Three way partitioning of an array around a given range

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Given an array and a range [lowVal, highVal], partition the array around the range such that array is divided in three parts. 

• All elements smaller than lowVal come first. 
• All elements in range lowVal to highVal come next. 
• All elements greater than highVal appear in the end. 

The individual elements of the 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}
Explanation: all elements which are less than 14 are present in the range of 0 to 6
                       all elements which are greater than 14 and less than 20 are present in the range of 7 to 8
                       all elements which are greater than 20 are present in the range of 9 to 12        

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} 

The idea is based on Dutch National Flag based QuickSort. We traverse the given array of elements from left. We keep track of two pointers, first to store next position of smaller element (smaller than range) from beginning, and second to store next position of greater element from end. while traversing the array use these two pointers to place elements according to their range.

Follow the steps mentioned below to implement the idea:

• Create two variables start and end to store the index of the vacant place to store the elements according to their range.
• Traverse the array from 0 to end.
• If an element is less than lowVal then swap it with the element present at index start and increase the value of start by 1.
• If an element is greater than highVal then swap it with the element present at index end and decrease the value of end by 1.
• Print the array.                                                                                                                                                                                                                                        

Below is the implementation of the above approach:

// 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 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 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# 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] + " ");
        }
    }
}

// 

<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>

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

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