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 ``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 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 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 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

 ``

Output:
`1 3 5`

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

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