Implement Various Types of Partitions in Quick Sort in Java
Last Updated :
07 Aug, 2021
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
import java.io.*;
import java.util.*;
public class GFG {
static int partition(int a[], int start, int high)
{
int temp[] = new int[(high - start) + 1];
int pivot = a[high];
int index = 0;
for (int i = start; i <= high; ++i) {
if (a[i] < pivot)
{
temp[index++] = a[i];
}
}
int position = index;
temp[index++] = pivot;
for (int i = start; i <= high; ++i)
{
if (a[i] > pivot)
{
temp[index++] = a[i];
}
}
for (int i = start; i <= high; ++i) {
a[i] = temp[i - start];
}
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);
}
}
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 };
quicksort(numbers, 0, numbers.length - 1);
print(numbers);
}
}
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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
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;
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);
}
}
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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
import java.io.*;
class GFG {
static int partition(int[] arr, int low, int high)
{
int pivot = arr[low];
int i = low - 1, j = high + 1;
while (true)
{
do {
i++;
} while (arr[i] < pivot);
do {
j--;
} while (arr[j] > pivot);
if (i >= j)
return j;
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
}
static void quickSort(int[] arr, int low, int high)
{
if (low < high) {
int pi = partition(arr, low, high);
quickSort(arr, low, pi);
quickSort(arr, pi + 1, high);
}
}
static void printArray(int[] arr, int n)
{
for (int i = 0; i < n; ++i)
System.out.print(" " + arr[i]);
System.out.println();
}
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);
}
}
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