Queue And Stack In C++ Pdf

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How to implement it? Keep an index for pointing to the top of the stack.

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Data Structure and Algorithms - Queue

In computer science , a stack is an abstract data type that serves as a collection of elements, with two main principal operations:.

The order in which elements come off a stack gives rise to its alternative name, LIFO last in, first out. Additionally, a peek operation may give access to the top without modifying the stack. This structure makes it easy to take an item off the top of the stack, while getting to an item deeper in the stack may require taking off multiple other items first.

Considered as a linear data structure , or more abstractly a sequential collection, the push and pop operations occur only at one end of the structure, referred to as the top of the stack. This data structure makes it possible to implement a stack as a singly linked list and a pointer to the top element.

A stack may be implemented to have a bounded capacity. If the stack is full and does not contain enough space to accept an entity to be pushed, the stack is then considered to be in an overflow state. The pop operation removes an item from the top of the stack. A stack is needed to implement depth-first search. Stacks entered the computer science literature in , when Alan M. Turing used the terms "bury" and "unbury" as a means of calling and returning from subroutines.

Klaus Samelson and Friedrich L. Bauer of Technical University Munich proposed the idea of a stack in [5] [6] and filed a patent in Stacks are often described using the analogy of a spring-loaded stack of plates in a cafeteria.

When a plate is removed from the stack, the one below it pops up to become the new top plate. In many implementations, a stack has more operations than the essential "push" and "pop" operations. An example of a non-essential operation is "top of stack", or "peek", which observes the top element without removing it from the stack. If the stack is empty, an underflow condition will occur upon execution of either the "stack top" or "pop" operations.

Also, implementations often have a function which just returns whether the stack is empty. A stack can be easily implemented either through an array or a linked list.

What identifies the data structure as a stack, in either case, is not the implementation but the interface: the user is only allowed to pop or push items onto the array or linked list, with few other helper operations. The following will demonstrate both implementations, using pseudocode. An array can be used to implement a bounded stack, as follows. The first element, usually at the zero offset , is the bottom, resulting in array[0] being the first element pushed onto the stack and the last element popped off.

The program must keep track of the size length of the stack, using a variable top that records the number of items pushed so far, therefore pointing to the place in the array where the next element is to be inserted assuming a zero-based index convention. Thus, the stack itself can be effectively implemented as a three-element structure:. The push operation adds an element and increments the top index, after checking for overflow:.

Similarly, pop decrements the top index after checking for underflow, and returns the item that was previously the top one:. Using a dynamic array , it is possible to implement a stack that can grow or shrink as much as needed.

The size of the stack is simply the size of the dynamic array, which is a very efficient implementation of a stack since adding items to or removing items from the end of a dynamic array requires amortized O 1 time. Another option for implementing stacks is to use a singly linked list.

A stack is then a pointer to the "head" of the list, with perhaps a counter to keep track of the size of the list:. Pushing and popping items happens at the head of the list; overflow is not possible in this implementation unless memory is exhausted :. Some languages, notably those in the Forth family including PostScript , are designed around language-defined stacks that are directly visible to and manipulated by the programmer. PHP has an SplStack class. Java's library contains a Stack class that is a specialization of Vector.

Following is an example program in Java language, using that class. A common use of stacks at the architecture level is as a means of allocating and accessing memory. A typical stack is an area of computer memory with a fixed origin and a variable size.

Initially the size of the stack is zero. A stack pointer, usually in the form of a hardware register, points to the most recently referenced location on the stack; when the stack has a size of zero, the stack pointer points to the origin of the stack. There are many variations on the basic principle of stack operations. Every stack has a fixed location, in memory, at which it begins. As data items are added to the stack, the stack pointer is displaced to indicate the current extent of the stack, which expands away from the origin.

Stack pointers may point to the origin of a stack or to a limited range of addresses either above or below the origin depending on the direction in which the stack grows ; however, the stack pointer cannot cross the origin of the stack. In other words, if the origin of the stack is at address and the stack grows downwards towards addresses , , and so on , the stack pointer must never be incremented beyond to , , etc.

If a pop operation on the stack causes the stack pointer to move past the origin of the stack, a stack underflow occurs. If a push operation causes the stack pointer to increment or decrement beyond the maximum extent of the stack, a stack overflow occurs. Stacks are often visualized growing from the bottom up like real-world stacks. They may also be visualized growing from left to right, so that "topmost" becomes "rightmost", or even growing from top to bottom.

The important feature is that the bottom of the stack is in a fixed position. The illustration in this section is an example of a top-to-bottom growth visualization: the top 28 is the stack "bottom", since the stack "top" 9 is where items are pushed or popped from.

A right rotate will move the first element to the third position, the second to the first and the third to the second. Here are two equivalent visualizations of this process:. A stack is usually represented in computers by a block of memory cells, with the "bottom" at a fixed location, and the stack pointer holding the address of the current "top" cell in the stack.

The top and bottom terminology are used irrespective of whether the stack actually grows towards lower memory addresses or towards higher memory addresses. Pushing an item on to the stack adjusts the stack pointer by the size of the item either decrementing or incrementing, depending on the direction in which the stack grows in memory , pointing it to the next cell, and copies the new top item to the stack area. Depending again on the exact implementation, at the end of a push operation, the stack pointer may point to the next unused location in the stack, or it may point to the topmost item in the stack.

