        2    3
       /    / \
      4    5   7
     / \        \
    10  11       8
Output: 1 3 5


Input:
          1
         /  \
        2    3
       /    / \
      40   5   7
                \
                 8
Output: 1 2 40

Approach: The idea is to use a queue to perform level order traversal, a map parent to store the nodes that will be present in the shortest path. Using level order traversal, we find the leftmost leaf. Once we find the leftmost leaf, we print path using the map.

Efficient Approach:

• Create a struct Node with left and right pointers and a data value.
• Create a function newNode that creates a new binary tree node and initializes its data and pointers to null.
• Create a recursive function printPath that takes in the data value of a node and a parent map, and prints the path from that node to the root using the parent map. The parent map is a hash map that maps a node’s data value to its parent’s data value.
• Create a function leftMostShortest that takes in a root node and performs a level order traversal of the binary tree until it finds the first leaf node. It uses a queue to keep track of the nodes to visit and a parent map to keep track of the parent of each node. When it finds the first leaf node, it calls the printPath function to print the path from the leaf node to the root.
• In the main function, create a binary tree using the newNode function, and call the leftMostShortest function with the root node.

Below is the implementation of the above approach:

C++

// C++ program to print first shortest
// root to leaf path
#include <bits/stdc++.h>
using namespace std;

// Binary tree node
struct Node {
    struct Node* left;
    struct Node* right;
    int data;
};

// Function to create a new
// Binary node
struct Node* newNode(int data)
{
    struct Node* temp = new Node;

    temp->data = data;
    temp->left = NULL;
    temp->right = NULL;

    return temp;
}

// Recursive function used by leftMostShortest
// to print the first shortest root to leaf path
void printPath(int Data, unordered_map<int,
                             int> parent)
{
    // If the root's data is same as
    // its parent data then return
    if (parent[Data] == Data)
        return;

    // Recur for the function printPath
    printPath(parent[Data], parent);

    // Print the parent node's data
    cout << parent[Data] << " ";
}

// Function to perform level order traversal
// until we find the first leaf node
void leftMostShortest(struct Node* root)
{
    // Queue to store the nodes
    queue<struct Node*> q;

    // Push the root node
    q.push(root);

    // Initialize the value of first
    // leaf node to occur as -1
    int LeafData = -1;

    // To store the current node
    struct Node* temp = NULL;

    // Map to store the parent node's data
    unordered_map<int, int> parent;

    // Parent of root data is set as it's
    // own value
    parent[root->data] = root->data;

    // We store first node of the smallest level
    while (!q.empty()) {
        temp = q.front();
        q.pop();

        // If the first leaf node has been found
        // set the flag variable as 1
        if (!temp->left && !temp->right) {
            LeafData = temp->data;
            break;
        }
        else {

            // If current node has left
            // child, push in the queue
            if (temp->left) {
                q.push(temp->left);

                // Set temp's left node's parent as temp
                parent[temp->left->data] = temp->data;
            }

            // If current node has right
            // child, push in the queue
            if (temp->right) {
                q.push(temp->right);

                // Set temp's right node's parent
                // as temp
                parent[temp->right->data] = temp->data;
            }
        }
    }

    // Recursive function to print the first
    // shortest root to leaf path
    printPath(LeafData, parent);

    // Print the leaf node of the first
    // shortest path
    cout << LeafData << " ";
}

// Driver code
int main()
{
    struct Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->right->left = newNode(5);
    root->right->right = newNode(7);
    root->left->left->left = newNode(10);
    root->left->left->right = newNode(11);
    root->right->right->left = newNode(8);

    leftMostShortest(root);

    return 0;
}

Java

// Java program to print first shortest
// root to leaf path
import java.util.*;

class GFG{

// Binary tree node
static class Node
{
    Node left;
    Node right;
    int data;
};

// Function to create a new
// Binary node
static Node newNode(int data)
{
    Node temp = new Node();

    temp.data = data;
    temp.left = null;
    temp.right = null;

    return temp;
}

// Recursive function used by leftMostShortest
// to print the first shortest root to leaf path
static void printPath(int Data,
                      HashMap<Integer,
                              Integer> parent)
{

    // If the root's data is same as
    // its parent data then return
    if (parent.get(Data) == Data)
        return;

    // Recur for the function printPath
    printPath(parent.get(Data), parent);

