Find the node with minimum value in a Binary Search Tree
Write a function to find the node with minimum value in a Binary Search Tree.
Example:
Input:
first example BST
Output: 8
Input:
second example BST
Output: 10
Approach: To solve the problem follow the below idea:
This is quite simple. Just traverse the node from root to left recursively until left is NULL. The node whose left is NULL is the node with minimum value
Below is the implementation of the above approach:
C++
// C++ program to find minimum value node in binary search // Tree. #include <bits/stdc++.h> using namespace std; /* A binary tree node has data, pointer to left child and a pointer to right child */ struct node { int data; struct node* left; struct node* right; }; /* Helper function that allocates a new node with the given data and NULL left and right pointers. */ struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } /* Give a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). */ struct node* insert( struct node* node, int data) { /* 1. If the tree is empty, return a new, single node */ if (node == NULL) return (newNode(data)); else { /* 2. Otherwise, recur down the tree */ if (data <= node->data) node->left = insert(node->left, data); else node->right = insert(node->right, data); /* return the (unchanged) node pointer */ return node; } } /* Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. */ int minValue( struct node* node) { struct node* current = node; /* loop down to find the leftmost leaf */ while (current->left != NULL) { current = current->left; } return (current->data); } /* Driver Code*/ int main() { struct node* root = NULL; root = insert(root, 4); insert(root, 2); insert(root, 1); insert(root, 3); insert(root, 6); insert(root, 5); // Function call cout << "\n Minimum value in BST is " << minValue(root); getchar (); return 0; } // This code is contributed by Mukul Singh. |
C
// C program to find minimum value node in binary search // Tree. #include <stdio.h> #include <stdlib.h> /* A binary tree node has data, pointer to left child and a pointer to right child */ struct node { int data; struct node* left; struct node* right; }; /* Helper function that allocates a new node with the given data and NULL left and right pointers. */ struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } /* Give a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). */ struct node* insert( struct node* node, int data) { /* 1. If the tree is empty, return a new, single node */ if (node == NULL) return (newNode(data)); else { /* 2. Otherwise, recur down the tree */ if (data <= node->data) node->left = insert(node->left, data); else node->right = insert(node->right, data); /* return the (unchanged) node pointer */ return node; } } /* Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. */ int minValue( struct node* node) { struct node* current = node; /* loop down to find the leftmost leaf */ while (current->left != NULL) { current = current->left; } return (current->data); } /* Driver code*/ int main() { struct node* root = NULL; root = insert(root, 4); insert(root, 2); insert(root, 1); insert(root, 3); insert(root, 6); insert(root, 5); // Function call printf ( "\n Minimum value in BST is %d" , minValue(root)); getchar (); return 0; } |
Java
// Java program to find minimum value node in Binary Search // Tree // A binary tree node class Node { int data; Node left, right; Node( int d) { data = d; left = right = null ; } } class BinaryTree { static Node head; /* Given a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). */ Node insert(Node node, int data) { /* 1. If the tree is empty, return a new, single node */ if (node == null ) { return ( new Node(data)); } else { /* 2. Otherwise, recur down the tree */ if (data <= node.data) { node.left = insert(node.left, data); } else { node.right = insert(node.right, data); } /* return the (unchanged) node pointer */ return node; } } /* Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. */ int minvalue(Node node) { Node current = node; /* loop down to find the leftmost leaf */ while (current.left != null ) { current = current.left; } return (current.data); } // Driver code public static void main(String[] args) { BinaryTree tree = new BinaryTree(); Node root = null ; root = tree.insert(root, 4 ); tree.insert(root, 2 ); tree.insert(root, 1 ); tree.insert(root, 3 ); tree.insert(root, 6 ); tree.insert(root, 5 ); // Function call System.out.println( "Minimum value of BST is " + tree.minvalue(root)); } } // This code is contributed by Mayank Jaiswal |
Python3
