Find the node with minimum value in a Binary Search Tree

1.3

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

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

#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("The minimum value of BST is " + tree.minvalue(root));
    }
}

// This code has been 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)



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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