14. Stacks and Queues

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Set of operations on those values. Some are built in Java: int, double, String,... Most are : Complex, Picture, Charge,... Data structures Represent data.

1 Section Data types and data structures Data types APIs Clients Strawman implementation Linked lists Implementations Set of values. Set of operations on those values. Some are built in Java: int, double, String,... Most are : Complex, Picture, Charge,... Data structures Represent data. Represent relationships among data. Some are built in Java: D arrays, 2D arrays,... Most are : linked list, circular list, tree,... Design challenge f every data type: Which data structure use? Resource : How much memy is needed? Resource 2: How much time do data-type use? 4

2 Stack and Queue APIs Example of stack operations A collection is an ADT whose values are a multiset of items, all of the same type. Two fundamental collection ADTs differ in just a detail of the specification of their operations. Add the ginning Stack operations Add an item the collection. Remove and return the item most recently added (LIFO). Test if the collection is empty. Return the size of the collection. Take from the ginning Last In Out Stacks and queues both arise naturally in countless applications. A key characteristic. No limit on the size of the collection. Queue operations Add an item the collection. Remove and return the item least recently added (FIFO). Test if the collection is empty. Return the size of the collection. Take from the ginning In Out Add the end Push. Add an item the collection. Pop. Remove and return the item most recently added. push is pop stack contents after operation push the ginning pop from the ginning push the ginning pop from the ginning Last In Out is 6 Example of queue operations dequeue from the ginning Parameterized data types Goal. Simple, safe, and clear client code f collections of any type of data. Enqueue. Add an item the collection. Dequeue. Remove and return the item least recently added. In Out Java approach: Parameterized data types (generics) Use placeholder type name in definition. Substitute concrete type f placeholder in clients. stay tuned f examples public class Stack<Item> enqueue is dequeue queue contents after operation dequeue from the ginning enqueue at the end enqueue at the end is 7 Stack API Queue API Stack<Item>() create a stack of objects, all of type Item void push(item item) add item stack Item pop() remove and return the item most recently pushed boolean isempty() is the stack empty? int size() # of objects on the stack public class Queue<Item> Queue<Item>() create a queue of objects, all of type Item void enqueue(item item) add item queue Item dequeue() remove and return the item least recently enqueued boolean isempty() is the queue empty? int size() # of objects on the queue 8

Perfmance specifications Challenge. Provide guarantees on perfmance. Goal. Simple, safe, clear, and efficient client code. Perfmance specifications All operations are constant-time.

Typically required f client code scalable APIs Clients Strawman implementation Linked lists Implementations RS+KW. Implementations do meet perfmance specs do implement the abstractions.

3 Perfmance specifications Challenge. Provide guarantees on perfmance. Goal. Simple, safe, clear, and efficient client code. Perfmance specifications All operations are constant-time. Memy use is proptional the size of the collection, when it is nonempty. No limits within the code on the collection size. Java. Any implementation of the API implements the stack/queue abstractions. Typically required f client code scalable APIs Clients Strawman implementation Linked lists Implementations RS+KW. Implementations do meet perfmance specs do implement the abstractions. 9 APIs Clients Strawman implementation Linked lists Implementations Stack and queue applications Queues -come--served resource allocation. Asynchronous data transfer (StdIn, StdOut). Dispensing requests on a shared resource (printer, process). Simulations of the real wld (guitar string, traffic analysis, ) Stacks Last-come--served processes (browser, ). Function calls in programming languages. Basic mechanism in interpreters, compilers

Queue client example: Read all strings from StdIn in an array Queue client example: Read all strings from StdIn in an array Challenge Can t sre strings in array fe creating the array.

public class QEx Note: StdIn has this functionality public static String[] readallstrings() // See next slide.

txt moby dick herman melville call me ishmael some years ago never mind how long precisely having little no money % java QEx < moby.

Copy the strings in the array. public class QEx public static String[] readallstrings() Queue<String> q = new Queue<String>(); q.enqueue(stdin.readstring()); int N = q.

