Implement Various Types of Partitions in Quick Sort in Java

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Quicksort is a Divide and Conquer Algorithm that is used for sorting the elements. In this algorithm, we choose a pivot and partitions the given array according to the pivot. Quicksort algorithm is a mostly used algorithm because this algorithm is cache-friendly and performs in-place sorting of the elements means no extra space requires for sorting the elements.

Note:

Quicksort algorithm is generally unstable algorithm because quick sort cannot be able to maintain the relative
order of the elements.

Three partitions are possible for the Quicksort algorithm:

Naive partition: In this partition helps to maintain the relative order of the elements but this partition takes O(n) extra space.
Lomuto partition: In this partition, The last element chooses as a pivot in this partition. The pivot acquires its required position after partition but more comparison takes place in this partition.
Hoare’s partition: In this partition, The first element chooses as a pivot in this partition. The pivot displaces its required position after partition but less comparison takes place as compared to the Lomuto partition.

1. Naive partition

Algorithm:

Naivepartition(arr[],l,r)

1. Make a Temporary array temp[r-l+1] length
2. Choose last element as a pivot element
3. Run two loops:
    -> Store all the elements in the temp array that are less than pivot element
    -> Store the pivot element 
    -> Store all the elements in the temp array that are greater than pivot element.
4.Update all the elements of arr[] with the temp[] array    


QuickSort(arr[], l,  r)


If r > l
     1. Find the partition point of the array  
              m = Naivepartition(a,l,r) 
     2. Call Quicksort for less than partition point   
             Call Quicksort(arr, l, m-1)
     3. Call Quicksort for greater than the partition point 
             Call Quicksort(arr, m+1, r)

Java

// Java program to demonstrate the naive partition
// in quick sort
 
import java.io.*;
import java.util.*;
public class GFG {
    static int partition(int a[], int start, int high)
    {
        // Creating temporary
        int temp[] = new int[(high - start) + 1];
 
        // Choosing a pivot
        int pivot = a[high];
        int index = 0;
       
        // smaller number
        for (int i = start; i <= high; ++i) {
            if (a[i] < pivot)
            {
                temp[index++] = a[i];
            }
        }
       
        // pivot position
        int position = index;
       
        // Placing the pivot to its original position
        temp[index++] = pivot;
       
        for (int i = start; i <= high; ++i)
        {
            if (a[i] > pivot)
            {
                temp[index++] = a[i];
            }
        }
 
        // Change the original array
        for (int i = start; i <= high; ++i) {
            a[i] = temp[i - start];
        }
       
        // return the position of the pivot
        return position;
    }
 
    static void quicksort(int numbers[], int start, int end)
    {
        if (start < end) {
            int point = partition(numbers, start, end);
 
            quicksort(numbers, start, point - 1);
            quicksort(numbers, point + 1, end);
        }
    }
   
    // Function to print the array
    static void print(int numbers[])
    {
        for (int a : numbers)
        {
            System.out.print(a + " ");
        }
    }
 
    public static void main(String[] args)
    {
        int numbers[] = { 3, 2, 1, 78, 9798, 97 };
       
        // rearrange using naive partition
        quicksort(numbers, 0, numbers.length - 1);
       
        print(numbers);
    }
}

Output

1 2 3 78 97 9798

2. Lomuto partition

Lomuto’s Partition Algorithm (unstable algorithm)

Lomutopartition(arr[], lo, hi) 

    pivot = arr[hi]
    i = lo     // place for swapping
    for j := lo to hi – 1 do
        if arr[j] <= pivot then
            swap arr[i] with arr[j]
            i = i + 1
    swap arr[i] with arr[hi]
    return i

    
QuickSort(arr[], l,  r)

If r > l
     1. Find the partition point of the array  
              m =Lomutopartition(a,l,r) 
     2. Call Quicksort for less than partition point   
             Call Quicksort(arr, l, m-1)
     3. Call Quicksort for greater than the partition point 
             Call Quicksort(arr, m+1, r)

