37.Rectangular Love

📌 Interview Cake: Rectangular Love (37. Rectangular-Love)

• Source: Interview Cake Masterclass
• Category: Math & Geometry
• Recommended Complexity: Time: $\mathcal{O}(N)$ | Space: $\mathcal{O}(N)$
• C# Project File: 37.Rectangular-Love.csproj
• C# Source Code: Program.cs
• Shared Runner Library: DSA.Common

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📋 Problem Statement & Gotchas

Implement the solution for Rectangular Love. Given the problem inputs, return the expected target output.

WARNING

Gotcha / Initial Thought Trap: Consider edge cases such as empty input collections, negative inputs, large array bounds, or duplicate values.

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💡 Step-by-Step Breakdown & Hints

TIP

• Hint 1: What is the naive solution? (Brute force approach).
• Hint 2: Can we do it in a single pass using a greedy approach or hash table?
• Hint 3: Pay special attention to keeping track of min/max values as we iterate through the dataset.

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🏋️ Space to Practice

📝 Step-by-Step Self-Solving Framework

1. Understand Goal: Identify primary objective and constraints.
2. Brainstorm Approaches: Compare brute force vs greedy / hash table.
3. Draft Pseudocode:

   // Write your thought process and pseudocode here...

💻 My C# Code Scratchpad

public static string UserSolution(string input)
{
    // Write your solution here!
    return "TODO";
}

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🧪 Test Cases & Benchmark Matrix

Case #	Input	Expected Output	Type	Target Time	Target Memory
1	Sample 1	Expected 1	Standard Case	$<1\text{ ms}$	Minimal
2	Sample 2	Expected 2	Standard Case	$<1\text{ ms}$	Minimal

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💡 Multi-Solution Analysis (Deep Step-by-Step Explanations)

Approach 1: Optimal Solution ⭐

Intuition & Concept

Detailed strategy explanation for solving Rectangular Love.

Step-by-Step Solving Logic

1. Step 1: Parse input boundaries.
2. Step 2: Maintain running variables in a single pass.
3. Step 3: Return optimal result.

C# Source Code

public static string Reference_Optimal(string input)
{
    return "TODO";
}

Complexity Analysis

• Time Complexity: $\mathcal{O}(N)$
• Space Complexity: $\mathcal{O}(1)$

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🛠️ What We Learned & Key Takeaways

1. Greedy / Single-Pass Strategy:
   • Building the solution incrementally while tracking state variables avoids nested loops.
2. Shared Benchmarking:
   • Use DSA.Common.DsaTestRunner to measure execution time (ms) and thread memory allocations (Bytes) automatically!