# Solution: Find Minimum Value in Binary Search Tree

Let’s solve the Find Minimum Value in Binary Search Tree problem.

## Statement

Given the `root`

node of a binary search tree (BST), find and return the minimum value present in the BST.

**Constraints:**

Let `n`

be the number of nodes in a binary search tree.

$0 \leq$ `n`

$\leq500$ $-10^4\leq$ `Node.data`

$\leq10^4$

## Solution 1: Iterative approach

The essence of the algorithm lies in the property of a BST, where the left subtree of a node contains values smaller than the node's value. Therefore, by traversing always to the left child, the algorithm guarantees that it reaches the minimum value node in the BST.

The steps of the algorithm are given below:

If the

`root`

is NULL, return NULL to indicate that the tree is empty.Initialize a

`current`

pointer to the`root`

.Start traversing the tree using

`current`

until`current`

has a left child (i.e.,`current.left`

is not NULL).While traversing the tree, update

`current`

to be its left child:`current = current.left`

. This step effectively moves down the left side of the tree until reaching a leaf node (a node without a left child).When the loop exits (because

`current.left`

is NULL),`current`

points to the leftmost node in the tree. This leftmost node is the node with the minimum value in the BST.

Let’s look at the illustration below to better understand the solution:

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