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Encyclopedia > Stack (data structure)
Simple representation of a stack
Simple representation of a stack
Linear data structures

Array
Deque
Linked list
Queue
Stack
Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A binary tree, a simple type of branching linked data structure. ... This article or section does not cite its references or sources. ... In computer science, a deque (short for double-ended queue) is a data structure for which elements can be added to or removed from the front or back. ... In computer science, a linked list is one of the fundamental data structures used in computer programming. ... In providing services in computer science, transport, and operations research a queue (pronounced kyew) is a buffer where various entities such as data, objects, persons, or events are stored and waiting to be processed. ...

In computer science, a stack is a temporary abstract data type and data structure based on the principle of Last In First Out (LIFO). Stacks are used extensively at every level of a modern computer system. For example, a modern PC uses stacks at the architecture level, which are used in the basic design of an operating system for interrupt handling and operating system function calls. Among other uses, stacks are used to run a Java Virtual Machine, and the Java language itself has a class called "Stack", which can be used by the programmer. The stack is ubiquitous. Computer scaence, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... In computing, an abstract data type (ADT) is a specification of a set of data and the set of operations that can be performed on the data. ... A binary tree, a simple type of branching linked data structure. ... In a stack, the topmost item, which is added last, is taken out first. ... A typical vision of a computer architecture as a series of abstraction layers: hardware, firmware, assembler, kernel, operating system and applications (see also Tanenbaum 79). ... A Java Virtual Machine (JVM), originally developed by Sun Microsystems, is a virtual machine that executes Java bytecode. ... Java is an object-oriented applications programming language developed by Sun Microsystems in the early 1990s. ...


A stack-based computer system is one that stores temporary information primarily in stacks, rather than hardware CPU registers (a register-based computer system). In computer architecture, a processor register is a small amount of very fast computer memory used to speed the execution of computer programs by providing quick access to commonly used values—typically, the values being in the midst of a calculation at a given point in time. ...

Contents

Abstract data type

As an abstract data type, the stack is a container (data structure) of nodes and has two basic operations: push and pop. Push adds a given node to the top of the stack leaving previous nodes below. Pop removes and returns the current top node of the stack. A frequently used metaphor is the idea of a stack of plates in a spring loaded cafeteria stack. In such a stack, only the top plate is visible and accessible to the user, all other plates remain hidden. As new plates are added (pushed), each new plate becomes the top of the stack, and hides each plate below. As plates are removed (popped) from the stack, they can be used, and second plate becomes the top of the stack. Two important principles are illustrated by this metaphor, the Last In First Out principle is one. The second is that the contents of the stack are hidden. Only the top plate is visible, so to see what is on the third plate, the first and second plates will have to be removed. In computing, an abstract data type (ADT) is a specification of a set of data and the set of operations that can be performed on the data. ... A container is a type of data structure. ... A node is a basic unit used to build data structures, such as linked lists and tree data structures. ... In a stack, the topmost item, which is added last, is taken out first. ...


Operations

In modern computer languages, the stack is usually implemented with more operations than just "push" and "pop". The length of a stack can often be returned as a parameter. Another helper operation top[1] (also known as peek and peak) can return the current top element of the stack without removing it from the stack.


This section gives pseudocode for adding or removing nodes from a stack, as well as the length and top functions. Throughout we will use null to refer to an end-of-list marker or sentinel value, which may be implemented in a number of ways using pointers. Pseudocode (derived from pseudo and code) is a compact and informal high-level description of a computer programming algorithm that uses the structural conventions of programming languages, but omits detailed subroutines, variable declarations or language-specific syntax. ... KK Null, a Japanese musician Null, a special value in computer programming. ... In computer programming, a sentinel value (also referred to as a flag value, rogue value, or signal value) is a special value that is used to terminate a loop that processes structured (especially sequential) data. ... In computer science, a pointer is a programming language data type whose value refers directly to (or “points to”) another value stored elsewhere in the computer memory using its address. ...

