# Minimum and maximum node that lies in the path connecting two nodes in a Binary Tree

Given a binary tree and two nodes a and b, the task is to print the minimum and the maximum node value that lies in the path connecting the given nodes a and b. If either of the two nodes is not present in the tree then print -1 for both minimum and maximum value.

Examples:

```Input:
1
/  \
2    3
/ \    \
4   5    6
/    / \
7    8   9
a = 5, b = 6
Output:
Min = 1
Max = 6

Input:
20
/   \
8     22
/   \  /   \
5     3 4    25
/ \
10  14
a = 5, b = 14
Output:
Min = 3
Max = 14
```

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

Approach: The idea is to find the LCA of both the nodes. Then start searching for the minimum and the maximum node in the path from LCA to the first node and then from LCA to the second node and print the minimum and the maximum of these values. In case either of the node is not present in the tree then print -1 for the minimum as well as the maximum value

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Structure of binary tree ` `struct` `Node { ` `    ``Node* left; ` `    ``Node* right; ` `    ``int` `data; ` `}; ` ` `  `// Function to create a new node ` `Node* newNode(``int` `key) ` `{ ` `    ``Node* node = ``new` `Node(); ` `    ``node->left = node->right = NULL; ` `    ``node->data = key; ` `    ``return` `node; ` `} ` ` `  `// Function to store the path from root node ` `// to given node of the tree in path vector and ` `// then returns true if the path exists ` `// otherwise false ` `bool` `FindPath(Node* root, vector<``int``>& path, ``int` `key) ` `{ ` `    ``if` `(root == NULL) ` `        ``return` `false``; ` ` `  `    ``path.push_back(root->data); ` ` `  `    ``if` `(root->data == key) ` `        ``return` `true``; ` ` `  `    ``if` `(FindPath(root->left, path, key) ` `        ``|| FindPath(root->right, path, key)) ` `        ``return` `true``; ` ` `  `    ``path.pop_back(); ` `    ``return` `false``; ` `} ` ` `  `// Function to print the minimum and the maximum ` `// value present in the path connecting the ` `// given two nodes of the given binary tree ` `int` `minMaxNodeInPath(Node* root, ``int` `a, ``int` `b) ` `{ ` ` `  `    ``// To store the path from the root node to a ` `    ``vector<``int``> Path1; ` ` `  `    ``// To store the path from the root node to b ` `    ``vector<``int``> Path2; ` ` `  `    ``// To store the minimum and the maximum value ` `    ``// in the path from LCA to a ` `    ``int` `min1 = INT_MAX; ` `    ``int` `max1 = INT_MIN; ` ` `  `    ``// To store the minimum and the maximum value ` `    ``// in the path from LCA to b ` `    ``int` `min2 = INT_MAX; ` `    ``int` `max2 = INT_MIN; ` ` `  `    ``int` `i = 0; ` `    ``int` `j = 0; ` ` `  `    ``// If both a and b are present in the tree ` `    ``if` `(FindPath(root, Path1, a) && FindPath(root, Path2, b)) { ` ` `  `        ``// Compare the paths to get the first different value ` `        ``for` `(i = 0; i < Path1.size() && Path2.size(); i++) ` `            ``if` `(Path1[i] != Path2[i]) ` `                ``break``; ` ` `  `        ``i--; ` `        ``j = i; ` ` `  `        ``// Find minimum and maximum value ` `        ``// in the path from LCA to a ` `        ``for` `(; i < Path1.size(); i++) { ` `            ``if` `(min1 > Path1[i]) ` `                ``min1 = Path1[i]; ` `            ``if` `(max1 < Path1[i]) ` `                ``max1 = Path1[i]; ` `        ``} ` ` `  `        ``// Find minimum and maximum value ` `        ``// in the path from LCA to b ` `        ``for` `(; j < Path2.size(); j++) { ` `            ``if` `(min2 > Path2[j]) ` `                ``min2 = Path2[j]; ` `            ``if` `(max2 < Path2[j]) ` `                ``max2 = Path2[j]; ` `        ``} ` ` `  `        ``// Minimum of min values in first ` `        ``// path and second path ` `        ``cout << ``"Min = "` `<< min(min1, min2) << endl; ` ` `  `        ``// Maximum of max values in first ` `        ``// path and second path ` `        ``cout << ``"Max = "` `<< max(max1, max2); ` `    ``} ` ` `  `    ``// If no path exists ` `    ``else` `        ``cout << ``"Min = -1\nMax = -1"``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``Node* root = newNode(20); ` `    ``root->left = newNode(8); ` `    ``root->right = newNode(22); ` `    ``root->left->left = newNode(5); ` `    ``root->left->right = newNode(3); ` `    ``root->right->left = newNode(4); ` `    ``root->right->right = newNode(25); ` `    ``root->left->right->left = newNode(10); ` `    ``root->left->right->right = newNode(14); ` ` `  `    ``int` `a = 5; ` `    ``int` `b = 1454; ` ` `  `    ``minMaxNodeInPath(root, a, b); ` ` `  `    ``return` `0; ` `} `

