# 530. Minimum Absolute Difference in BST

## Description

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

Example 1:

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


Example 2:

Input: root = [1,0,48,null,null,12,49]
Output: 1


Constraints:

• The number of nodes in the tree is in the range [2, 104].
• 0 <= Node.val <= 105

Note: This question is the same as 783: https://leetcode.com/problems/minimum-distance-between-bst-nodes/

## Solutions

• /**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode() {}
*     TreeNode(int val) { this.val = val; }
*     TreeNode(int val, TreeNode left, TreeNode right) {
*         this.val = val;
*         this.left = left;
*         this.right = right;
*     }
* }
*/
class Solution {
private int ans;
private int prev;
private int inf = Integer.MAX_VALUE;

public int getMinimumDifference(TreeNode root) {
ans = inf;
prev = inf;
dfs(root);
return ans;
}

private void dfs(TreeNode root) {
if (root == null) {
return;
}
dfs(root.left);
ans = Math.min(ans, Math.abs(root.val - prev));
prev = root.val;
dfs(root.right);
}
}

• /**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode() : val(0), left(nullptr), right(nullptr) {}
*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
const int inf = INT_MAX;
int ans;
int prev;

int getMinimumDifference(TreeNode* root) {
ans = inf, prev = inf;
dfs(root);
return ans;
}

void dfs(TreeNode* root) {
if (!root) return;
dfs(root->left);
ans = min(ans, abs(prev - root->val));
prev = root->val;
dfs(root->right);
}
};

• # Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
def getMinimumDifference(self, root: TreeNode) -> int:
def dfs(root):
if root is None:
return
dfs(root.left)
nonlocal ans, prev
ans = min(ans, abs(prev - root.val))
prev = root.val
dfs(root.right)

ans = prev = inf
dfs(root)
return ans


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func getMinimumDifference(root *TreeNode) int {
inf := 0x3f3f3f3f
ans, prev := inf, inf
var dfs func(*TreeNode)
dfs = func(root *TreeNode) {
if root == nil {
return
}
dfs(root.Left)
ans = min(ans, abs(prev-root.Val))
prev = root.Val
dfs(root.Right)
}
dfs(root)
return ans
}

func abs(x int) int {
if x < 0 {
return -x
}
return x
}

• // Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//     TreeNode {
//       val,
//       left: None,
//       right: None
//     }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
pub fn get_minimum_difference(root: Option<Rc<RefCell<TreeNode>>>) -> i32 {
let mut ret = i32::MAX;
let mut prev = i32::MAX;
Self::traverse(root, &mut prev, &mut ret);
ret
}

fn traverse(root: Option<Rc<RefCell<TreeNode>>>, prev: &mut i32, ans: &mut i32) {
let left = root.as_ref().unwrap().borrow().left.clone();
let right = root.as_ref().unwrap().borrow().right.clone();
let val = root.as_ref().unwrap().borrow().val;
if !left.is_none() {
Self::traverse(left.clone(), prev, ans);
}
*ans = std::cmp::min(*ans, (*prev - val).abs());
*prev = val;
if !right.is_none() {
Self::traverse(right.clone(), prev, ans);
}
}
}


• /**
* Definition for a binary tree node.
* class TreeNode {
*     val: number
*     left: TreeNode | null
*     right: TreeNode | null
*     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
*         this.val = (val===undefined ? 0 : val)
*         this.left = (left===undefined ? null : left)
*         this.right = (right===undefined ? null : right)
*     }
* }
*/
function getMinimumDifference(root: TreeNode | null): number {
if (!root) return 0;

let prev = Number.MIN_SAFE_INTEGER;
let min = Number.MAX_SAFE_INTEGER;

const dfs = (node: TreeNode | null) => {
if (!node) return;

dfs(node.left);
min = Math.min(min, node.val - prev);
prev = node.val;
dfs(node.right);
};

dfs(root);

return min;
}


• /**
* Definition for a binary tree node.
* function TreeNode(val, left, right) {
*     this.val = (val===undefined ? 0 : val)
*     this.left = (left===undefined ? null : left)
*     this.right = (right===undefined ? null : right)
* }
*/
/**
* @param {TreeNode} root
* @return {number}
*/
var getMinimumDifference = function (root) {
let [ans, pre] = [Infinity, -Infinity];
const dfs = root => {
if (!root) {
return;
}
dfs(root.left);
ans = Math.min(ans, root.val - pre);
pre = root.val;
dfs(root.right);
};
dfs(root);
return ans;
};