 record Node { data // The data being stored in the node next // A reference to the next node; null for last node } 
 record Stack { Node stackPointer // points to the 'top' node; null for an empty stack } 
 function push(Stack stack, Element element) { // push element onto stack new(newNode) // Allocate memory to hold new node newNode.data := element newNode.next := stack.stackPointer stack.stackPointer := newNode } 
 function pop(Stack stack) { // increase the stack pointer and return 'top' node // You could check if stack.stackPointer is null here. // If so, you may wish to error, citing the stack underflow. node := stack.stackPointer stack.stackPointer := node.next element := node.data return element } 
 function top(Stack stack) { // return 'top' node return stack.stackPointer.data } 
 function length(Stack stack) { // return the amount of nodes in the stack length := 0 node := stack.stackPointer while node not null { length := length + 1 node := node.next } return length } 

As you can see, these functions pass the stack and the data elements as parameters and return values, not the data nodes that, in this implementation, include pointers. A stack may also be implemented as a linear section of memory (i.e. an array), in which case the function headers would not change, just the internals of the functions. In general, a reference is something that refers to or designates something else, or acts as a connection or a link between two things. ...


Implementation

A typical storage requirement for a stack of n elements is O(n). The typical time requirement of O(1) operations is also easy to satisfy with a dynamic array or (singly) linked list implementation. Big O notation or Big Oh notation, and also Landau notation or asymptotic notation, is a mathematical notation used to describe the asymptotic behavior of functions. ... Big O notation or Big Oh notation, and also Landau notation or asymptotic notation, is a mathematical notation used to describe the asymptotic behavior of functions. ... A dynamic array, growable array, resizable array, dynamic table, or array list is a data structure, an array which is automatically expanded to accommodate new objects if filled beyond its current size. ... In computer science, a linked list is one of the fundamental data structures used in computer programming. ...


C++'s Standard Template Library provides a "stack" templated class which is restricted to only push/pop operations. Java's library contains a Stack class that is a specialization of Vector. This could be considered a design flaw because the inherited get() method from Vector ignores the LIFO constraint of the Stack. The Standard Template Library (STL) is a software library included in the C++ Standard Library. ...


Here is a simple example of a stack with the operations described above in Python. It does not have any type of error checking. Python is a high-level programming language first released by Guido van Rossum in 1991. ...

 class Stack: def __init__(self): self.stack_pointer = None def push(self, element): self.stack_pointer = Node(element, self.stack_pointer) def pop(self): (e, self.stack_pointer) = (self.stack_pointer.element, self.stack_pointer.next) return e def peek(self): return self.stack_pointer.element def __len__(self): i = 0 sp = self.stack_pointer while sp: i += 1 sp = sp.next return i class Node: def __init__(self, element=None, next=None): self.element = element self.next = next if __name__ == '__main__': # small use example s = Stack() [s.push(i) for i in xrange(10)] print [s.pop() for i in xrange(len(s))] 

The above is admittedly redundant as Python supports the 'pop' and 'append' functions to lists.


Related Data Structures

The abstract data type and data structure of the First In First Out (FIFO) principle is the queue, and the combination of stack and queue operations is provided by the deque. For example, changing a stack into a queue in a search algorithm can change the algorithm from a depth-first search (DFS) into a breadth-first search (BFS). A bounded stack is a stack limited to a fixed size. FIFO is an acronym for First In, First Out. ... In providing services in computer science, transport, and operations research a queue (pronounced kyew) is a buffer where various entities such as data, objects, persons, or events are stored and waiting to be processed. ... In computer science, a deque (short for double-ended queue) is a data structure for which elements can be added to or removed from the front or back. ... In computer science, a search algorithm, broadly speaking, is an algorithm that takes a problem as input and returns a solution to the problem, usually after evaluating a number of possible solutions. ... Depth-first search (DFS) is an algorithm for traversing or searching a tree, tree structure, or graph. ... In graph theory, breadth-first search (BFS) is a graph search algorithm that begins at the root node and explores all the neighboring nodes. ...


