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
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++
// C++ implementation of the approach #include <bits/stdc++.h> 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; } |
Java
// Java implementation of the approach import java.util.*; class GFG { // Structure of binary tree static class Node { Node left; Node right; int data; }; // Function to create a new node static Node newNode( int key) { Node node = new Node(); node.left = node.right = null ; node.data = key; return node; } static Vector<Integer> path; // 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 static boolean FindPath(Node root, int key) { if (root == null ) return false ; path.add(root.data); if (root.data == key) return true ; if (FindPath(root.left, key) || FindPath(root.right, key)) return true ; path.remove(path.size()- 1 ); 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 static int minMaxNodeInPath(Node root, int a, int b) { // To store the path from the root node to a path = new Vector<Integer> (); boolean flag = true ; // To store the path from the root node to b Vector<Integer> Path2 = new Vector<Integer>(), Path1 = new Vector<Integer>(); // To store the minimum and the maximum value // in the path from LCA to a int min1 = Integer.MAX_VALUE; int max1 = Integer.MIN_VALUE; // To store the minimum and the maximum value // in the path from LCA to b int min2 = Integer.MAX_VALUE; int max2 = Integer.MIN_VALUE; int i = 0 ; int j = 0 ; flag = FindPath(root, a); Path1 = path; path = new Vector<Integer>(); flag&= FindPath(root, b); Path2 = path; // If both a and b are present in the tree if ( flag) { // Compare the paths to get the first different value for (i = 0 ; i < Path1.size() && i < Path2.size(); i++) if (Path1.get(i) != Path2.get(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.get(i)) min1 = Path1.get(i); if (max1 < Path1.get(i)) max1 = Path1.get(i); } // Find minimum and maximum value // in the path from LCA to b for (; j < Path2.size(); j++) { if (min2 > Path2.get(j)) min2 = Path2.get(j); if (max2 < Path2.get(j)) max2 = Path2.get(j); } // Minimum of min values in first // path and second path System.out.println( "Min = " + Math.min(min1, min2) ); // Maximum of max values in first // path and second path System.out.println( "Max = " + Math.max(max1, max2)); } // If no path exists else System.out.println( "Min = -1\nMax = -1" ); return 0 ; } // Driver Code public static void main(String args[]) { 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 = 14 ; minMaxNodeInPath(root, a, b); } } // This code is contributed by Arnab Kundu |
Python3
# 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 |
C#
// C# implementation of the approach using System; using System.Collections; class GFG{ // Structure of binary tree class Node { public Node left; public Node right; public int data; }; // Function to create a new node static Node newNode( int key) { Node node = new Node(); node.left = node.right = null ; node.data = key; return node; } static ArrayList path; // 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 static bool FindPath(Node root, int key) { if (root == null ) return false ; path.Add(root.data); if (root.data == key) return true ; if (FindPath(root.left, key) || FindPath(root.right, key)) return true ; path.Remove(( int )path[path.Count - 1]); 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 static int minMaxNodeInPath(Node root, int a, int b) { // To store the path from the root node to a path = new ArrayList(); bool flag = true ; // To store the path from the root node to b ArrayList Path2 = new ArrayList(); ArrayList Path1 = new ArrayList(); // To store the minimum and the maximum value // in the path from LCA to a int min1 = Int32.MaxValue; int max1 = Int32.MinValue; // To store the minimum and the maximum value // in the path from LCA to b int min2 = Int32.MaxValue; int max2 = Int32.MinValue; int i = 0; int j = 0; flag = FindPath(root, a); Path1 = path; path = new ArrayList(); flag &= FindPath(root, b); Path2 = path; // If both a and b are present in the tree if (flag) { // Compare the paths to get the // first different value for (i = 0; i < Path1.Count && i < Path2.Count; i++) if (( int )Path1[i] != ( int )Path2[i]) break ; i--; j = i; // Find minimum and maximum value // in the path from LCA to a for (; i < Path1.Count; i++) { if (min1 > ( int )Path1[i]) min1 = ( int )Path1[i]; if (max1 < ( int )Path1[i]) max1 = ( int )Path1[i]; } // Find minimum and maximum value // in the path from LCA to b for (; j < Path2.Count; j++) { if (min2 > ( int )Path2[j]) min2 = ( int )Path2[j]; if (max2 < ( int )Path2[j]) max2 = ( int )Path2[j]; } // Minimum of min values in first // path and second path Console.Write( "Min = " + Math.Min(min1, min2) + "\n" ); // Maximum of max values in first // path and second path Console.Write( "Max = " + Math.Max(max1, max2) + "\n" ); } // If no path exists else Console.Write( "Min = -1\nMax = -1" ); return 0; } // Driver Code public static void Main( string []arg) { 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 = 14; minMaxNodeInPath(root, a, b); } } // This code is contributed by rutvik_56 |
Javascript
<script> // JavaScript implementation of the approach // Structure of binary tree class Node { constructor(key) { this .left = null ; this .right = null ; this .data = key; } } // Function to create a new node function newNode(key) { let node = new Node(key); return node; } let path = []; // 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 function FindPath(root, key) { if (root == null ) return false ; path.push(root.data); if (root.data == key) return true ; if (FindPath(root.left, key) || FindPath(root.right, 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 function minMaxNodeInPath(root, a, b) { // To store the path from the root node to a path = []; let flag = true ; // To store the path from the root node to b let Path2 = [], Path1 = []; // To store the minimum and the maximum value // in the path from LCA to a let min1 = Number.MAX_VALUE; let max1 = Number.MIN_VALUE; // To store the minimum and the maximum value // in the path from LCA to b let min2 = Number.MAX_VALUE; let max2 = Number.MIN_VALUE; let i = 0; let j = 0; flag = FindPath(root, a); Path1 = path; path = []; flag&= FindPath(root, b); Path2 = path; // If both a and b are present in the tree if ( flag) { // Compare the paths to get the first different value for (i = 0; i < Path1.length && i < Path2.length; 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.length; 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.length; 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 document.write( "Min = " + Math.min(min1, min2) + "</br>" ); // Maximum of max values in first // path and second path document.write( "Max = " + Math.max(max1, max2) + "</br>" ); } // If no path exists else document.write( "Min = -1\nMax = -1" + "</br>" ); return 0; } let 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); let a = 5; let b = 14; minMaxNodeInPath(root, a, b); </script> |
Output:
Min = 3 Max = 14
Time Complexity: O(N)
Auxiliary Space: O(N)