    // Print the parent node's data
    System.out.print(parent.get(Data) + " ");
}

// Function to perform level order traversal
// until we find the first leaf node
static void leftMostShortest(Node root)
{

    // Queue to store the nodes
    Queue<Node> q = new LinkedList<>();

    // Add the root node
    q.add(root);

    // Initialize the value of first
    // leaf node to occur as -1
    int LeafData = -1;

    // To store the current node
    Node temp = null;

    // Map to store the parent node's data
    HashMap<Integer,
            Integer> parent = new HashMap<>();

    // Parent of root data is set as it's
    // own value
    parent.put(root.data, root.data);

    // We store first node of the smallest level
    while (!q.isEmpty())
    {
        temp = q.poll();

        // If the first leaf node has been found
        // set the flag variable as 1
        if (temp.left == null &&
            temp.right == null)
        {
            LeafData = temp.data;
            break;
        }
        else
        {

            // If current node has left
            // child, add in the queue
            if (temp.left != null)
            {
                q.add(temp.left);

                // Set temp's left node's parent
                // as temp
                parent.put(temp.left.data,
                           temp.data);
            }

            // If current node has right
            // child, add in the queue
            if (temp.right != null)
            {
                q.add(temp.right);

                // Set temp's right node's parent
                // as temp
                parent.put(temp.right.data,
                                 temp.data);
            }
        }
    }

    // Recursive function to print the
    // first shortest root to leaf path
    printPath(LeafData, parent);

    // Print the leaf node of the first
    // shortest path
    System.out.println(LeafData + " ");
}

// Driver Code
public static void main(String[] args)
{
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.right.left = newNode(5);
    root.right.right = newNode(7);
    root.left.left.left = newNode(10);
    root.left.left.right = newNode(11);
    root.right.right.left = newNode(8);

    leftMostShortest(root);
}
}

// This code is contributed by sanjeev2552

Python3

# Python3 program to print first
# shortest root to leaf path

# Binary tree node
class Node:

    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Recursive function used by leftMostShortest
# to print the first shortest root to leaf path
def printPath(Data, parent):

    # If the root's data is same as
    # its parent data then return
    if parent[Data] == Data:
        return

    # Recur for the function printPath
    printPath(parent[Data], parent)

    # Print the parent node's data
    print(parent[Data], end = " ")

# Function to perform level order traversal
# until we find the first leaf node
def leftMostShortest(root):

    # Queue to store the nodes
    q = []

    # Push the root node
    q.append(root)

    # Initialize the value of first
    # leaf node to occur as -1
    LeafData = -1

    # To store the current node
    temp = None

    # Map to store the parent node's data
    parent = {}

    # Parent of root data is set
    # as it's own value
    parent[root.data] = root.data

    # We store first node of the
    # smallest level
    while len(q) != 0:
        temp = q.pop(0)

        # If the first leaf node has been
        # found set the flag variable as 1
        if not temp.left and not temp.right:
            LeafData = temp.data
            break

        else:

            # If current node has left
            # child, push in the queue
            if temp.left:
                q.append(temp.left)

                # Set temp's left node's parent as temp
                parent[temp.left.data] = temp.data

            # If current node has right
            # child, push in the queue
            if temp.right:
                q.append(temp.right)

                # Set temp's right node's parent
                # as temp
                parent[temp.right.data] = temp.data

    # Recursive function to print the first
    # shortest root to leaf path
    printPath(LeafData, parent)

    # Print the leaf node of the
    # first shortest path
    print(LeafData, end = " ")

# Driver code
if __name__ == "__main__":

    root = Node(1)
    root.left = Node(2)
    root.right = Node(3)
    root.left.left = Node(4)
    root.right.left = Node(5)
    root.right.right = Node(7)
    root.left.left.left = Node(10)
    root.left.left.right = Node(11)
    root.right.right.left = Node(8)

    leftMostShortest(root)

# This code is contributed by Rituraj Jain

C#

// C# program to print first shortest
// root to leaf path
using System;
using System.Collections;
using System.Collections.Generic;

class GFG{

// Binary tree node
public class Node
{
    public Node left;
    public Node right;
    public int data;
};

// Function to create a new
// Binary node
public static Node newNode(int data)
{
    Node temp = new Node();

    temp.data = data;
    temp.left = null;
    temp.right = null;

    return temp;
}

// Recursive function used by leftMostShortest
// to print the first shortest root to leaf path
static void printPath(int Data,
           Dictionary<int, int> parent)
{

