Leetcode #972: Equal Rational Numbers

In this guide, we solve Leetcode #972 Equal Rational Numbers in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

Given two strings s and t, each of which represents a non-negative rational number, return true if and only if they represent the same number. The strings may use parentheses to denote the repeating part of the rational number.

Quick Facts

• Difficulty: Hard
• Premium: No
• Tags: Math, String

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

• Identify the math relationship.
• Compute the result with a loop or formula.
• Handle edge cases.

Example

Python Solution

Complexity

The time complexity is O(n) or O(1). The space complexity is O(1).

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.