3-Way QuickSort (Dutch National Flag)

CServer Side ProgrammingProgramming

Here we will see the quicksort technique but we will use three-way quicksort. The basic quicksort technique is just finding an element as pivot then partition the array around pivot, after that, recur for sub arrays on left and right of the pivot.

The three-way quicksort is similar, but there are three sections. array arr[1 to n] is divided into three parts.

  • arr[1 to i]
  • arr[i + 1, j]
  • arr[j + 1, n]

Algorithm

partition(arr, left, right, i, j) −

begin
   if right – left <= 1, then
      if arr[right] < arr[left], then
         swap arr[right] and arr[left]
      i := left
      j := right
      return
   end if
   mid := left, pivot = arr[right]
   while mid <= right, do
      if arr[mid] < pivot, then
         swap arr[left], arr[mid]
         increase left and mid by 1
      else if arr[mid] = pivot, then increase mid by 1
      else
         swap arr[mid], arr[right]
         decrease right by 1
   done
   i := left – 1
   j := mid
end

quicksort(arr, left, right) −

begin
   if left >= right, then
      return
   end if
   define i and j
   partition(arr, left, right, i, j)
   quicksort(arr, left, i)
   quicksort(arr, j, right)
end

Example

#include<iostream>
#include<vector>
using namespace std;
void partition(int arr[], int left, int right, int &i, int &j) {
   if (right - left <= 1) {
      if (arr[right] < arr[left])
         swap(arr[right], arr[left]);
      i = left;
      j = right;
      return;
}
int mid = left;
int pivot = arr[right];
while (mid <= right) {
   if (arr[mid]<pivot)
      swap(arr[left++], arr[mid++]);
      else if (arr[mid]==pivot)
         mid++;
      else if (arr[mid] > pivot)
         swap(arr[mid], arr[right--]);
   }
   i = left-1;
   j = mid;
}
void quicksort(int arr[], int left, int right) {
   if (left >= right) //1 or 0 elements
      return;
   int i, j;
   partition(arr, left, right, i, j);
   quicksort(arr, left, i);
   quicksort(arr, j, right);
}
void display(int arr[], int n) {
   for (int i = 0; i < n; ++i)
   cout << " " << arr[i];
   cout << endl;
}
int main() {
   int a[] = {4, 9, 4, 3, 1, 9, 4, 3, 9, 4, 3, 1, 4};
   int n = sizeof(a) / sizeof(int);
   display(a, n);
   quicksort(a, 0, n - 1);
   display(a, n);
}

Output

4 9 4 3 1 9 4 3 9 4 3 1 4
1 1 3 3 3 4 4 4 4 4 9 9 9
raja
Published on 20-Aug-2019 06:56:42
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