# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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.

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; ` `} `

## 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 `

Output:

```1 3 5
```

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Improved By : rituraj_jain