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.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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 
?> 

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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My Personal Notes

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

C

Java

Python

C#

PHP

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