Three way partitioning of an Array without changing the relative ordering

Last Updated : 12 May, 2022

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

All elements smaller than lowVal come first.
All elements in range lowVal to highVal come next.
All elements greater than highVVal appear in the end.
The relative ordering of numbers shouldn't be changed.

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 3 1 14 20 20 54 87 98 32 }

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 3 1 20 20 54 87 98 32 }

Approach: This approach is based on using extra data structures to store the elements lesser than lowVal, in between lowVal and highVal, and elements greater than highVal. We will be using 3 queue for maintaining the original order of elements.

Traverse the array one by one
Insert the array elements into the respective queue one by one
At the end,
- Pop out all the elements in queue 1 with elements lesser than lowVal
- Then Pop out all the elements in queue 2 with elements in between lowVal and highVal
- Then Pop out all the elements in queue 3 with elements greater than highVal.

Below is the implementation of the above approach:

C++

// C++ code to implement three way // partitioning of an array without // changing the relative ordering  #include <bits/stdc++.h> using namespace std;  // Function to do three way partitioning vector<int> pivotArray(vector<int>& nums, int lowVal,                        int highVal) {     // Declaring 3 queues     queue<int> before, same, after;      // Traverse the array elements one by one     for (int i = 0; i < nums.size(); i++) {          // If the element is         // less than pivot range         // insert it into queue before         if (nums[i] < lowVal)             before.push(nums[i]);          // Else If the element is         // in between pivot range         // insert it into queue same         else if (nums[i] > highVal)             after.push(nums[i]);          // Else If the element is         // less than pivot range         // insert it into queue after         else             same.push(nums[i]);     }      int k = 0;     // Now insert all elements     // in queue before and     // insert into final vector     while (before.size() > 0) {         nums[k++] = before.front();         before.pop();     }      // Now insert all elements     // in queue same and     // insert into final vector     while (same.size() > 0) {         nums[k++] = same.front();         same.pop();     }      // Now insert all elements     // in queue after and     // insert into final vector     while (after.size() > 0) {         nums[k++] = after.front();         after.pop();     }      // Return the final vector     return nums; }  // Driver code int main() {     vector<int> arr         = { 1, 14, 5, 20, 4, 2, 54,             20, 87, 98, 3, 1, 32 };     int lowVal = 20, highVal = 20;      pivotArray(arr, lowVal, highVal);     for (int i = 0; i < arr.size(); i++) {         cout << arr[i] << " ";     }     return 0; }

Java

// JAVA code to implement three way // partitioning of an array without // changing the relative ordering import java.util.*; class GFG {     // Function to do three way partitioning     public static int[] pivotArray(int[] nums, int lowVal,                                    int highVal)     {         // Declaring 3 queues         Queue<Integer> before = new LinkedList<>();         Queue<Integer> same = new LinkedList<>();         Queue<Integer> after = new LinkedList<>();          // Traverse the array elements one by one         for (int i = 0; i < nums.length; i++) {              // If the element is             // less than pivot range             // insert it into queue before             if (nums[i] < lowVal)                 before.add(nums[i]);              // Else If the element is             // in between pivot range             // insert it into queue same             else if (nums[i] > highVal)                 after.add(nums[i]);              // Else If the element is             // less than pivot range             // insert it into queue after             else                 same.add(nums[i]);         }          int k = 0;         // Now insert all elements         // in queue before and         // insert into final vector         while (before.size() > 0) {             nums[k++] = before.poll();         }          // Now insert all elements         // in queue same and         // insert into final vector         while (same.size() > 0) {             nums[k++] = same.poll();         }          // Now insert all elements         // in queue after and         // insert into final vector         while (after.size() > 0) {             nums[k++] = after.poll();         }          // Return the final vector         return nums;     }      // Driver code     public static void main(String[] args)     {         int arr[] = new int[] { 1,  14, 5,  20, 4, 2, 54,                                 20, 87, 98, 3,  1, 32 };         int lowVal = 20, highVal = 20;          pivotArray(arr, lowVal, highVal);         for (int i = 0; i < arr.length; i++) {             System.out.print(arr[i] + " ");         }     } }  // This code is contributed by Taranpreet