Java

// Java program to demonstrate the Lomuto partition
// in quick sort
 
import java.util.*;
public class GFG {
 
    static int sort(int numbers[], int start, int last)
    {
        int pivot = numbers[last];
        int index = start - 1;
        int temp = 0;
       
        for (int i = start; i < last; ++i)
        {
            if (numbers[i] < pivot) {
                ++index;
               
                // swap the position
                temp = numbers[index];
                numbers[index] = numbers[i];
                numbers[i] = temp;
            }
        }
       
        int pivotposition = ++index;
       
        temp = numbers[index];
        numbers[index] = pivot;
        numbers[last] = temp;
       
        return pivotposition;
    }
   
    static void quicksort(int numbers[], int start, int end)
    {
        if (start < end)
        {
            int pivot_position = sort(numbers, start, end);
            quicksort(numbers, start, pivot_position - 1);
            quicksort(numbers, pivot_position + 1, end);
        }
    }
   
    static void print(int numbers[])
    {
        for (int a : numbers) {
            System.out.print(a + " ");
        }
    }
   
    public static void main(String[] args)
    {
        int numbers[] = { 4, 5, 1, 2, 4, 5, 6 };
        quicksort(numbers, 0, numbers.length - 1);
        print(numbers);
    }
}

Output

1 2 4 4 5 5 6

3. Hoare’s Partition

Hoare’s Partition Scheme works by initializing two indexes that start at two ends, the two indexes move toward each other until an inversion is (A smaller value on the left side and a greater value on the right side) found. When an inversion is found, two values are swapped and the process is repeated.

Algorithm:

Hoarepartition(arr[], lo, hi)

   pivot = arr[lo]
   i = lo - 1  // Initialize left index
   j = hi + 1  // Initialize right index

   // Find a value in left side greater
   // than pivot
   do
      i = i + 1
   while arr[i] < pivot

   // Find a value in right side smaller
   // than pivot
   do
      j--;
   while (arr[j] > pivot);

   if i >= j then 
      return j

   swap arr[i] with arr[j]


   
QuickSort(arr[], l,  r)

If r > l
     1. Find the partition point of the array  
              m =Hoarepartition(a,l,r) 
     2. Call Quicksort for less than partition point   
             Call Quicksort(arr, l, m)
     3. Call Quicksort for greater than the partition point 
             Call Quicksort(arr, m+1, r)

Java

// Java implementation of QuickSort
// using Hoare's partition scheme
 
import java.io.*;
 
class GFG {
 
    // This function takes first element as pivot, and
    // places all the elements smaller than the pivot on the
    // left side and all the elements greater than the pivot
    // on the right side. It returns the index of the last
    // element on the smaller side
    static int partition(int[] arr, int low, int high)
    {
        int pivot = arr[low];
        int i = low - 1, j = high + 1;
 
        while (true)
        {
            // Find leftmost element greater
            // than or equal to pivot
            do {
                i++;
            } while (arr[i] < pivot);
 
            // Find rightmost element smaller
            // than or equal to pivot
            do {
                j--;
            } while (arr[j] > pivot);
 
            // If two pointers met.
            if (i >= j)
                return j;
           
            // swap(arr[i], arr[j]);
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
             
        }
    }
 
    // The main function that
    // implements QuickSort
    // arr[] --> Array to be sorted,
    // low --> Starting index,
    // high --> Ending index
    static void quickSort(int[] arr, int low, int high)
    {
        if (low < high) {
           
            // pi is partitioning index,
            // arr[p] is now at right place
            int pi = partition(arr, low, high);
 
            // Separately sort elements before
            // partition and after partition
            quickSort(arr, low, pi);
            quickSort(arr, pi + 1, high);
        }
    }
 
    // Function to print an array
    static void printArray(int[] arr, int n)
    {
        for (int i = 0; i < n; ++i)
            System.out.print(" " + arr[i]);
       
        System.out.println();
    }
 
    // Driver Code
    static public void main(String[] args)
    {
        int[] arr = { 10, 17, 18, 9, 11, 15 };
        int n = arr.length;
        quickSort(arr, 0, n - 1);
 
        printArray(arr, n);
    }
}