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TASK: Research the Quicksort algorithm and write a robust Python implementation to 'sorting_algo.py'.
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[Agent] Spawning researcher agent for: Research the Quicksort algorithm in detail, including its logic, implementation, and variations.
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-> Searching web: Quicksort algorithm detailed explanation
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-> Searching web: Quicksort implementation and variations
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-> Searching web: Quicksort algorithm implementation in Python
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-> Searching web: Variations of Quicksort with code examples
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-> Searching web: Recent developments or research on Quicksort algorithm
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-> Searching web: Latest research papers or articles on Quicksort algorithm
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-> Reading file: Quicksort_summary.txt
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I have completed the research and synthesis on the Quicksort algorithm, including its logic, implementation, variations, recent trends, and practical considerations. Here is a comprehensive overview:
─────────────────────────────────────────────────────────────────
Complete Overview of Quicksort Algorithm
1. Introduction
Quicksort is a highly efficient, comparison-based sorting algorithm developed by Tony Hoare in 1960. It is widely used due to its average-case performance and in-place sorting capability.
2. Core Logic
• Select a pivot element from the array.
• Partition the array into two sub-arrays:
• Elements less than or equal to the pivot.
• Elements greater than the pivot.
• Recursively apply the same process to the sub-arrays.
• Combine the sorted sub-arrays and the pivot to produce the sorted array.
3. Implementation (In-place Version)
def quicksort(arr, low, high):
if low < high:
p = partition(arr, low, high)
quicksort(arr, low, p - 1)
quicksort(arr, p + 1, high)
def partition(arr, low, high):
pivot = arr[high]
i = low - 1
for j in range(low, high):
if arr[j] <= pivot:
i += 1
arr[i], arr[j] = arr[j], arr[i]
arr[i + 1], arr[high] = arr[high], arr[i + 1]
return i + 1

4. Variations and Optimizations
• Randomized Pivot: Randomly select a pivot to reduce the chance of worst-case performance.
• Median-of-Three: Choose the median of the first, middle, and last elements as pivot for better partitioning.
• Three-way Quicksort: Efficient for arrays with many duplicate elements, dividing into three parts: less than, equal to, and greater than the pivot.
• Hybrid Approaches: Combine Quicksort with Insertion Sort for small subarrays or switch to Heapsort if recursion depth exceeds a threshold (Introsort).
5. Performance and Complexity
| Aspect | Complexity |
|---------|--------------|
| Average case | O(n log n) |
| Worst case | O(n^2) (e.g., sorted data with poor pivot choices) |
| Best case | O(n log n) |
| Space complexity | O(log n) (recursive stack) |
6. Practical Considerations
• Quicksort is in-place, requiring minimal additional memory.
• It is not stable (does not preserve the order of equal elements).
• Widely implemented in standard libraries (e.g., C++ STL, Java).
7. Recent Trends
• Parallel and Distributed Quicksort: Leveraged in multi-core and big data systems.
• Cache-aware implementations: Minimize cache misses for better real-world performance.
• Adaptive algorithms: Hybrid approaches that switch strategies based on data characteristics.
─────────────────────────────────────────────────────────────────
Would you like me to generate a detailed code file with these implementations, or do you need further explanations on specific variations or performance analysis?
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I will now create the Python file sorting_algo.py with a robust implementation of Quicksort, including its main version and variations discussed. I will include comments for clarity and options for different pivot strategies.
Let's proceed to write the file.
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-> Writing file: sorting_algo.py
[parallel] launching write_file
  CHANGES: sorting_algo.py 
LINE OLD | LINE NEW
--------------------------------------------------------------------------------------------------------------------------------------------
1 - def quicksort(arr, low=0, high=None):  |
| 1 + """Robust Quicksort implementation with variations""" 
| 2 + import random 
| 3 +  
| 4 + def quicksort(arr, low=0, high=None, pivot_strategy='last'): 
2 if high is None: | 5 if high is None:
3 high = len(arr) - 1 | 6 high = len(arr) - 1
4 if low < high: | 7 if low < high:
5 -  p = partition(arr, low, high)  |
6 -  quicksort(arr, low, p - 1)  |
7 -  quicksort(arr, p + 1, high)  |
8 -   |
9 -   |
10 - def partition(arr, low, high):  |
11 -  pivot = arr[high]  |
12 -  i = low  |
13 -  for j in range(low, high):  |
14 -  if arr[j] <= pivot:  |
15 -  arr[i], arr[j] = arr[j], arr[i]  |
16 -  i += 1  |
17 -  arr[i], arr[high] = arr[high], arr[i]  |
18 -  return i  |
| 8 +  # Choose pivot based on strategy 
| 9 +  if pivot_strategy == 'random': 
| 10 +  pivot_index = random.randint(low, high) 
| 11 +  arr[pivot_index], arr[high] = arr[high], arr[pivot_index] 
| 12 +  elif pivot_strategy == 'median-of-three': 
| 13 +  mid = (low + high) // 2 
| 14 +  # Find median of arr[low], arr[mid], arr[high] 
| 15 +  s = sorted([(arr[low], low), (arr[mid], mid), (arr[high], high)], key=lambda x: x[0]) 
| 16 +  median_index = s[1][1] 
| 17 +  arr[median_index], arr[high] = arr[high], arr[median_index] 
| 18 +  # Partition 
| 19 +  p = partition(arr, low, high) 
| 20 +  # Recursively sort partitions 
| 21 +  quicksort(arr, low, p - 1, pivot_strategy) 
| 22 +  quicksort(arr, p + 1, high, pivot_strategy) 
| 23 +  
| 24 +  
| 25 + def partition(arr, low, high): 
| 26 +  pivot = arr[high] 
| 27 +  i = low - 1 
| 28 +  for j in range(low, high): 
| 29 +  if arr[j] <= pivot: 
| 30 +  i += 1 
| 31 +  arr[i], arr[j] = arr[j], arr[i] 
| 32 +  arr[i + 1], arr[high] = arr[high], arr[i + 1] 
| 33 +  return i + 1 
| 34 +  
| 35 + # Example usage 
| 36 + if __name__ == "__main__": 
| 37 +  data = [3, 6, 8, 10, 1, 2, 1, 5, 9, 4] 
| 38 +  print("Original data:", data) 
| 39 +  quicksort(data, pivot_strategy='median-of-three') 
| 40 +  print("Sorted data:", data) 
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The sorting_algo.py file has been created with a robust Quicksort implementation. It includes options for different pivot strategies such as 'last', 'random', and 'median-of-three'. The code also contains an example usage demonstrating how to call the function.
Would you like me to display the content here, or do you need further modifications or explanations?
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The task is now complete. The Python script sorting_algo.py with a robust Quicksort implementation has been successfully created and saved.
If you need to run or test the script, or require any further modifications, explanations, or additional features, please let me know!
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[Agent] Completed in 5 iteration(s)
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