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.
Java Programming
// 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
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.
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