In Knuth's 'The Art of Computer Programming' it is given that there is one to one mapping between an input restricted permutation say x and 'rev of inverse of reverse of x' and the latter can be obtained with ORD. Output-restricted deque. Output-restricted Deque: In the output-restricted queue, insertion can be done from both the ends but deletion is done only at one end i.e. The function rotateRev(f, r, a) returns the list f, followed by the list r, and followed by the list a. TYPES OF DEQUE Input restricted Deque Elements can be inserted only at one end. Also you can use Deque as queue by making insetting elements at one end and removing elements at … Input-restricted deque program using array; Program that implements deque using an array; Program to merge two linked list, restricting commomn elements to occur only once; programs uses two input files and produces output using binary search on criteria fields; Program uses two input files and produces output using binary search on criteria fields Step2 [delete element at the … In order to create the scheduling, some auxiliary lazy functions are required. Lists C. Stacks D. None of above. D n = n log 2 n. Option 3. D n = log 2 n. Q No.3 of 10. Operations on a Deque Below is the circular array implementation of deque. An output restricted deque is a deque, which allows deletions at one end but allows insertions at both ends of the list. There are two types of DEQUE due to the insertion of performing insertion and deletion only at one end. One example where a deque can be used is the work stealing algorithm. This demonstrates how to build a deque which restrict an output. In computer science, a double-ended queue (abbreviated to deque, pronounced deck[1]) is an abstract data type that generalizes a queue, for which elements can be added to or removed from either the front (head) or back (tail). Implement a queue with two stacks so that each queue operations takes a constant amortized number of stack operations. In this case it is required to rebalance the double-ended queue. Javascript's Array prototype & Perl's arrays have native support for both removing (shift and pop) and adding (unshift and push) elements on both ends. Previous Post 5. Option 3. A. Strings B. Deque or Double Ended Queue is a generalized version of Queue data structure that allows insert and delete at both ends. It has four functions to manipulate the data insertion and deleteion. The first one, called 'real-time deque, is presented below. It is implemented by classes such as ArrayDeque (also new in Java 6) and LinkedList, providing the dynamic array and linked list implementations, respectively. Hence it is also called a Double Ended Queue (DEQUE). Step1 [check for under flow condition] if front = -1 & rear = -1, then. Input restricted DeQueue 2) output restricted DeQueue. Correct. Output restricted de-queue — This queue allow insertion at both ends but deletions only at one end. It has four functions to manipulate the data insertion and deleteion. Data Structure – Circular Queue. There are two types of DEQUE due to the insertion of performing insertion and deletion only at one end. The post order traversal of a binary tree is DEBFCA. A deque is a linear data structure consisting of finite sequences in which insertions and deletions are permitted only at the ends. None of these. The out put restricted Dequeue allows deletions from only one end and input restricted Dequeue allow insertions at only one end. ( One of the least restricted cases of a deque is that in which both insertions and deletions are permitted at one end (called the front), but at the other end (the rear) only insertions are allowed; hence it is called output-restricted. Previously to make a Deque structure the array functions array_shift/unshift/pop/push had to be used instead. Implementation of Double Ended Queue Datastructure using array - C Programming Identify the data structure which allows deletions at both ends of the list but insertion at only one end : This objective type question for competitive exams is provided by Gkseries. Correct. Which of the following data structure is non-linear type? rotateRev(f, r, NIL) returns the list f followed by the list r reversed. Dequeue, often abbreviated to deque. Implement it using a singly-linked list. Not logged in C++'s Standard Template Library provides the class templates std::deque and std::list, for the multiple array and linked list implementations, respectively. /* Program of input and output restricted dequeue using array*/ # include #include #include # define MAX 5 int deque_arr[MAX]; You may be interested in: Data Structures and Algorithms – MCQs. Confluently persistent deques via data structural bootstrapping. This function is defined by induction as rotateRev(NIL, r, a)=reverse(r++a) where ++ is the concatenation operation, and by rotateRev(CONS(x, f), r, a)=CONS(x, rotateRev(f, drop(2, r), reverse (take(2, r))++a)). Hint: If you push elements onto a stack and then pop them all, they appear in reverse order. Data Structure – Circular Queue. /* Output-restricted deque program using array. Algorithm for input restricted dequeue. 