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QuickSort

Certification: Intermediate Level Accuracy: 42.86% Submissions: 14 Points: 10

Write a Java program to implement the QuickSort algorithm. QuickSort is a divide-and-conquer sorting 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. The sub-arrays are then recursively sorted.

Your task is to implement the QuickSort algorithm to sort an array of integers in ascending order.

Example 1
    
  
  • Input: arr = [10, 7, 8, 9, 1, 5]
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  • Output: [1, 5, 7, 8, 9, 10]
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  • Explanation: Using QuickSort, the array is sorted in ascending order.
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Example 2
    
  
  • Input: arr = [38, 27, 43, 3, 9, 82, 10]
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  • Output: [3, 9, 10, 27, 38, 43, 82]
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  • Explanation: The QuickSort algorithm partitions and sorts the array to produce the sorted output.
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Constraints
    
  
  • 1 <= arr.length <= 10^5
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  • -10^9 <= arr[i] <= 10^9
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  • All elements in the array are unique
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  • Time Complexity: O(n log n) on average, where n is the size of the array
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  • Space Complexity: O(log n) for the recursion stack
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  • You must implement the basic QuickSort algorithm with partition function
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Hint
Solution

Solution Hints

    
  
  • Implement a partition function that selects a pivot and places it at its correct position
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  • Choose a pivot (typically the last element) and move all smaller elements to the left and all greater elements to the right
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  • Return the pivot's final position from the partition function
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  • Recursively call QuickSort on the sub-arrays before and after the pivot
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  • Handle base cases where the sub-array has 0 or 1 elements
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  • Be careful with array indices to avoid out-of-bounds errors
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  • Consider optimizations like choosing a better pivot or using insertion sort for small arrays
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Steps to solve by this approach:

 Step 1: Check if the array has more than one element; if not, it's already sorted.
 Step 2: Choose a pivot element (typically the last element in the array).
 Step 3: Partition the array around the pivot so that elements less than pivot are on the left and elements greater than pivot are on the right.
 Step 4: Track the position where the pivot will end up (partitioning index).
 Step 5: Swap elements that are less than the pivot to the left side of the array.
 Step 6: Place the pivot in its final sorted position by swapping it with the element at the partitioning index.
 Step 7: Recursively apply the same process to the sub-arrays on either side of the pivot until the entire array is sorted.

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