Hardware Stacks

A common use of stacks at the Architecture level is as a means of allocating and accessing memory.


Basic architecture of a stack

A typical stack, storing local data and call information for nested procedures. This stack grows downward from its origin. The stack pointer points to the current topmost data item on the stack. A push operation decrements the pointer and copies the data to the stack; a pop operation copies data from the stack and then increments the pointer. Each procedure called in the program stores procedure return information (in yellow) and local data (in other colors) by pushing them onto the stack. This type of stack implementation is extremely common, but it is vulnerable to buffer overflow attacks (see the text).
A typical stack, storing local data and call information for nested procedures. This stack grows downward from its origin. The stack pointer points to the current topmost data item on the stack. A push operation decrements the pointer and copies the data to the stack; a pop operation copies data from the stack and then increments the pointer. Each procedure called in the program stores procedure return information (in yellow) and local data (in other colors) by pushing them onto the stack. This type of stack implementation is extremely common, but it is vulnerable to buffer overflow attacks (see the text).

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. Image File history File links Download high resolution version (1582x1879, 78 KB) Summary A simple diagram of the stack structure used to store information in memory by many computer architectures and programming languages. ... Image File history File links Download high resolution version (1582x1879, 78 KB) Summary A simple diagram of the stack structure used to store information in memory by many computer architectures and programming languages. ... In computer security and programming, a buffer overflow, or buffer overrun, is a programming error which may result in a memory access exception and program termination, or in the event of the user being malicious, a possible breach of system security. ...


The two operations applicable to all stacks are:

  • a push operation, in which a data item is placed at the location pointed to by the stack pointer, and the address in the stack pointer is adjusted by the size of the data item;
  • a pop or pull operation: a data item at the current location pointed to by the stack pointer is removed, and the stack pointer is adjusted by the size of the data item.

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 (either up or down, depending on the specific implementation).


For example, a stack might start at a memory location of one thousand, and expand towards lower addresses, in which case new data items are stored at locations ranging below 1000, and the stack pointer is decremented each time a new item is added. When an item is removed from the stack, the stack pointer is incremented.


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 1000 and the stack grows downwards (towards addresses 999, 998, and so on), the stack pointer must never be incremented beyond 1000 (to 1001, 1002, 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.


Some environments that rely heavily on stacks may provide additional operations, for example:

  • Dup(licate): the top item is popped and pushed again so that an additional copy of the former top item is now on top, with the original below it.
  • Peek: the topmost item is popped, but the stack pointer is not changed, and the stack size does not change (meaning that the item remains on the stack). This is also called top operation in many articles.
  • Swap or exchange: the two topmost items on the stack exchange places.
  • Rotate: the n topmost items are moved on the stack in a rotating fashion. For example, if n=3, items 1, 2, and 3 on the stack are moved to positions 2, 3, and 1 on the stack, respectively. Many variants of this operation are possible, with the most common being called left rotate and right rotate.

Stacks are either visualized growing from the bottom up (like real-world stacks), or, with the top of the stack in a fixed position (see image), a coin holder ([1]) or growing from left to right, so that "topmost" becomes "rightmost". This visualization may be independent of the actual structure of the stack in memory. This means that 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 visualisations of this process:

 apple banana banana ==right rotate==> cucumber cucumber apple 
 cucumber banana apple ==left rotate==> apple cucumber banana 

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, it 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.


