What is the optimal time complexity of solving Addition of two fractions?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Addition of two fractions?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Addition of two fractions?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Addition of two fractions?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Addition of two fractions

Learn how to solve the 'Addition of two fractions' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function add_fractions(a, b, c, d) that takes four integers representing two fractions a/b and c/d, and returns the result as a tuple (numerator, denominator) in its simplest form (reduced by GCD).

The formula for adding fractions is: a/b + c/d = (a*d + b*c) / (b*d), then simplify by dividing both numerator and denominator by their GCD.

Constraints

•1 <= b, d <= 1000
•-1000 <= a, c <= 1000
•b and d are not zero

Examples

Example 1

Input

add_fractions(1, 2, 1, 3)

Output

(5, 6)

Explanation

1/2 + 1/3 = (1×3 + 2×1) / (2×3) = 5/6. GCD(5,6) = 1, so result is 5/6.

Example 2

Input

add_fractions(2, 4, 3, 6)

Output

(1, 1)

Explanation

2/4 + 3/6 = (2×6 + 4×3) / (4×6) = 24/24 = 1/1.

Example 3

Input

add_fractions(1, 3, 2, 3)

Output

(1, 1)

Explanation

1/3 + 2/3 = 3/3 = 1/1.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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