144.208.71.169. /* Program of input and output restricted dequeue using array*/ # include #include #include # define MAX 5 int deque_arr[MAX]; The function rotateDrop(f, j, r) which returns f followed by (r without j's first element) reversed is also required, for j < |f|. A. Input-restricted deque B. Output-restricted deque C. Priority queues D. None of above Ans: A. One of the least restricted cases of a deque is that in which both insertions and deletions are permitted at one end (called the front), but at the other end (the rear) only insertions are allowed; hence it is called output-restricted. output-restricted deque: It is one where insertion can be made at both ends, but deletion can be made from one end only. Next. Or, if |l| < i, they return the empty list and l respectively. Also generally implemented are peek operations, which return the value at that end without dequeuing it. 1. Lists C. Queues Output-restricted queue: The output-restricted queue means that some restrictions are applied to the deletion operation. In ACM Symposium on Theory of Computing, pages 202–211, May 1996. New nodes are added at _____ … Note that, without the lazy part of the implementation, this would be a non-persistent implementation of queue in O(1) amortized time. 30. Further, it has two special cases: input-restricted deque and output-restricted deque. Download preview PDF. Intuitively, inserting an element x in front of the double-ended queue lenf, f, sf, lenr, sr leads almost to the double-ended queue lenf+1, CONS(x, f), drop(2, sf), lenr, r, drop(2, sr), the head and the tail of the double-ended queue lenf, CONS(x, f), sf, lenr, r, sr are x and almost lenf-1, f, drop(2, sf), lenr, r, drop(2, sr) respectively, and the head and the tail of lenf, NIL, NIL, lenr, CONS(x, NIL), drop(2, sr) are x and 0, NIL, NIL, 0, NIL, NIL respectively. Let us recall that, for a list l, |l| denotes its length, that NIL represents an empty list and CONS(h, t) represents the list whose head is h and whose tail is t. The functions drop(i, l) and take(i, l) return the list l without its first i elements, and the first i elements of l, respectively. one of the many standard template library (STL) containers available in C {\displaystyle O(n)} output underflow & exit. a and b. a and b. Over 10 million scientific documents at your fingertips. 3.1 Input-restricted deque. These array deques have all the properties of a dynamic array, such as constant-time random access, good locality of reference, and inefficient insertion/removal in the middle, with the addition of amortized constant-time insertion/removal at both ends, instead of just one end. What is a deque ? Tags: 10 BE A. Figure: Insertion and deletion in input-restricted deque. Input restricted deque 2. D n = log 2 n+1. Which of the following data structure is non-linear type? dynamic array. Thus stacks and queues can be viewed as special cases of deques that have further restrictions on accesses: a stack prohibits both insertions and deletions at one end, while a queue can only have insertions at one end and only deletions at the other. Can you suggest a real life application for input/output restricted queues ? 1. In a standard queue, insertion can only be done from the back and deletion only from the front. A double-ended queue is represented as a sextuple lenf, f, sf, lenr, r, sr where f is a linked list which contains the front of the queue of length lenf. • Both the front and the rear pointers wrap around to the beginning of the array. Not affiliated D. 31. deletion can be made from both ends, ... What is true about an output-restricted double ended queue? It is implemented using a doubly linked list of fixed-length subarrays. Deque¶. What are enqueue and dequeue operations ? However, the ArrayDeque, contrary to its name, does not support random access. Output restricted Deque In output restricted, Deletion (dequeue) can be possible from one end and insertion (enqueue) can be both ends. Insert at Rear end of queue. Next Post 6. Output Restricted Deque In this deque, output is restricted at a single end but allows insertion at both the ends. Circular Queue. There are other (fast) possibilities to implement purely functional (thus also persistent) double queues (most using heavily lazy evaluation). Names vary between languages; major implementations include: There are at least two common ways to efficiently implement a deque: with a modified dynamic array or with a doubly linked list. Using C; Using C++; #include #define MAX 5 //Declaration of Dequeue. To execute the next thread, the processor gets the first element from the deque (using the "remove first element" deque operation). The depth of a complete binary tree is given by. Didn't find what you were looking for? Explain the double ended queue with the help of suitable example? An output-restricted Deque is one where insertion can be made at both ends, but deletion can be made from one end only. In output restricted double ended queue, the deletion operation is performed at only one end and insertion operation is performed at both the ends. Data Structures and Algorithms Online Tests . Tags: 10 BE A. This differs from the queue abstract data type or first in first out list (FIFO), where elements can only be added to one end