Hardware support

Many CPUs have registers that can be used as stack pointers. Some, like the Intel x86, have special instructions that implicitly use a register dedicated to the job of being a stack pointer. Others, like the DEC PDP-11 and the Motorola 68000 family have addressing modes that make it possible to use any of a set of registers as a stack pointer. The Intel 80x87 series of numeric coprocessors has a set of registers that can be accessed either as a stack or as a series of numbered registers. Some microcontrollers, for example some PICs, have a fixed-depth stack that is not directly accessible. Die of an Intel 80486DX2 microprocessor (actual size: 12×6. ... Intel Corporation (NASDAQ: INTC; SEHK: 4335) is the worlds largest semiconductor company and the inventor of the x86 series of microprocessors, the processors found in many personal computers. ... x86 or 80x86 is the generic name of a microprocessor architecture first developed and manufactured by Intel. ... The DEC logo Digital Equipment Corporation was a pioneering American company in the computer industry. ... The PDP-11 was a 16-bit minicomputer sold by Digital Equipment Corp. ... Motorola (NYSE: MOT) is an American multinational communications company based in Schaumburg, Illinois, a Chicago suburb. ... The Motorola 680x0, 0x0, m68k, or 68k family of CISC microprocessor CPU chips were 32_bit from the start, and were the primary competition for the Intel x86 family of chips. ... Intel Corporation (NASDAQ: INTC; SEHK: 4335) is the worlds largest semiconductor company and the inventor of the x86 series of microprocessors, the processors found in many personal computers. ... Intel C8087 Math Coprocessor The 8087 was the first math coprocessor designed by Intel and it was built to be paired with the ass] microprocessors. ... It has been suggested that this article or section be merged with embedded microprocessor. ... PIC microcontrollers in DIP and QFN packages PIC is a family of Harvard architecture microcontrollers made by Microchip Technology, derived from the PIC1650 originally developed by General Instruments Microelectronics Division. ...


There are also a number of microprocessors which implement a stack directly in hardware:

  • Computer Cowboys MuP21
  • Harris RTX line
  • Novix NC4016

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 B5000. Forth is a programming language and programming environment, initially developed by Charles H. Moore at the US National Radio Astronomy Observatory in the early 1970s. ... A microprogram is a program consisting of microcode that controls the different parts of a computers central processing unit (CPU). ... In computer science, a stack machine is a model of computation in which the computers memory takes the form of one or more stacks. ... The Burroughs large systems were the largest of three series of Burroughs Corporation mainframe computers. ...


Software support

In application programs written in a high level language, a stack can be implemented efficiently using either arrays or linked lists. In LISP there is no need to implement the stack, as the functions push and pop are available for any list. Adobe PostScript is also designed around a stack that is directly visible to and manipulated by the programmer. A high-level programming language is a programming language that is more user-friendly, to some extent platform-independent, and abstract from low-level computer processor operations such as memory accesses. ... This article or section does not cite its references or sources. ... In computer science, a linked list is one of the fundamental data structures used in computer programming. ... For the programming language, see Lisp (programming language). ... PostScript (PS) is a page description language and programming language used primarily in the electronic and desktop publishing areas. ...


Applications

Stacks are ubiquitous in the computing world.


Expression evaluation and syntax parsing

Calculators employing reverse Polish notation use a stack structure to hold values. Expressions can be represented in prefix, postfix or infix notations. Conversion from one form of the expression to another form needs a stack. Many compilers use a stack for parsing the syntax of expressions, program blocks etc. before translating into low level code. Most of the programming languages are context-free languages allowing them to be parsed with stack based machines. Postfix notation is a mathematical notation wherein every operator follows all of its operands. ... In linguistics and computer science, a context-free grammar (CFG) is a formal grammar in which every production rule is of the form V → w where V is a nonterminal symbol and w is a string consisting of terminals and/or non-terminals. ...


For example, The calculation: ((1 + 2) * 4) + 3 can be written down like this in postfix notation with the advantage of no precedence rules and parentheses needed:

 1 2 + 4 * 3 + 

The expression is evaluated from the left to right using a stack:

  • push when encountering an operand and
  • pop two operands and evaluate the value when encountering an operation.
  • push the result

Like the following way (the Stack is displayed after Operation has taken place):

Input Operation Stack
1 Push operand 1
2 Push operand 1, 2
+ Add 3
4 Push operand 3, 4
* Multiply 12
3 Push operand 12, 3
+ Add 15

The final result, 15, lies on the top of the stack at the end of the calculation.