    // If the root's data is same as
    // its parent data then return
    if (parent[Data] == Data)
        return;

    // Recur for the function printPath
    printPath(parent[Data], parent);

    // Print the parent node's data
    Console.Write(parent[Data] + " ");
}

// Function to perform level order traversal
// until we find the first leaf node
static void leftMostShortest(Node root)
{

    // Queue to store the nodes
    Queue q = new Queue();

    // Add the root node
    q.Enqueue(root);

    // Initialize the value of first
    // leaf node to occur as -1
    int LeafData = -1;

    // To store the current node
    Node temp = null;

    // Map to store the parent node's data
    Dictionary<int,
               int> parent = new Dictionary<int,
                                            int>();

    // Parent of root data is set as it's
    // own value
    parent[root.data] = root.data;

    // We store first node of the
    // smallest level
    while (q.Count != 0)
    {
        temp = (Node)q.Dequeue();

        // If the first leaf node has been
        // found set the flag variable as 1
        if (temp.left == null &&
           temp.right == null)
        {
            LeafData = temp.data;
            break;
        }
        else
        {

            // If current node has left
            // child, add in the queue
            if (temp.left != null)
            {
                q.Enqueue(temp.left);

                // Set temp's left node's parent
                // as temp
                parent[temp.left.data] = temp.data;
            }

            // If current node has right
            // child, add in the queue
            if (temp.right != null)
            {
                q.Enqueue(temp.right);

                // Set temp's right node's parent
                // as temp
                parent[temp.right.data] = temp.data;
            }
        }
    }

    // Recursive function to print the
    // first shortest root to leaf path
    printPath(LeafData, parent);

    // Print the leaf node of the first
    // shortest path
    Console.Write(LeafData + " ");
}

// Driver Code
public static void Main(string[] args)
{
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.right.left = newNode(5);
    root.right.right = newNode(7);
    root.left.left.left = newNode(10);
    root.left.left.right = newNode(11);
    root.right.right.left = newNode(8);

    leftMostShortest(root);
}
}

// This code is contributed by rutvik_56

Javascript

<script>

    // JavaScript program to print first
    // shortest root to leaf path

    // Binary tree node
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }

    // Function to create a new
    // Binary node
    function newNode(data)
    {
        let temp = new Node(data);
        return temp;
    }

    // Recursive function used by leftMostShortest
    // to print the first shortest root to leaf path
    function printPath(Data, parent)
    {

        // If the root's data is same as
        // its parent data then return
        if (parent.get(Data) == Data)
            return;

        // Recur for the function printPath
        printPath(parent.get(Data), parent);

        // Print the parent node's data
        document.write(parent.get(Data) + " ");
    }

    // Function to perform level order traversal
    // until we find the first leaf node
    function leftMostShortest(root)
    {

        // Queue to store the nodes
        let q = [];

        // Add the root node
        q.push(root);

        // Initialize the value of first
        // leaf node to occur as -1
        let LeafData = -1;

        // To store the current node
        let temp = null;

        // Map to store the parent node's data
        let parent = new Map();

        // Parent of root data is set as it's
        // own value
        parent.set(root.data, root.data);

        // We store first node of the smallest level
        while (q.length > 0)
        {
            temp = q[0];
            q.shift();

            // If the first leaf node has been found
            // set the flag variable as 1
            if (temp.left == null &&
                temp.right == null)
            {
                LeafData = temp.data;
                break;
            }
            else
            {

                // If current node has left
                // child, add in the queue
                if (temp.left != null)
                {
                    q.push(temp.left);

                    // Set temp's left node's parent
                    // as temp
                    parent.set(temp.left.data,
                               temp.data);
                }

                // If current node has right
                // child, add in the queue
                if (temp.right != null)
                {
                    q.push(temp.right);

                    // Set temp's right node's parent
                    // as temp
                    parent.set(temp.right.data,
                                     temp.data);
                }
            }
        }

        // Recursive function to print the
        // first shortest root to leaf path
        printPath(LeafData, parent);

        // Print the leaf node of the first
        // shortest path
        document.write(LeafData + " ");
    }

    let root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.right.left = newNode(5);
    root.right.right = newNode(7);
    root.left.left.left = newNode(10);
    root.left.left.right = newNode(11);
    root.right.right.left = newNode(8);

    leftMostShortest(root);

</script>

Output:

1 3 5

Time Complexity: O(N) 
Auxiliary Space: O(N)