Introduction
Having a good knowledge of Data Structures and Algorithms is a must if your aim is to crack top productbased companies like Facebook, Amazon, and Google.
As it is tested rigorously by top companies wherein multiple interview rounds are conducted.
Questions related to Queues are frequently asked in the initial stages of interviews. A Queue is a linear Data Structure that follows the FirstInFirstOut(FIFO) methodology for performing operations. The elements are always inserted to the last of the queue and are removed from the beginning of the queue.
This blog discusses an important interview question, Sorting of Queue
Sorting of QueueProblem Statement
The problem statement is, βGiven a queue of random elements, you need to sort the queue in ascending order with constant space complexityβ
For Example:
Input: 1 4 7 2 5 8
Output 1 2 4 5 7 8 Explanation:
Input: 1 3 3 2 1 8 0
Output: 0 1 1 2 3 3 8
Explanation:

As an interviewee, even if you donβt have any idea of the solution, it is recommended to start with the brute force solution, it could be the one that is not optimized at all. In the problem statement, the most simple solution could be:
 Convert the queue to an Array
 Sort the array using inbuilt methods
 Convert the sorted array back to the queue and print it.
The approach will require a linear traversal of the queue making the time complexity O(N) where N is the size of the queue and the space complexity will be O(N) because of the auxiliary array needed to store queue elements.
But the problem statement at hand requires us to solve it in constant space complexity.
Now let us figure out the approach for Sorting of Queue with O(1) space complexity.
Approach 1: Sorting of Queue
As per the problem statement, the operations allowed on the queue are insertion, deletion, and finding the first element of the queue.
Before moving on to the approach, it is essential to understand the insertion operation in a queue:
As Queue follows FIFO methodology, it can be easily concluded that if an element x is to be inserted into the queue it will be inserted into the rear. Similarly, if another element y is to be inserted into the queue, it will be inserted into the rear i.e. one position right of x.
Refer to the below image for understanding insertion operation in a queue.
And the deletion operation will work as:
If you observe carefully, you will notice that in order to sort the queue, you need to place the minimum element at the rear position followed by the next minimum element, and so on. Proceeding this way will have the minimum element at the front and the maximum element at the back. Because in each insertion of an element, the remaining elements are shifted one place to the left.
Algorithm
 Linearly traverse the queue, in every iteration search for the minimum element, store the index of the minimum element.
 In the next step insert the element corresponding to the minimum index to the rear of the queue. Now the rearmost element will contain the minimum element of the sequence.
 Now again traverse the queue, from start to one position behind the rear of the queue. Repeat the above two steps in sequence till the queue becomes sorted.
Refer to the below illustration for a better understanding.
Given an unsorted queue of 6 elements. Iterate over the queue for finding the minimum element.
The minimum element is 0. This will element will now be shifted to the rear of the queue.
0 is now the rearmost element of the queue. The next minimum element is 2, now 2 will be shifted to the right.
2 is now the rearmost element of the queue. The next minimum element is 3, now 2 will be shifted to the right.
3 is now the rearmost element of the queue. The next minimum element is 6, now 6 will be shifted to the right.
6 is now the rearmost element of the queue. The next minimum element is 11, now 11 will be shifted to the right.
11 is now the rearmost element of the queue. The next minimum element is 12, now 12 will be shifted to the right.
The queue is thus sorted now.
The overall problem thus reduces to the following main subproblems:
 Finding the index of the minimum element in the queue.
In the program below, findIndexOfMinimumElement is used for this purpose.
 Placing the minimum element at the rear of the queue.
In the program below, insertElementToRear is used for this purpose.