Runtime memory management

Main articles: Stack-based memory allocation and Stack machine

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. To meet Wikipedias quality standards, this article or section may require cleanup. ... In computer science, a stack machine is a model of computation in which the computers memory takes the form of a stack. ... A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. ... A stack-oriented programming language is one that relies on a stack machine model for passing parameters. ... PostScript (PS) is a page description language and programming language used primarily in the electronic and desktop publishing areas. ...


Forth uses two stacks, one for argument passing and one for subroutine return addresses. The use of a return stack is extremely commonplace, but the somewhat unusual use of an argument stack for a human-readable programming language is the reason Forth is referred to as a stack-based language. Forth is a programming language and programming environment, initially developed by Charles H. Moore at the US National Radio Astronomy Observatory in the early 1970s. ... In both conventional and electronic messaging, a return address is an explicit inclusion of the address of the person sending the message. ... A stack-oriented programming language is one that relies on a stack machine model for passing parameters. ...


Many virtual machines are also stack-oriented, including the p-code machine and the Java virtual machine. In computer science, a virtual machine is software that creates a virtualized environment between the computer platform and its operating system, so that the end user can operate software on an abstract machine. ... In computer programming, a P-code machine or pseudo-code machine is a specification of a cpu whose instructions are expected to be executed in software rather than in hardware (ie, interpreted). ... A Java Virtual Machine (JVM), originally developed by Sun Microsystems, is a virtual machine that executes Java bytecode. ...


Almost all computer runtime memory environments use a special stack (the "call stack") to hold information about procedure/function calling and nesting in order to switch to the context of the called function and restore to the caller function when the calling finishes. They 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. This type of stack is used implicitly by the compiler to support CALL and RETURN statements (or their equivalents) and is not manipulated directly by the programmer. In computer science, a call stack is a special stack which stores information about the active subroutines of a computer program. ... A visual form of recursion known as the Droste effect. ...


Some programming languages use the stack to store data that is local to a procedure. Space for local data items is allocated from the stack when the procedure is entered, and is deallocated when the procedure exits. The C programming language is typically implemented in this way. Using the same stack for both data and procedure calls has important security implications (see below) of which a programmer must be aware in order to avoid introducing serious security bugs into a program. C is a general-purpose, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...


Solving search problems

Solving a search problem, regardless of whether the approach is exhaustive or optimal, needs stack space. Examples of exhaustive search methods are bruteforce and backtracking. Examples of optimal search exploring methods are branch and bound and heuristic solutions. All of these algorithms use stacks to remember the search nodes that have been noticed but not explored yet. The only alternative to using a stack is to use recursion and let the compiler do the remembering for you (but in this case the compiler is still using a stack internally). The use of stacks is prevalent in many problems, ranging from simple in-order traversals of trees or depth-first traversals of graphs to a crossword puzzle solver or computer chess game. Some of these problems can be solved by alternative data structures like a queue, when a different order of traversal is required. In computability theory, a search problem is a type of computational problem represented by a binary relation. ... For heuristics in computer science, see heuristic (computer science) Heuristic is the art and science of discovery and invention. ... In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ... Crossword Puzzle was the second to last album made by The Partridge Family, and was not one of the most popular albums. ... 1990s Pressure-sensory Chess Computer with LCD screen The idea of creating a chess-playing machine dates back to the eighteenth century. ... In providing services in computer science, transport, and operations research a queue (pronounced kyew) is a buffer where various entities such as data, objects, persons, or events are stored and waiting to be processed. ...


Security

Some computing environments use stacks in ways that may make them vulnerable to security breaches and attacks. Programmers working in such environments must take special care to avoid the pitfalls of these implementations.