# Python3 program to find the node with minimum value in bst # A binary tree node class Node: # Constructor to create a new node def __init__( self , key): self .data = key self .left = None self .right = None """ Give a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). """ def insert(node, data): # 1. If the tree is empty, return a new, # single node if node is None : return (Node(data)) else : # 2. Otherwise, recur down the tree if data < = node.data: node.left = insert(node.left, data) else : node.right = insert(node.right, data) # Return the (unchanged) node pointer return node """ Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. """ def minValue(node): current = node # loop down to find the leftmost leaf while (current.left is not None ): current = current.left return current.data # Driver code if __name__ = = '__main__' : root = None root = insert(root, 4 ) insert(root, 2 ) insert(root, 1 ) insert(root, 3 ) insert(root, 6 ) insert(root, 5 ) # Function call print ( "\nMinimum value in BST is %d" % (minValue(root))) # This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
C#
// C# program to find minimum value node in Binary Search // Tree using System; // C# program to find minimum value node in Binary Search // Tree // A binary tree node public class Node { public int data; public Node left, right; public Node( int d) { data = d; left = right = null ; } } public class BinaryTree { public static Node head; /* Given a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). */ public virtual Node insert(Node node, int data) { /* 1. If the tree is empty, return a new, single node */ if (node == null ) { return ( new Node(data)); } else { /* 2. Otherwise, recur down the tree */ if (data <= node.data) { node.left = insert(node.left, data); } else { node.right = insert(node.right, data); } /* return the (unchanged) node pointer */ return node; } } /* Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. */ public virtual int minvalue(Node node) { Node current = node; /* loop down to find the leftmost leaf */ while (current.left != null ) { current = current.left; } return (current.data); } // Driver code public static void Main( string [] args) { BinaryTree tree = new BinaryTree(); Node root = null ; root = tree.insert(root, 4); tree.insert(root, 2); tree.insert(root, 1); tree.insert(root, 3); tree.insert(root, 6); tree.insert(root, 5); // Function call Console.WriteLine( "Minimum value of BST is " + tree.minvalue(root)); } } // This code is contributed by Shrikant13 |
PHP
<?php // PHP program to find the node with // minimum value in bst // create a binary tree class node { private $node , $left , $right ; function __construct( $node ) { $this ->node = $node ; $left = $right = NULL; } // set the left node in tree function set_left( $left ) { $this ->left = $left ; } // set the right node in tree function set_right( $right ) { $this ->right = $right ; } // get left node function get_left() { return $this ->left; } // get right node function get_right() { return $this ->right; } // get value of current node function get_node() { return $this ->node; } } // Find the node with minimum value // in a Binary Search Tree function get_minimum_value( $node ) { /*travel till last left node to get the minimum value*/ while ( $node ->get_left() != NULL) { $node = $node ->get_left(); } return $node ->get_node(); } // code to creating a tree $node = new node(4); $lnode = new node(2); $lnode ->set_left( new node(1)); $lnode ->set_right( new node(3)); $rnode = new node(6); $rnode ->set_left( new node(5)); $node ->set_left( $lnode ); $node ->set_right( $rnode ); $minimum_value = get_minimum_value( $node ); echo 'Minimum value of BST is ' . $minimum_value ; // This code is contributed // by Deepika Pathak ?> |
Javascript
<script> // JavaScript program to find minimum // value node in Binary Search Tree class Node { constructor(data) { this .left = null ; this .right = null ; this .data = data; } } let head; /* Given a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the caller should then use (the standard trick to avoid using reference parameters). */ function insert(node, data) { /* 1. If the tree is empty, return a new, single node */ if (node == null ) { return ( new Node(data)); } else { /* 2. Otherwise, recur down the tree */ if (data <= node.data) { node.left = insert(node.left, data); } else { node.right = insert(node.right, data); } /* return the (unchanged) node pointer */ return node; } } /* Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree does not need to be searched. */ function minvalue(node) { if (node === null ) return null ; let current = node; /* loop down to find the leftmost leaf */ while (current.left != null ) { current = current.left; } return (current.data); } let root = null ; root = insert(root, 4); insert(root, 2); insert(root, 1); insert(root, 3); insert(root, 6); insert(root, 5); document.write( "Minimum value in BST is " + minvalue(root)); </script> |
Output
Minimum value in BST is 1
Time Complexity: O(Height of the BST)
Auxiliary Space: O(1)
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