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 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
# 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.
<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>
Output1 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)
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