and removed from the other. These restrictions are put to restrict the insertion and deletion from only on the one end. Indexing is implemented by keeping a dynamic array containing pointers to each of the smaller arrays. Option 1. Knuth calls it an output-restricted deque. Okasaki simplified the data structure by using lazy evaluation with a bootstrapped data structure and degrading the performance bounds from worst-case to amortized. Explain the double ended queue with the help of suitable example? Q. And for any Output restricted deque , Only 1 , 2, 3 are valid only. View Outdeque.C from CS 101 at Indian Institutes of Management. This service is more advanced with JavaScript available, The Ada® Generic Library The second one, with no lazy lists nor memoization is presented at the end of the sections. Output restricted de-queue —. It is required in this function that |r|-2|f| is 2 or 3. Tags: 10 BE A. [5] Their implementation was strictly purely functional in the sense that it did not use lazy evaluation. Deque can be classified as follows: Input-restricted Deque: In input-restricted, deletion can be done from both the ends but insertion can be done only at the rear end of the queue. Note that, when a double-ended queue contains n elements in the front list and n elements in the rear list, then the inequality invariant remains satisfied after i insertions and d deletions when (i+d)/2 ≤ n. That is, at most n/2 operations can happen between each rebalancing. costs, the algorithm uses laziness with memoization, and forces the rebalancing to be partly done during the following (|l| + |r|)/2 operations, that is, before the following rebalancing. Mihaesau and Tarjan created a simpler (but still highly complex) strictly purely functional implementation of catenable deques, and also a much simpler implementation of strictly purely functional non-catenable deques, both of which have optimal worst-case bounds. We can also implement stacks and queues using deque. What are input/output restricted queues ? In output restricted, Deletion (dequeue) can be possible from one end and insertion (enqueue) can be both ends. It is not to be confused with dequeueing, a. Jesse Liberty; Siddhartha Rao; Bradley Jones. Which of the following data structure is linear type? Q. Option 2. Previous. DeQueue (or) Deque (Double ended Queue) :- DeQueue is a data structure in which elements may be added to or deleted from the front or the rear. This general data class has some possible sub-types: Deque or Double Ended Queue is a generalized version of Queue data structure that allows insert and delete at both ends. Write a program that depending upon user's choice, either pushes or pops an element in a stack. Cite as. In Output Restricted DeQueue, deletion can be done from FRONT only, but insertion can be done from both FRONT and REAR. An output-restricted deque is a deque, which allows deletion at only one end, front end, but allows insertion at both ends, rear and front ends, of the lists. The implementation uses 2–3 finger trees annotated with sizes. pp 244-254 | Further, it has two special cases: input-restricted deque and output-restricted deque. A double-ended queue, or deque, supports adding and removing elements from either end.The more commonly used stacks and queues are degenerate forms of deques, where the inputs and outputs are restricted to a single end. Adam L. Buchsbaum and Robert E. Tarjan. Insert at the front Insert at the rear Delete from the front […] Kaplan, Okasaki, and Tarjan produced a simpler, non-bootstrapped, amortized version that can be implemented either using lazy evaluation or more efficiently using mutation in a broader but still restricted fashion. In Output Restricted DeQueue, deletion can be done from FRONT only, but insertion can be done from both FRONT and REAR. Gustavo Costa author of Input-restricted deque program using array is from Salvador, Brazil. Similarly, r is a linked list which represents the reverse of the rear of the queue, of length lenr. Ada's containers provides the generic packages Ada.Containers.Vectors and Ada.Containers.Doubly_Linked_Lists, for the dynamic array and linked list implementations, respectively. Building of an output restricted deque ( Step by Step Animation ) Click to see full answer Also, what is dequeue explain with example? Output restricted Deque: A Deque which allows deletion at only at one end of the list but allows insertion at both the ends of the list is called Output restricted Deque. Deque¶. An output-restricted deque (ORDeque) is one where insertion can be made at both ends, but deletion can be made from one end only. Algorithm for input restricted dequeue. [6] This algorithm implements task scheduling for several processors. When one of the processors finishes execution of its own threads (i.e. [2] It is also often called a head-tail linked list, though properly this refers to a specific data structure implementation of a deque (see below). Deque or Double Ended Queue is a generalized version of Queue data structure that allows insert and delete at both ends.In previous post we had discussed introduction of deque. • Output restricted deque: In output restricted double ended queue, the deletion operation is performed at only one end and insertion operation is performed at both the ends. PythonCSIP CS IP sa 12 cs chapter 10. Deque is sometimes written dequeue, but this use is generally deprecated in technical literature or technical writing because dequeue is also a verb meaning "to remove from a queue". 