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Three way partitioning of an array around a given range

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  • Difficulty Level : Medium
  • Last Updated : 16 Jun, 2022

Given an array and a range [lowVal, highVal], partition the array around the range such that array is divided in three parts. 
1) All elements smaller than lowVal come first. 
2) All elements in range lowVal to highVal come next. 
3) All elements greater than highVal appear in the end. 
The individual elements of three sets can appear in any order.

Examples: 

Input: arr[] = {1, 14, 5, 20, 4, 2, 54, 20, 87, 98, 3, 1, 32}  
        lowVal = 14, highVal = 20
Output: arr[] = {1, 5, 4, 2, 1, 3, 14, 20, 20, 98, 87, 32, 54}

Input: arr[] = {1, 14, 5, 20, 4, 2, 54, 20, 87, 98, 3, 1, 32}  
       lowVal = 20, highVal = 20       
Output: arr[] = {1, 14, 5, 4, 2, 1, 3, 20, 20, 98, 87, 32, 54} 

A simple solution is to sort the array. This solution does a lot of extra rearrangements and requires O(n Log n) time.
An efficient solution is based on Dutch National Flag based QuickSort. We traverse given array elements from left. We keep track of two pointers, first (called start in the code below) to store next position of smaller element (smaller than range) from beginning; and second (called end in the code below) to store next position of greater element from end. 

C++




// C++ program to implement three way partitioning
// around a given range.
#include<iostream>
using namespace std;
 
// Partitions arr[0..n-1] around [lowVal..highVal]
void threeWayPartition(int arr[], int n,
                int lowVal, int highVal)
{
    // Initialize next available positions for
    // smaller (than range) and greater elements
    int start = 0, end = n-1;
 
    // Traverse elements from left
    for (int i=0; i<=end;)
    {
        // If current element is smaller than
        // range, put it on next available smaller
        // position.
        if (arr[i] < lowVal)
        {
          //if i and start are same in that case we can't swap
          //swap only if i is greater than start
          if(i==start)
          {
            start++;
            i++;
          }
          else
            swap(arr[i++], arr[start++]);
        }
 
        // If current element is greater than
        // range, put it on next available greater
        // position.
        else if (arr[i] > highVal)
            swap(arr[i], arr[end--]);
 
        else
            i++;
    }
}
 
// Driver code
int main()
{
    int arr[] = {1, 14, 5, 20, 4, 2, 54, 20, 87,
                98, 3, 1, 32};
    int n = sizeof(arr)/sizeof(arr[0]);
 
    threeWayPartition(arr, n, 10, 20);
 
    cout << "Modified array \n";
    for (int i=0; i<n; i++)
        cout << arr[i] << " ";
}


Java




// Java program to implement three way partitioning
// around a given range.
import java.io.*;
 
class GFG
{
     
    // Partitions arr[0..n-1] around [lowVal..highVal]
    public static void threeWayPartition(int[] arr, int lowVal, int highVal)
    {
         
        int  n = arr.length;
         
        // Initialize ext available positions for
        // smaller (than range) and greater elements
        int start = 0, end = n-1;
         
         // Traverse elements from left
        for(int i = 0; i <= end;)
        {
             
            // If current element is smaller than
            // range, put it on next available smaller
            // position.
             
            if(arr[i] < lowVal)
            {
                 
                int temp = arr[start];
                arr[start] = arr[i];
                arr[i] = temp;
                start++;
                i++;
                 
            }
             
            // If current element is greater than
            // range, put it on next available greater
            // position.
            else if(arr[i] > highVal)
            {
                 
                int temp = arr[end];
                arr[end] = arr[i];
                arr[i] = temp;
                end--;
                  
            }
             
            else
               i++;
        }
         
    }
     
    public static void main (String[] args)
    {
     
     
        int arr[] = {1, 14, 5, 20, 4, 2, 54, 20, 87, 98, 3, 1, 32};
         
        threeWayPartition(arr, 10, 20);
  
        System.out.println("Modified array ");
        for (int i=0; i < arr.length; i++)
        {
            System.out.print(arr[i] + " ");
     