 `# Python3 implementation of the approach ` ` `  `class` `Node:  ` `     `  `    ``def` `__init__(``self``, key): ` `        ``self``.data ``=` `key ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# Function to store the path from root  ` `# node to given node of the tree in  ` `# path vector and then returns true if  ` `# the path exists otherwise false ` `def` `FindPath(root, path, key): ` ` `  `    ``if` `root ``=``=` `None``: ` `        ``return` `False` ` `  `    ``path.append(root.data) ` ` `  `    ``if` `root.data ``=``=` `key: ` `        ``return` `True` ` `  `    ``if` `(FindPath(root.left, path, key) ``or` `        ``FindPath(root.right, path, key)): ` `        ``return` `True` ` `  `    ``path.pop() ` `    ``return` `False` ` `  `# Function to print the minimum and the  ` `# maximum value present in the path  ` `# connecting the given two nodes of the  ` `# given binary tree ` `def` `minMaxNodeInPath(root, a, b): ` ` `  `    ``# To store the path from the  ` `    ``# root node to a ` `    ``Path1 ``=` `[] ` ` `  `    ``# To store the path from the ` `    ``# root node to b ` `    ``Path2 ``=` `[] ` ` `  `    ``# To store the minimum and the maximum ` `    ``# value in the path from LCA to a ` `    ``min1, max1 ``=` `float``(``'inf'``), ``float``(``'-inf'``) ` ` `  `    ``# To store the minimum and the maximum  ` `    ``# value in the path from LCA to b ` `    ``min2, max2 ``=` `float``(``'inf'``), ``float``(``'-inf'``) ` `     `  `    ``i, j ``=` `0``, ``0` `     `  `    ``# If both a and b are present in the tree ` `    ``if` `(FindPath(root, Path1, a) ``and`  `        ``FindPath(root, Path2, b)):  ` ` `  `        ``# Compare the paths to get the  ` `        ``# first different value ` `        ``while` `i < ``len``(Path1) ``and` `i < ``len``(Path2): ` `            ``if` `Path1[i] !``=` `Path2[i]: ` `                ``break` `            ``i ``+``=` `1` `             `  `        ``i ``-``=` `1` `        ``j ``=` `i ` ` `  `        ``# Find minimum and maximum value ` `        ``# in the path from LCA to a ` `        ``while` `i < ``len``(Path1):  ` `            ``if` `min1 > Path1[i]: ` `                ``min1 ``=` `Path1[i] ` `            ``if` `max1 < Path1[i]: ` `                ``max1 ``=` `Path1[i] ` `            ``i ``+``=` `1` `         `  `        ``# Find minimum and maximum value ` `        ``# in the path from LCA to b ` `        ``while` `j < ``len``(Path2):  ` `            ``if` `min2 > Path2[j]: ` `                ``min2 ``=` `Path2[j] ` `            ``if` `max2 < Path2[j]: ` `                ``max2 ``=` `Path2[j] ` `            ``j ``+``=` `1` `         `  `        ``# Minimum of min values in first ` `        ``# path and second path ` `        ``print``(``"Min ="``, ``min``(min1, min2)) ` ` `  `        ``# Maximum of max values in first ` `        ``# path and second path ` `        ``print``(``"Max ="``, ``max``(max1, max2)) ` `     `  `    ``# If no path exists ` `    ``else``: ` `        ``print``(``"Min = -1\nMax = -1"``) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``root ``=` `Node(``20``) ` `    ``root.left ``=` `Node(``8``) ` `    ``root.right ``=` `Node(``22``) ` `    ``root.left.left ``=` `Node(``5``) ` `    ``root.left.right ``=` `Node(``3``) ` `    ``root.right.left ``=` `Node(``4``) ` `    ``root.right.right ``=` `Node(``25``) ` `    ``root.left.right.left ``=` `Node(``10``) ` `    ``root.left.right.right ``=` `Node(``14``) ` ` `  `    ``a, b ``=` `5``, ``14` ` `  `    ``minMaxNodeInPath(root, a, b) ` ` `  `# This code is contributed by Rituraj Jain `

Output:
```Min = 3
Max = 14
```

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Improved By : rituraj_jain

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