Find the node with minimum value in a Binary Search Tree
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.
For the above tree, we start with 20, then we move left 8, we keep on moving to left until we see NULL. Since left of 4 is NULL, 4 is the node with minimum value.
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); cout << "\n Minimum value in BST is " << minValue(root); getchar(); return 0; } // This code is contributed by Mukul Singh. |
C
#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 program to test sameTree function*/ 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); 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 nodeclass 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 program to test above functions 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); System.out.println("Minimum value of BST is " + tree.minvalue(root)); }} // This code is contributed by Mayank Jaiswal |
Python
# Python program to find the node with minimum value in bst # A binary tree nodeclass 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 lefmost leaf while(current.left is not None): current = current.left return current.data # Driver programroot = Noneroot = insert(root,4)insert(root,2)insert(root,1)insert(root,3)insert(root,6)insert(root,5) print "\nMinimum value in BST is %d" %(minValue(root)) # This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
C#
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 program to test above functions 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); 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 treeclass 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 $this->node; } } // Find the node with minimum value // in a Binary Search Treefunction get_minimum_value($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?> |
Output:
Minimum value in BST is 1
Time Complexity: O(n) Worst case happens for left skewed trees.
Similarly we can get the maximum value by recursively traversing the right node of a binary search tree.
References:
http://cslibrary.stanford.edu/110/BinaryTrees.html
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