For example, some programming languages use a common stack to store both data local to a called procedure and the linking information that allows the procedure to return to its caller. This means that the program moves data into and out of the same stack that contains critical return addresses for the procedure calls. If data is moved to the wrong location on the stack, or an oversized data item is moved to a stack location that is not large enough to contain it, return information for procedure calls may be corrupted, causing the program to fail.


Malicious parties may attempt to take advantage of this type of implementation by providing oversized data input to a program that does not check the length of input. Such a program may copy the data in its entirety to a location on the stack, and in so doing it may change the return addresses for procedures that have called it. An attacker can experiment to find a specific type of data that can be provided to such a program such that the return address of the current procedure is reset to point to an area within the stack itself (and within the data provided by the attacker), which in turn contains instructions that carry out unauthorized operations.


This type of attack is a variation on the buffer overflow attack and is an extremely frequent source of security breaches in software, mainly because some of the most popular programming languages (such as C) use a shared stack for both data and procedure calls, and do not verify the length of data items. Frequently programmers do not write code to verify the size of data items, either, and when an oversized or undersized data item is copied to the stack, a security breach may occur. In computer security and programming, a buffer overflow, or buffer overrun, is a programming error which may result in a memory access exception and program termination, or in the event of the user being malicious, a possible breach of system security. ... C is a general-purpose, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...


History

The stack method of expression evaluation was first proposed in 1955 and then patented in 1957 by early German computer scientist Friedrich L. Bauer, who received the IEEE Computer Society Pioneer Award in 1988 for his work on Computer Stacks. Friedrich Ludwig Bauer (born June 10, 1924 in Regensburg) is a German computer scientist and professor emeritus at Munich University of Technology. ... The Institute of Electrical and Electronics Engineers or IEEE (pronounced as eye-triple-ee) is an international non-profit, professional organization incorporated in the State of New York, United States. ...


See also

In providing services in computer science, transport, and operations research a queue (pronounced kyew) is a buffer where various entities such as data, objects, persons, or events are stored and waiting to be processed. ... In computer science, a deque (short for double-ended queue) is a data structure for which elements can be added to or removed from the front or back. ... In computer science, a call stack is a special stack which stores information about the active subroutines of a computer program. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... “Computer Networks” redirects here. ... It has been suggested that this article or section be merged with communications protocol. ... In computer science, a stack machine is a model of computation in which the computers memory takes the form of a stack. ...

References

  1. ^ Horowitz, Ellis: "Fundamentals of Data Structures in Pascal", page 67. Computer Science Press, 1984

Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... Thomas H. Cormen is the co-author of Introduction to Algorithms, along with Charles Leiserson, Ron Rivest, and Cliff Stein. ... Charles E. Leiserson is a computer scientist, specializing in the theory of parallel computing and distributed computing, and particularly practical applications thereof; as part of this effort, he developed the Cilk multithreaded language. ... Professor Ron Rivest Professor Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer, and is the Viterbi Professor of Computer Science at MITs Department of Electrical Engineering and Computer Science. ... Clifford Stein is a computer scientist, currently working as a professor at Columbia University in New York, NY. He earned his BSE from Princeton University in 1987, a MS from Massachusetts Institute of Technology in 1989, and a PhD from Massachusetts Institute of Technology in 1992. ... Cover of the second edition Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. ...

External links


  Results from FactBites:
 
Stack (data structure) - Wikipedia, the free encyclopedia (2564 words)
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.
Stacks are either visualized growing from the bottom up (like real-world stacks, see image, or, with the top of the stack in a fixed position, a coin holder [1]) or growing from left to right, so that "topmost" becomes "rightmost".
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.
Stack - Wikipedia, the free encyclopedia (182 words)
Stack (geology), a large vertical column of rock in the sea
Stack (data structure), a temporary data structure based on Last in, First out (LIFO)
Stack machine, a model of computation in which the computer's memory takes the form of one or more stacks
  More results at FactBites »

 
 

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