        }   
    }
}
 
//This code is contributed by Dheerendra Singh


Python3




# Python3 program to implement three way
# partitioning around a given range.
 
# Partitions arr[0..n-1] around [lowVal..highVal]
def threeWayPartition(arr, n, lowVal, highVal):
 
    # Initialize ext available positions for
    # smaller (than range) and greater elements
    start = 0
    end = n - 1
    i = 0
 
    # Traverse elements from left
    while i <= end:
 
        # If current element is smaller than
        # range, put it on next available smaller
        # position.
        if arr[i] < lowVal:
              arr[i], arr[start] = arr[start], arr[i]
            i += 1
            start += 1
 
        # If current element is greater than
        # range, put it on next available greater
        # position.
        elif arr[i] > highVal:
              arr[i], arr[end] = arr[end], arr[i]
            end -= 1
 
        else:
            i += 1
 
# Driver code
if __name__ == "__main__":
    arr = [1, 14, 5, 20, 4, 2, 54,
           20, 87, 98, 3, 1, 32]
    n = len(arr)
 
    threeWayPartition(arr, n, 10, 20)
 
    print("Modified array")
    for i in range(n):
        print(arr[i], end = " ")
 
# This code is contributed by
# sanjeev2552


C#




// C# program to implement three way
// partitioning around a given range.
using System;
 
class GFG {
 
    // Partitions arr[0..n-1]
    // around [lowVal..highVal]
    public static void threeWayPartition(int[] arr,
                           int lowVal, int highVal)
    {
        int n = arr.Length;
 
        // Initialize ext available positions for
        // smaller (than range) and greater elements
        int start = 0, end = n - 1;
 
        // Traverse elements from left
        for (int i = 0; i <= end;) {
 
            // If current element is smaller than
            // range, put it on next available smaller
            // position.
 
            if (arr[i] < lowVal) {
 
                int temp = arr[start];
                arr[start] = arr[i];
                arr[i] = temp;
                start++;
                i++;
            }
 
            // If current element is greater than
            // range, put it on next available greater
            // position.
            else if (arr[i] > highVal) {
 
                int temp = arr[end];
                arr[end] = arr[i];
                arr[i] = temp;
                end--;
            }
 
            else
                i++;
        }
    }
     
    // Driver code
    public static void Main()
    {
        int[] arr = { 1, 14, 5, 20, 4, 2, 54,
                      20, 87, 98, 3, 1, 32 };
 
        threeWayPartition(arr, 10, 20);
 
        Console.WriteLine("Modified array ");
        for (int i = 0; i < arr.Length; i++) {
            Console.Write(arr[i] + " ");
        }
    }
}
 
// This article is contributed by vt_m.


Javascript




<script>
 
// JavaScript program to implement three
// way partitioning around a given range.
 
// Partitions arr[0..n-1] around [lowVal..highVal]
function threeWayPartition(arr, n, lowVal, highVal)
{
     
    // Initialize ext available positions for
    // smaller (than range) and greater elements
    let start = 0, end = n - 1;
 
    // Traverse elements from left
    for(let i = 0; i <= end;)
    {
         
        // If current element is smaller than
        // range, put it on next available smaller
        // position.
        if (arr[i] < lowVal)
        
            let temp = arr[start];
            arr[start] = arr[i];
            arr[i] = temp;
            start++;
            i++;
        }
 
        // If current element is greater than
        // range, put it on next available greater
        // position.
        else if(arr[i] > highVal)
        {    
            let temp = arr[end];
            arr[end] = arr[i];
            arr[i] = temp;
            end--;
        }
        else
            i++;
    }
}
 
// Driver code
let arr = [ 1, 14, 5, 20, 4, 2, 54,
            20, 87, 98, 3, 1, 32 ];
let n = arr.length;
 
threeWayPartition(arr, n, 10, 20);
 
document.write("Modified array <br>");
for(let i = 0; i < n; i++)
    document.write(arr[i] + " ");
 
// This code is contributed by Surbhi Tyagi.
 
</script>


Output: 

Modified array 
1 5 4 2 1 3 14 20 20 98 87 32 54 

Time Complexity: O(n) 
Auxiliary Space: O(1)

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