Python3

# Python 3 code to implement three way # partitioning of an array without # changing the relative ordering  # Function to do three way partitioning def pivotArray(nums,  lowVal,                highVal):      # Declaring 3 queues     before = []     same = []     after = []      # Traverse the array elements one by one     for i in range(len(nums)):          # If the element is         # less than pivot range         # insert it into queue before         if (nums[i] < lowVal):             before.append(nums[i])          # Else If the element is         # in between pivot range         # insert it into queue same         elif (nums[i] > highVal):             after.append(nums[i])          # Else If the element is         # less than pivot range         # insert it into queue after         else:             same.append(nums[i])      k = 0     # Now insert all elements     # in queue before and     # insert into final vector     while (len(before) > 0):         nums[k] = before[0]         k += 1         before.pop(0)      # Now insert all elements     # in queue same and     # insert into final vector     while (len(same) > 0):         nums[k] = same[0]         same.pop(0)         k += 1      # Now insert all elements     # in queue after and     # insert into final vector     while (len(after) > 0):         nums[k] = after[0]         k += 1         after.pop(0)      # Return the final vector     return nums  # Driver code if __name__ == "__main__":      arr = [1, 14, 5, 20, 4, 2, 54,            20, 87, 98, 3, 1, 32]     lowVal = 20     highVal = 20      pivotArray(arr, lowVal, highVal)     for i in range(len(arr)):         print(arr[i], end=" ")          # This code is contributed by ukasp.

// C# code to implement three way using System; using System.Collections;  public class GFG{    // partitioning of an array without   // changing the relative ordering    // Function to do three way partitioning   static int[] pivotArray(int[] nums, int lowVal,                           int highVal)   {          // Declaring 3 queues     Queue before = new Queue();     Queue same = new Queue();     Queue after = new Queue();      // Traverse the array elements one by one     for (int i = 0; i < nums.Length; i++) {        // If the element is       // less than pivot range       // insert it into queue before       if (nums[i] < lowVal)         before.Enqueue(nums[i]);        // Else If the element is       // in between pivot range       // insert it into queue same       else if (nums[i] > highVal)         after.Enqueue(nums[i]);        // Else If the element is       // less than pivot range       // insert it into queue after       else         same.Enqueue(nums[i]);     }      int k = 0;     // Now insert all elements     // in queue before and     // insert into final vector     while (before.Count > 0) {       nums[k++] = (int)before.Peek();       before.Dequeue();     }      // Now insert all elements     // in queue same and     // insert into final vector     while (same.Count > 0) {       nums[k++] = (int)same.Peek();       same.Dequeue();     }      // Now insert all elements     // in queue after and     // insert into final vector     while (after.Count > 0) {       nums[k++] = (int)after.Peek();       after.Dequeue();     }      // Return the final vector     return nums;   }    // Driver code   static public void Main (){      int [ ] arr       = { 1, 14, 5, 20, 4, 2, 54,          20, 87, 98, 3, 1, 32 };     int lowVal = 20, highVal = 20;      pivotArray(arr, lowVal, highVal);     for (int i = 0; i < arr.Length; i++) {       Console.Write(arr[i] + " ");      }   } }  // This code is contributed by hrithikgarg03188.

JavaScript

    <script>         // JavaScript code to implement three way         // partitioning of an array without         // changing the relative ordering           // Function to do three way partitioning         const pivotArray = (nums, lowVal, highVal) => {             // Declaring 3 queues             let before = [], same = [], after = [];              // Traverse the array elements one by one             for (let i = 0; i < nums.length; i++) {                  // If the element is                 // less than pivot range                 // insert it into queue before                 if (nums[i] < lowVal)                     before.push(nums[i]);                  // Else If the element is                 // in between pivot range                 // insert it into queue same                 else if (nums[i] > highVal)                     after.push(nums[i]);                  // Else If the element is                 // less than pivot range                 // insert it into queue after                 else                     same.push(nums[i]);             }              let k = 0;             // Now insert all elements             // in queue before and             // insert into final vector             while (before.length > 0) {                 nums[k++] = before[0];                 before.shift();             }              // Now insert all elements             // in queue same and             // insert into final vector             while (same.length > 0) {                 nums[k++] = same[0];                 same.shift();             }              // Now insert all elements             // in queue after and             // insert into final vector             while (after.length > 0) {                 nums[k++] = after[0];                 after.shift();             }              // Return the final vector             return nums;         }          // Driver code          let arr = [1, 14, 5, 20, 4, 2, 54,             20, 87, 98, 3, 1, 32];         let lowVal = 20, highVal = 20;          pivotArray(arr, lowVal, highVal);         for (let i = 0; i < arr.length; i++) {             document.write(`${arr[i]} `);         }      // This code is contributed by rakeshsahni      </script>

Output

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

Time Complexity: O(N), where N is the size of the array.
Auxiliary Space: O(N)

Split the array and add the first part to the end

krishmurarka

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Three way partitioning of an Array without changing the relative ordering

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