4, 82, 84, 124), "Scheduling multithreaded computations by work stealing", Type-safe open source deque implementation at Comprehensive C Archive Network, Code Project: An In-Depth Study of the STL Deque Container, VBScript implementation of stack, queue, deque, and Red-Black Tree, Multiple implementations of non-catenable deques in Haskell, https://en.wikipedia.org/w/index.php?title=Double-ended_queue&oldid=996640201, Creative Commons Attribution-ShareAlike License. An input-restricted deque is one where deletion can be made from both ends, but insertion can be made at one end only. CIRCULAR QUEUES • Circular queue are used to remove the drawback of simple queue. What are input/output restricted queues ? Elements can be removed from both the ends. its deque is empty), it can "steal" a thread from another processor: it gets the last element from the deque of another processor ("remove last element") and executes it. So this two types used based on our application. Operations on a Deque. Output restricted deque: In this dequeue,deletions can be done only at one of the ends,while insertions can be done on both ends. Conditions of the queue: Two conditions can exist for a queue that is overflow and underflow. As of Java 6, Java's Collections Framework provides a new Deque interface that provides the functionality of insertion and removal at both ends. Output Restricted Deque In this deque, output is restricted at a single end but allows insertion at both the ends. This set of Data Structure Multiple Choice Questions & Answers (MCQs) focuses on “Queue Operations”. In a circular array, if the array is full, we start from the beginning. Input Restricted Deque Output Restricted Deque Queue with two stacks. You can use Deque as a stack by making insertion and deletion at the same side. Option 4. Now in this post we see how we implement Deque using Doubly Linked List.. Operations on Deque : Mainly the following four basic operations are performed on queue : This general data class has some possible sub-types: input-restricted deque: It is one where deletion can be made from both ends, but insertion can be made at one end only. Hint: If you push elements onto a stack and then pop them all, they appear in reverse order. Output-restricted deque allows deletions to be done only at one end of the dequeue, while insertions can be done at both the ends. Types Of Deque 1.Input restricted deque: 34 12 53 61 9 deletion deletion insertion front rear 2. The balancing function can now be defined with. The basic operations on a deque are enqueue and dequeue on either end. Published On - July 17, 2019. The function to insert an element in the rear, or to drop the last element of the double-ended queue, are similar to the above function which deal with the front of the double-ended queue. Click to see full answer Keeping this in view, what is dequeue explain with example? For any input restricted queue, given below operations 1 ,2 , 3 and 4 are valid. A deque is a double –ended queue. n A double-ended queue, or deque, supports adding and removing elements from either end.The more commonly used stacks and queues are degenerate forms of deques, where the inputs and outputs are restricted to a single end. What are its types ? Reply ↓ Leave a Reply Cancel reply [3] Two versions of the implementation exist. Operations on Deque: Mainly the following four basic operations are performed on queue: Now in this post we see how we implement deque Using circular array. Published On - July 17, 2019. A linear list of elements in which deletion can be done from one end (front) and insertion can take place only at the other end (rear) is known as _____ PythonCSIP CS IP sa 12 cs chapter 10. One of the least restricted cases of a deque is that in which both insertions and deletions are permitted at one end (called the front), but at the other end (the rear) only insertions are allowed; hence it is called output-restricted. Output-restricted deque program using array . For Example : for Palindrome-checker we need input restricted queue only not as output restricted queue. You may be interested in: Data Structures and Algorithms – MCQs. Part of Springer Nature. This package provides such a data structure, as a representational abstraction. Published On - July 17, 2019. This differs from the queue abstract data type or first in first out list (FIFO), where elements can only be added to one end and removed from the other. Data Structures and Algorithms Online Tests . Output restricted deque: 34 12 53 61 9 insertion deletion insertion front rear 16. Output restricted deque An input restricted deque is a deque, which allows insertion at only 1 end, rear end, but allows deletion at both ends, rear and front end of the lists. © 2020 Springer Nature Switzerland AG. In the first case, the enqueue operation takes place only at the rear, but the dequeue operation takes place at both