If the stack points to the current topmost item, the stack pointer will be updated before a new item is pushed onto the stack; if it points to the next available location in the stack, it will be updated after the new item is pushed onto the stack.

Popping the stack is simply the inverse of pushing. The topmost item in the stack is removed and the stack pointer is updated, in the opposite order of that used in the push operation. Many CISC -type CPU designs, including the x86 , Z80 and , have a dedicated register for use as the call stack stack pointer with dedicated call, return, push, and pop instructions that implicitly update the dedicated register, thus increasing code density.

Some CISC processors, like the PDP and the , also have special addressing modes for implementation of stacks , typically with a semi-dedicated stack pointer as well such as A7 in the In contrast, most RISC CPU designs do not have dedicated stack instructions and therefore most if not all registers may be used as stack pointers as needed. The x87 floating point architecture is an example of a set of registers organised as a stack where direct access to individual registers relative the current top is also possible.

As with stack-based machines in general, having the top-of-stack as an implicit argument allows for a small machine code footprint with a good usage of bus bandwidth and code caches , but it also prevents some types of optimizations possible on processors permitting random access to the register file for all two or three operands.

A stack structure also makes superscalar implementations with register renaming for speculative execution somewhat more complex to implement, although it is still feasible, as exemplified by modern x87 implementations.

Sun SPARC , AMD Am , and Intel i are all examples of architectures using register windows within a register-stack as another strategy to avoid the use of slow main memory for function arguments and return values.

There are also a number of small microprocessors that implements a stack directly in hardware and some microcontrollers have a fixed-depth stack that is not directly accessible. Many stack-based microprocessors were used to implement the programming language Forth at the microcode level. Stacks were also used as a basis of a number of mainframes and mini computers. Such machines were called stack machines , the most famous being the Burroughs B Calculators employing reverse Polish notation use a stack structure to hold values.

Expressions can be represented in prefix, postfix or infix notations and conversion from one form to another may be accomplished using a stack. Many compilers use a stack for parsing the syntax of expressions, program blocks etc. Most programming languages are context-free languages , allowing them to be parsed with stack based machines.

Another important application of stacks is backtracking. Consider a simple example of finding the correct path in a maze. There are a series of points, from the starting point to the destination. We start from one point. To reach the final destination, there are several paths. Suppose we choose a random path. After following a certain path, we realise that the path we have chosen is wrong.

So we need to find a way by which we can return to the beginning of that path. This can be done with the use of stacks. With the help of stacks, we remember the point where we have reached. This is done by pushing that point into the stack. In case we end up on the wrong path, we can pop the last point from the stack and thus return to the last point and continue our quest to find the right path.

This is called backtracking. The prototypical example of a backtracking algorithm is depth-first search , which finds all vertices of a graph that can be reached from a specified starting vertex. Other applications of backtracking involve searching through spaces that represent potential solutions to an optimization problem.

Branch and bound is a technique for performing such backtracking searches without exhaustively searching all of the potential solutions in such a space. A number of programming languages are stack-oriented , meaning they define most basic operations adding two numbers, printing a character as taking their arguments from the stack, and placing any return values back on the stack.

For example, PostScript has a return stack and an operand stack, and also has a graphics state stack and a dictionary stack. Many virtual machines are also stack-oriented, including the p-code machine and the Java Virtual Machine.

The functions follow a runtime protocol between caller and callee to save arguments and return value on the stack. Stacks are an important way of supporting nested or recursive function calls. Some programming languages use the stack to store data that is local to a procedure.

Stacks, Queues, Deques (list applications)

Queue is an abstract data structure, somewhat similar to Stacks. Unlike stacks, a queue is open at both its ends. One end is always used to insert data enqueue and the other is used to remove data dequeue. Queue follows First-In-First-Out methodology, i. A real-world example of queue can be a single-lane one-way road, where the vehicle enters first, exits first.

What is Stack Data Structure?

David Bernstein James Madison University Computer Science Department Motivation Queues are very straightforward but are slightly more complicated than stacks Queues can be implemented in a number of different ways using the same data structure i. Chapter Stacks And Queues Publishing as Pearson Addison-Wesley

Edit Reply. Queue is an abstract data structure that is similar to stacks. One end is always used to insert data enqueue and the other end to remove data dequeue.

Basic Operations

In computer science , a stack is an abstract data type that serves as a collection of elements, with two main principal operations:. The order in which elements come off a stack gives rise to its alternative name, LIFO last in, first out. Additionally, a peek operation may give access to the top without modifying the stack. This structure makes it easy to take an item off the top of the stack, while getting to an item deeper in the stack may require taking off multiple other items first. Considered as a linear data structure , or more abstractly a sequential collection, the push and pop operations occur only at one end of the structure, referred to as the top of the stack. This data structure makes it possible to implement a stack as a singly linked list and a pointer to the top element.

What is a Data Structure? A data structure is a way of organizing the data so that the data can be used efficiently. Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks.

What is a Data Structure? A data structure is a way of organizing the data so that the data can be used efficiently. Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, B-trees are particularly well-suited for the implementation of databases, while compiler implementations usually use hash tables to look up identifiers. Source: Wiki Page.

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Types of Queue in Data structure | Queue Data structure Introduction and Operations

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Queue (abstract data type)

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