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Find the node with minimum value in a Binary Search Tree

  • Difficulty Level : Basic
  • Last Updated : 05 Jul, 2021

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. 
 

BST_LCA

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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 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 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 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 lefmost leaf
    while(current.left is not None):
        current = current.left
 
    return current.data
 
# Driver program
root = None
root = 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 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) {
        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(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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