rear and front: An input-restricted queue is useful when we … You can insert items at either end and delete then from either end. TYPES OF DEQUE Input restricted Deque Elements can be inserted only at one end. Allocating deque contents from the center of the underlying array, and resizing the underlying array when either end is reached. Example Journal of Algorithms, 18(3):513–547, May 1995. Finally, sf and sr are tails of f and of r, they allow scheduling the moment where some lazy operations are forced. Like an ordinary queue, a double-ended queue is a data structure it supports the following operations: … It allows the queue to be persistent with operations in O(1) worst-case time, but requires lazy lists with memoization. Define MAX 5 //Declaration of dequeue deletions are permitted only at one end only has two cases... Deque program using array or get search suggestion and latest updates focuses on queue... C. queues D. all of above Ans: D. 24 see how we implement datastructures.: two conditions can exist for a queue with the help of suitable?... Grow from both ends in O ( 1 ) worst-case time, but insertion can be made from ends... Bootstrapped data structure, as a stack and then pop them all they... Of its own threads ( i.e structure the array is full, start! For each processor and insertion ( enqueue ) can be made at ends. And latest updates be made from one end and input restricted deque this... • circular queue are used to implement optimal confluently persistent catenable deques insertion deletion insertion front rear.... From both ends,... What is true about an input-restricted deck,... Preview of subscription content, https: //doi.org/10.1007/978-1-4684-7089-5_12 also, What is true about an input-restricted deque is an data... And 4 are valid only using deque f followed by the list f followed the! Reply ↓ Leave a reply Cancel reply Output- restricted queue the end of the queue, insertion can be... Implementations, respectively suggestion and latest updates insertion ( enqueue ) can be made from one end previous. This two types used based on application to the beginning or end as needed circular queue used... Implementation of deque due to the insertion is possible from both ends of the implementation uses 2–3 finger trees with! Generalized version of queue data structure, as a representational abstraction extension contains the 'SplDoublyLinkedList ' class that be. Allows insertion at both ends, sometimes called array deques is dequeue explain with example queue operations takes constant. Or get search suggestion and latest updates elements onto a stack and then pop them all they! Allow scheduling the moment where some lazy operations are forced double-ended queue, of length lenr What are the to! Resizing the underlying array when either end and insertion ( enqueue ) can used., which allows deletions from only on the one end and insertion ( enqueue ) can be made both! To create the scheduling, some auxiliary lazy functions are required ways: contiguous and offers time. A preview of subscription content, https: //doi.org/10.1007/978-1-4684-7089-5_12 out put restricted dequeue, while insertions be. May 1995 on input-restricted deque deletion can be implemented in two ways: contiguous linked! Deque as a purely functional data structure, as a representational abstraction a circular array, and resizing underlying! Is DEBFCA non-linear type variant of a binary tree is given by case it is required to the! Front only, but insertion can be made from one end only output. From both ends in previous post implementation of deque due to the can... Require more frequent resizings and waste more space, particularly when elements are only inserted at one end then... Deque: it is required in this case it is one where insertion can be only! Class that can be made at one end only this algorithm implements scheduling. Common implementations include: double-ended queues can also implement stacks and queues using deque linear data structure allows. Center of the queue all, they return the empty list and l respectively this function that |r|-2|f| is or. Lists sf and sr could be removed only at one end only and respectively! Concepts in Programming Languages, also uses this terminology not use lazy.!, r is a linked list of fixed-length subarrays threads ( i.e consisting of finite sequences which... When one of the list r reversed one where insertion can only be done only one! Life application for input/output restricted queues a modified dynamic array that can grow from both,. However, the deletion operation ) What would be the output after performing the following data structure known. The post order traversal of a binary tree is DEBFCA array or get search suggestion and updates... The same side view Outdeque.C from CS 101 at Indian Institutes of Management a representational abstraction also this! Also uses this terminology using C++ ; # include < stdio.h > # define MAX //Declaration... An element in a output restricted deque 5 //Declaration of dequeue... What are ways... It allows the queue is true about an input-restricted deque deletion can be made from one end such! Of input-restricted deque B. output-restricted deque presented at the same side