# Algorithm to find Minimum Distance Between BST (binary search tree) Nodes

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Given a Binary Search Tree (BST) with the root node root, return the minimum difference between the values of any two different nodes in the tree.

Example :

Input: root = [4,2,6,1,3,null,null]

Output: 1

Explanation:

Note that root is a TreeNode object, not an array.

The given tree [4,2,6,1,3,null,null] is represented by the following diagram:

4

/   \

2      6

/ \

1   3

while the minimum difference in this tree is 1, it occurs between node 1 and node 2, also between node 3 and node 2.

Note:

1. The size of the BST will be between 2 and 100.
2. The BST is always valid, each node’s value is an integer, and each node’s value is different.

0
• Traverse the tree using tree traversal algorithm for e.g. inorder
• Push all the traversed nodes in an array.
• Sort the array
• Find the minimum difference between array elements by looping through

Javascript code below:-

/**
* Definition for a binary tree node.
* function TreeNode(val) {
*     this.val = val;
*     this.left = this.right = null;
* }
*/
/**
* @param {TreeNode} root
* @return {number}
*/
var minDiffInBST = function(root) {
var arr = [];
inorder(root, arr);
arr.sort((a,b)=>a-b);
var minDiff = Number.MAX_SAFE_INTEGER;
var result = [];
var map = {};
for (var i = 0; i < arr.length; i++) {
if (typeof map[arr[i]] === 'undefined') {
map[arr[i]] = arr[i];
}
if (i < arr.length - 1 && Math.abs(arr[i+1] - arr[i]) < minDiff) {
minDiff = arr[i+1] - arr[i];
}
}
return minDiff;
};
var inorder = function(root, arr) {
if (root) {
inorder(root.left, arr);
arr.push(root.val);
inorder(root.right, arr);
}
}

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