LeetCode 530: Minimum Absolute Difference in BST — Python Solution

Solve LeetCode 530: Minimum Absolute Difference in BST in Python with a inorder adjacent difference approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Inorder traversal visits BST values in sorted order, so the minimum absolute difference appears between adjacent visited values.

Algorithm

1. Inorder traversal visits BST values in sorted order, so the minimum absolute difference appears between adjacent visited values.
2. Maintain this invariant: prev is the greatest value visited before the current node.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def getMinimumDifference(self, root):
        previous, best = None, float("inf")
        def inorder(node):
            nonlocal previous, best
            if not node: return
            inorder(node.left)
            if previous is not None: best = min(best, node.val - previous)
            previous = node.val
            inorder(node.right)
        inorder(root)
        return best

Why this is correct

The proof follows the maintained state: prev is the greatest value visited before the current node. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(h) recursion space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Initialize without a numeric sentinel so negative values are safe.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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