docs(divide-and-conquer): add structured README with concepts, complexity analysis, and problem coverage

Author: PavithraSharma14

15-divide-and-conquer/README.md

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+# 📘 Divide and Conquer (Folder 15)
+
+## 🧠 Overview
+Divide and Conquer is a problem-solving paradigm where a problem is:
+1. Divided into smaller subproblems  
+2. Solved recursively  
+3. Combined to get the final result  
+
+This approach is efficient for sorting, searching, and optimization problems.
+
+---
+
+## 📌 Topics Covered
+
+### 🔹 Sorting Algorithms
+- Merge Sort (Basic Implementation)
+- Merge Sort (Space Optimized)
+- Quick Sort
+
+### 🔹 Searching Technique
+- Search in Sorted and Rotated Array
+
+### 🔹 Analysis
+- Worst Case Analysis of Quick Sort
+
+### 🔹 Practice Problems
+- Additional problems  
+
+---
+
+## ⚡ Time & Space Complexity
+
+| Algorithm   | Best Case   | Average Case | Worst Case  | Space Complexity |
+|------------|------------|-------------|-------------|------------------|
+| Merge Sort | O(n log n) | O(n log n)  | O(n log n)  | O(n)             |
+| Quick Sort | O(n log n) | O(n log n)  | O(n^2)      | O(log n)         |
+
+---
+
+## 🔍 Key Concepts
+
+### ✅ Merge Sort
+- Stable sorting algorithm  
+- Uses extra space for merging  
+- Guaranteed O(n log n) performance  
+
+### ✅ Quick Sort
+- In-place sorting algorithm  
+- Faster in practice  
+- Performance depends on pivot selection  
+
+### ⚠️ Worst Case in Quick Sort
+Occurs when:
+- Array is already sorted  
+- Pivot is always smallest or largest  
+
+Result:
+- Time Complexity becomes O(n^2)  
+
+Optimization:
+- Random pivot  
+- Median-of-three  
+
+---
+
+## 🔁 Search in Rotated Sorted Array
+- Uses modified binary search  
+- One half of the array is always sorted  
+- Time Complexity: O(log n)  
+
+---
+
+## 🧪 Practice Focus
+- Strengthen recursion + divide and conquer thinking  
+- Improve problem-solving skills  
+- Understand optimization techniques  
+
+---
+
+## 🚨 Important Notes
+- Merge Sort is stable, Quick Sort is not  
+- Merge Sort uses extra memory, Quick Sort is in-place  
+- Algorithm choice depends on constraints  
+
+---
+
+## 📂 File Structure
+
+```
+15_divide_and_conquer/
+├── MergeSortBasic.java
+├── MergeSortOptimized.java
+├── QuickSort.java
+├── SearchInRotatedSortedArray.java
+├── PracticeProblems.java
+└── README.md
+```
+
+---
+
+## 🎯 Goal
+- Build strong understanding of Divide and Conquer  
+- Write clean and optimized code  
+- Prepare for interview-level problems  
+
+---
+
+## 📌 Final Takeaway
+Divide and Conquer is about breaking complex problems into smaller parts and solving them efficiently.