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Quick Sort Algorithm

Certification: Intermediate Level Accuracy: 100% Submissions: 2 Points: 15

Write a Python program that implements the Quick Sort algorithm to sort a list of integers in ascending order. Quick Sort is a divide-and-conquer algorithm that works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot.

Example 1
    
  
  • Input: [10, 7, 8, 9, 1, 5]
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  • Output: [1, 5, 7, 8, 9, 10]
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  • Explanation: 
    
      
      
    • Step 1: Take the input array [10, 7, 8, 9, 1, 5].
      • 
      
    • Step 2: Choose a pivot (e.g., 10) and partition the array.
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    • Step 3: After partitioning: [7, 8, 9, 1, 5] and [] with pivot 10.
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    • Step 4: Recursively apply Quick Sort to the sub-arrays.
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    • Step 5: Combine the results: [1, 5, 7, 8, 9, 10].
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    • Step 6: Return the sorted array [1, 5, 7, 8, 9, 10].
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    •
Example 2
    
  
  • Input: [64, 34, 25, 12, 22, 11, 90]
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  • Output: [11, 12, 22, 25, 34, 64, 90]
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  • Explanation: 
    
      
      
    • Step 1: Take the input array [64, 34, 25, 12, 22, 11, 90].
      • 
      
    • Step 2: Choose a pivot (e.g., 64) and partition the array.
      • 
      
    • Step 3: After partitioning: [34, 25, 12, 22, 11] and [90] with pivot 64.
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    • Step 4: Recursively apply Quick Sort to the sub-arrays.
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    • Step 5: Combine the results: [11, 12, 22, 25, 34, 64, 90].
      • 
      
    • Step 6: Return the sorted array [11, 12, 22, 25, 34, 64, 90].
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    •
Constraints
    
  
  • 1 ≤ len(arr) ≤ 10^5
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  • -10^6 ≤ arr[i] ≤ 10^6
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  • Time Complexity: O(n log n) average case, O(n²) worst case, where n is the length of the array
    • 
  
  • Space Complexity: O(log n) for recursion stack
    •
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Hint
Solution

Solution Hints

    
  
  • Choose a pivot element from the array
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  • Partition the array around the pivot such that elements smaller than the pivot are on the left and larger elements are on the right
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  • Recursively apply the above steps to the sub-arrays
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  • The base case is when a sub-array has one or zero elements
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  • Different pivot selection strategies: first element, last element, median of three, random
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  • Implement a partition function to rearrange the array around the pivot
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  • The recursion depth is log(n) on average, but can be n in the worst case
    •

Steps to solve by this approach:

 Step 1: Create a copy of the input array to avoid modifying the original.
 Step 2: Define a partition function that selects a pivot (rightmost element).
 Step 3: Rearrange the array so elements smaller than pivot are on left, larger on right.
 Step 4: Place the pivot at its correct sorted position and return its index.
 Step 5: Recursively apply quick_sort to the sub-array before the pivot.
 Step 6: Recursively apply quick_sort to the sub-array after the pivot.
 Step 7: Return the completely sorted array.

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