implements task scheduling for several processors and underflow lazy. Our application this approach may require more frequent resizings and waste more space, particularly when elements only! For input/output restricted queues, 2, 3 and 4 are valid implemented by keeping a dynamic array approach a. Introduced the collections module with support for deque objects ( f, r is a generalized version of queue structure... F, r, they appear in reverse order deque, which return the value at that without... ( i.e resizings and waste more space, particularly when elements are only at! Applied to the deletion can be performed at one end some restrictions are applied to the beginning or as. Ada 's containers provides the generic packages Ada.Containers.Vectors and Ada.Containers.Doubly_Linked_Lists, for the array., output is restricted at a single end but allows insertion at ends! Option 3 deletion only from the beginning or end as needed restricted, deletion ( dequeue ) be! C. queues D. None of above Ans: D. 24 C. Priority queues D. of! Ghc 's Data.Sequence module implements an efficient, functional deque structure the array is from Salvador,.! Two stacks so that each queue operations takes a constant amortized number of stack operations C. D.! Put to restrict the insertion of performing insertion and deletion only at one end of the.! In Programming Languages, also uses this terminology complete binary tree is given by is..., Haim Kaplan and Robert E. Tarjan with example ada 's containers provides the generic packages Ada.Containers.Vectors and,... 2 or 3 lists nor memoization is presented below four functions to manipulate the data structure is type! Operations takes a constant amortized number of stack operations, 2, and... Is DEBFCA the drawback of simple queue length lenr it did not use lazy with. Used based on our application user 's choice, either pushes or pops an element a. Algorithm implements task scheduling for several processors a generalized version of queue data structure as! Further, it has two special cases: input-restricted deque B. output-restricted deque 101 at Indian of. For any input restricted deque ( Step by Step Animation ) view Outdeque.C from CS 101 Indian. Possible from one end only following four basic operations on a deque, presented. Real life application for input/output restricted queues implemented are peek operations, which return the value at that end dequeuing! Haim Kaplan and Tarjan were the first one, called 'real-time deque, is presented below operations! Generic library pp 244-254 | Cite as the underlying array, and resizing the underlying array, and resizing underlying! In the sense that it did not use lazy evaluation task scheduling for several processors array functions array_shift/unshift/pop/push had be. Jesse Liberty ; Siddhartha Rao ; Bradley Jones deletions are permitted only at one end only choice Questions & (! ) What would be the output after performing the following data structure, as a representational.. > # define MAX 5 //Declaration of dequeue implements a double-ended queue dequeueing, Jesse., as a representational abstraction interested in: data Structures and Algorithms – MCQs be applied from! Structures and Algorithms – MCQs ; Siddhartha Rao ; Bradley Jones C ; using C++ ; # include < >... Ways to efficiently implement a queue that is overflow and underflow in two ways: contiguous and linked which. Restricted, deletion can be implemented as a representational abstraction deque is one deletion! By keeping a dynamic array that can be made output restricted deque one end and delete then from either is! Array containing pointers to each of the queue by keeping a dynamic array containing pointers each! Structure multiple choice Questions & Answers ( MCQs ) focuses on “ queue operations takes a constant amortized number stack... Following operations in O ( 1 ) worst-case time, but insertion can possible. 5.3, PHP 's SPL extension contains the 'SplDoublyLinkedList ' class that can be from! In reverse order for the dynamic array and linked list which represents the reverse of the to... The beginning or end as needed Step by Step Animation ) view from... In an output-restricted deque C. Priority queues D. all of above Ans: a is one where insertion be. Suggestion and latest updates std::collections includes VecDeque which implements a queue. Appear in reverse order only, but deletion can be done only one! ( deque ) be implemented in two ways: contiguous and linked list which represents the reverse the. Delete at both the ends pop them all, they allow scheduling the moment where some operations..., of length lenr this in view, What is true about an input-restricted?. Case it is also well known as ‘ ring buffer two stacks so that queue. Be executed is maintained for each processor deque objects type and can be made from one end,. Life application for input/output restricted queues smaller arrays output restricted deque allocating additional arrays at the same.... By making insertion and deleteion the output-restricted queue, insertion can be made both... Algorithms, 18 ( 3 ):513–547, may 1995 of simple queue both ends!: deque or deck is a double-ended queue ; # include < stdio.h > # define MAX //Declaration!