Must Read Algorithm Types
Implementation
import java.util.Queue;
import java.util.LinkedList;
public class sortQueueWithoutExtraSpace {
// Method to return the minimum element's index in a queue
// The method will check for the minimum element right from
// front of the queue to the index/position specified
// ! In this program, after the position of the index, element are sorted
public static int findIndexOfMinimumElement(Queue<Integer> queue, int index) {
// A general rule is that, if in a sequence minimum element is
// to be found compare each element of the list with the maximum
// possible value and vice versa
int min_index = 1;
int min_element = Integer.MAX_VALUE;
// size() method returns the number of elements in the Queue
int size = queue.size();
for (int i = 0; i < size; i++) {
// peek() method retrieves but does not remove the head of the
// linked list
int curr_element = queue.peek();
// poll() method retrieves and remove the head of the queue
queue.poll();
if (curr_element <= min_element && i <= index) {
min_index = i;
min_element = curr_element;
}
queue.add(curr_element);
}
return min_index;
}
// This function will insert the element
// at index position to the rear of the queue
public static void insertElementToRear(Queue<Integer> queue, int index) {
// Currently we don't have access to the element at index position. This
// parameter will store the value at index position as and when accessed in the
// loop
int min_value = 0;
int size = queue.size();
for (int i = 0; i < size; i++) {
// Retrieve but do not remove the element from the front of the queue
int element_at_front = queue.peek();
queue.poll();
if (i != index)
queue.add(element_at_front);
else
min_value = element_at_front;
}
queue.add(min_value);
}
// Main function to sort a queue
public static void sortQueue(Queue<Integer> queue) {
for (int i = 0; i <= queue.size(); i++) {
// Find the index of the minimum element from starting of queue to queue.size()
//  i
int index = findIndexOfMinimumElement(queue, queue.size()  i);
// Insert the element at index position to the rear of the queue
insertElementToRear(queue, index);
}
}
public static void main(String[] args) {
// Queue is an interface, we cannot directly create objects of queue
// A class is needed which extends Queue to create an object
Queue<Integer> q = new LinkedList<>();
int[] arr = { 10, 5, 13, 40, 2 };
// add() method inserts an element to the queue. This method returns true
// upon success and IllegalStateException if no space is currently availab;e
for (int i = 0; i < arr.length; i++) {
q.add(arr[i]);
}
// Printing the queue
System.out.println("Printing the original queue");
System.out.println(q);
// Call to the sortQueue function. This will sort the queue
sortQueue(q);
// Printing the sorted queue
System.out.println("Printing the sorted queue");
System.out.println(q);
}
}
The output of the above program is:
Printing the original queue [10, 5, 13, 40, 2] Printing the sorted queue [2, 5, 10, 13, 40]

The time complexity of the above program is O(N^2)
The space complexity is O(1).
Read about Application of Queue in Data Structure here.
Frequently Asked Questions
What is Queue Sorting?
Queue sorting involves the sorting of queue elements in ascending or descending order.
A queue can be sorted using the technique discussed above.
What are the applications of Queue Data Structure?
The queue data structure is based on FIFO or FirstInFirstOut technique. The applications of the queue data structure are:
(i)Handling of interrupts in realtime systems.
(ii)Serving requests on a single shared resource
(iii)When data is transferred asynchronously between two processes
What are the types of queues?
There are four types of queues
(i)Simple Queue
(ii)Circular queues
(iii)Priority Queues
(iv)Doubleended queues
Conclusion
This blog discussed the Sorting of queues with constant space complexity. This is an important interview question. With this done you must try different questions based on the Queue data structure.
Recommended Readings:
 Check if a Queue Can be Sorted into Another Queue Using Stack
 Difference Between Queue and Deque in C++
 How to Efficiently Implement K Queues in a Single Array
 Find the Index of the Array Elements After Performing Given Operation K Times
 Advantages of Circular Queue
 Application of Linked List
 Introduction to C++
 Introduction to C#
Do check out The Interview guide for Product Based Companies as well as some of the Popular Interview Problems from Top companies like Amazon, Adobe, Google, Uber, Microsoft, etc. on Coding Ninjas Studio.
Also check out some of the Guided Paths on topics such as Data Structure and Algorithms, Competitive Programming, Operating Systems, Computer Networks, DBMS, System Design, Basics of C++, Basics of Java, Basics of Python, etc. as well as some Contests, Test Series, Interview Bundles, and some Interview Experiences curated by top Industry Experts only on Coding Ninjas Studio.
βCuriosity is the spark behind the spark of every great idea. The future belongs to the curiousβ.