Adding The Article On Binary Search Questions

docs/binary-search/binary_search_questions.md

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+---
+id: binary-search-dsa
+sidebar_position: 10
+title: Binary Search
+sidebar_label: Binary Search
+description: "In this blog post, we'll dive into the binary search algorithm, a fundamental technique in computer science for efficiently finding an element in a sorted array."
+tags: [dsa, algorithms, binary search]
+---
+
+# Binary Search Patterns: A Comprehensive Guide
+
+Welcome to this in-depth exploration of binary search patterns! This guide is designed to help you master the art of binary search through a curated collection of problems, explanations, and real-world applications.
+
+
+## Introduction to Binary Search
+
+Binary search is a fundamental algorithm in computer science that efficiently locates an element in a sorted array. By repeatedly dividing the search interval in half, binary search achieves a time complexity of O(log n), making it significantly faster than linear search for large datasets.
+
+## Why Master Binary Search?
+
+Understanding binary search is crucial for several reasons:
+
+1. **Efficiency**: Binary search reduces time complexity from O(n) to O(log n), essential for working with large datasets.
+2. **Versatility**: The core concept of dividing the search space applies to various problem types, from simple searches to complex optimization problems.
+3. **Problem-Solving Skills**: Mastering binary search enhances your ability to think algorithmically and approach problems systematically.
+4. **Interview Preparation**: Binary search is a popular topic in technical interviews, appearing in questions from leading tech companies.
+5. **Foundation for Advanced Algorithms**: Many advanced algorithms and data structures build upon the principles of binary search.
+
+## Binary Search Patterns
+
+### Pattern 1: Binary Search on 1D Arrays
+
+This pattern focuses on applying binary search to one-dimensional sorted arrays. It covers:
+
+- Basic binary search implementation
+- Finding boundaries (first/last occurrences)
+- Searching in rotated sorted arrays
+- Finding peak elements
+
+**Key Techniques**:
+- Modifying search conditions
+- Handling duplicate elements
+- Identifying search spaces in modified arrays
+
+### Pattern 2: Binary Search on Answer Space
+
+This pattern applies binary search to a range of possible answers rather than a specific array. It's useful for:
+
+- Optimization problems
+- Finding roots of equations
+- Minimizing/maximizing values subject to constraints
+
+**Key Techniques**:
+- Defining a feasible answer range
+- Creating a condition to check answer validity
+- Adjusting the search space based on the condition
+
+### Pattern 3: Binary Search on 2D Arrays
+
+This pattern extends binary search to two-dimensional arrays or matrices. It covers:
+
+- Searching in row-wise and column-wise sorted matrices
+- Finding peak elements in 2D arrays
+- Calculating matrix medians
+
+**Key Techniques**:
+- Treating 2D arrays as flattened 1D arrays
+- Utilizing properties of sorted rows/columns
+- Combining binary search with other techniques (e.g., merge)
+
+## Problem Collections
+
+### Pattern 1: Binary Search on 1D Arrays
+
+| Problem | Difficulty | Practice Link | Explanation |
+|---------|------------|---------------|-------------|
+| Binary Search | Easy | [LeetCode](https://leetcode.com/problems/binary-search/) | [Explanation](https://takeuforward.org/data-structure/binary-search-explained/) |
+| Implement Lower Bound | Easy | [GeeksforGeeks](https://www.geeksforgeeks.org/problems/floor-in-a-sorted-array-1587115620/1) | [Explanation](https://takeuforward.org/arrays/implement-lower-bound-bs-2/) |
+| Search in Rotated Sorted Array | Medium | [LeetCode](https://leetcode.com/problems/search-in-rotated-sorted-array/) | [Explanation](https://takeuforward.org/data-structure/search-element-in-a-rotated-sorted-array/) |
+| Find Minimum in Rotated Sorted Array | Medium | [LeetCode](https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/) | [Explanation](https://takeuforward.org/data-structure/minimum-in-rotated-sorted-arrayy) |
+
+### Pattern 2: Binary Search on Answer Space
+
+| Problem | Difficulty | Practice Link | Explanation |
+|---------|------------|---------------|-------------|
+| Koko Eating Bananas | Medium | [LeetCode](https://leetcode.com/problems/koko-eating-bananas/) | [Explanation](https://takeuforward.org/binary-search/koko-eating-bananas/) |
+| Find the Smallest Divisor | Medium | [LeetCode](https://leetcode.com/problems/find-the-smallest-divisor-given-a-threshold/) | [Explanation](https://takeuforward.org/arrays/find-the-smallest-divisor-given-a-threshold/) |
+| Aggressive Cows | Hard | [GeeksforGeeks](https://www.geeksforgeeks.org/problems/aggressive-cows/0) | [Explanation](https://takeuforward.org/data-structure/aggressive-cows-detailed-solution/) |
+| Median of Two Sorted Arrays | Hard | [LeetCode](https://leetcode.com/problems/median-of-two-sorted-arrays/) | [Explanation](https://takeuforward.org/data-structure/median-of-two-sorted-arrays-of-different-sizes) |
+
+### Pattern 3: Binary Search on 2D Arrays
+
+| Problem | Difficulty | Practice Link | Explanation |
+|---------|------------|---------------|-------------|
+| Search a 2D Matrix | Medium | [LeetCode](https://leetcode.com/problems/search-a-2d-matrix/) | [Explanation](https://takeuforward.org/data-structure/search-in-a-sorted-2d-matrix/) |
+| Find Peak Element II | Hard | [LeetCode](https://leetcode.com/problems/find-a-peak-element-ii) | Not Available |
+| Matrix Median | Hard | [InterviewBit](https://www.interviewbit.com/problems/matrix-median/) | [Explanation](https://takeuforward.org/data-structure/median-of-row-wise-sorted-matrix/) |
+
+## Real-World Applications
+
+Binary search and its patterns find applications in various real-world scenarios:
+
+1. **Database Systems**: Efficient data retrieval in sorted indexes.
+2. **Machine Learning**: Hyperparameter tuning and model selection.
+3. **Computer Graphics**: Collision detection in video games and simulations.
+4. **Network Routing**: Finding optimal paths in network topologies.
+5. **Version Control**: Identifying commits in large repositories (e.g., git bisect).
+6. **Resource Allocation**: Optimizing resource distribution in cloud computing.
+7. **Financial Analysis**: Finding breakeven points or optimal investment strategies.
+
+## Benefits of Mastering Binary Search
+
+By working through these problems and understanding the patterns, you'll gain:
+
+1. **Improved Problem-Solving Skills**: Develop a systematic approach to breaking down complex problems.
+2. **Enhanced Algorithmic Thinking**: Learn to identify opportunities for optimization in various scenarios.
+3. **Interview Readiness**: Build confidence in tackling a wide range of coding challenges.
+4. **Efficiency Mindset**: Cultivate an intuition for designing efficient algorithms in your daily coding tasks.
+5. **Foundation for Advanced Topics**: Prepare yourself for more complex algorithmic concepts and data structures.
+
+## How to Use This Guide
+
+1. Start with the basic binary search implementation in Pattern 1.
+2. Progress through each pattern, solving problems of increasing difficulty.
+3. For each problem:
+   - Attempt to solve it independently.
+   - If stuck, refer to the provided explanation.
+   - After solving, compare your solution with the optimal approach.
+4. Reflect on the patterns and techniques used in each problem.
+5. Try to apply these patterns to new, unseen problems to reinforce your learning.
+
+