4 Queue client example: Read all strings from StdIn in an array Queue client example: Read all strings from StdIn in an array Challenge Can t sre strings in array fe creating the array. Can t create the array without knowing how many strings are in the input stream. Can t know how many strings are in the input stream without reading them all. Solution: Use a Queue<String>. public class QEx Note: StdIn has this functionality public static String[] readallstrings() // See next slide. public static void main(string[] args) String[] wds = readallstrings(); f (int i = 0; i < wds.length; i++) StdOut.println(wds[i]); % me moby.txt moby dick herman melville call me ishmael some years ago never mind how long precisely having little no money % java QEx < moby.txt moby dick herman melville call me ishmael some years 3 Solution: Use a Queue<String>. Sre strings in the queue. Get the size when all have en read from StdIn. Create an array of size. Copy the strings in the array. public class QEx public static String[] readallstrings() Queue<String> q = new Queue<String>(); q.enqueue(stdin.readstring()); int N = q.size(); String[] wds = new String[N]; f (int i = 0; i < N; i++) wds[i] = q.dequeue(); return wds; public static void main(string[] args) String[] wds = readallstrings(); f (int i = 0; i < wds.length; i++) StdOut.println(wds[i]); 4 Stack example: "Back" butn in a browser Auboxing Typical scenario Visit a page. Click a link aher page. Click a link aher page. Click a link aher page. Click "back" butn. Click "back" butn. Click "back" butn. Challenge. Use a primitive type in a parameterized ADT. Wrapper types Each primitive type has a wrapper reference type. Wrapper type has larger set of operations than primitive type. Example: Integer.parseInt(). Values of wrapper types are objects. Wrapper type can used in a parameterized ADT. primitive type int long double boolean wrapper type Integer Long Double Boolean Auboxing. Aumatic cast from primitive type wrapper type. Au-unboxing. Aumatic cast from wrapper type primitive type Simple client code (no casts) Stack<Integer> stack = new Stack<Integer>(); stack.push(7); // Aubox (int -> Integer) int a = stack.pop(); // Au-unbox (Integer -> int) 6

Stack client example: Postfix expression evaluation Postfix arithmetic expression evaluation Algithm Infix. Standard way of writing arithmetic expressions, using parentheses f precedence.

Write operar after operands (instead of in tween them). Example. 2 3 + 4 * * + also called "reverse Polish" ation (RPN) Jan ukasiewicz 878 96 2 3 + = 4 * * + Remarkable fact.

(2+3)4 * * + ((2+3)*(4*))+ (+((2+3)*(4*))) find operar, convert infix, enclose in () iterate, treating suxpressions in parentheses as amic Next. With a stack, postfix expressions are easy evaluate.

4 4 20 2 2 00 0 7 Stack client example: Postfix expression evaluation public class Postfix public static void main(string[] args) Stack<Double> stack = new Stack<Double>(); String ken = StdIn.

push((.0/stack.pop()) * stack.pop()); else if (ken.equals("sqrt")) stack.push(math.sqrt(stack.pop())); else stack.push(double.parsedouble(ken)); StdOut.println(stack.

6803398874989 Postfix program code (push literals; functions pop arguments). Add commands drive virtual graphics machine. Add loops, conditionals, functions, types, fonts, strings.

5 Stack client example: Postfix expression evaluation Postfix arithmetic expression evaluation Algithm Infix. Standard way of writing arithmetic expressions, using parentheses f precedence. While input stream is nonempty, read a ken. Value: Push on the stack. Operar: Pop operand(s), apply operar, push the result. Example. ( + ( ( ) * ( 4 * ) ) ) = ( + ( * 20) ) = 0 Postfix. Write operar after operands (instead of in tween them). Example * * + also called "reverse Polish" ation (RPN) Jan ukasiewicz = 4 * * + Remarkable fact. No parentheses are needed! * * + There is only one way parenthesize a postfix expression. (2+3)4 * * + ((2+3)*(4*))+ (+((2+3)*(4*))) find operar, convert infix, enclose in () iterate, treating suxpressions in parentheses as amic Next. With a stack, postfix expressions are easy evaluate Made slide rule obsolete (!) 4 * * + HP-3 (972) handheld calcular. "Enter" means "push". No parentheses Stack client example: Postfix expression evaluation public class Postfix public static void main(string[] args) Stack<Double> stack = new Stack<Double>(); String ken = StdIn.readString(); if (ken.equals("*")) stack.push(stack.pop() * stack.pop()); else if (ken.equals("+")) stack.push(stack.pop() + stack.pop()); else if (ken.equals("-")) stack.push(- stack.pop() + stack.pop()); else if (ken.equals("/")) stack.push((.0/stack.pop()) * stack.pop()); else if (ken.equals("sqrt")) stack.push(math.sqrt(stack.pop())); else stack.push(double.parsedouble(ken)); StdOut.println(stack.pop()); 2 = 20 = 0 = 00 8 Real-wld stack application: PostScript PostScript (Warnock-Geschke, 980s): A turtle with a stack. % java Postfix * * + 0 % java Postfix sqrt + 2 / Postfix program code (push literals; functions pop arguments). Add commands drive virtual graphics machine. Add loops, conditionals, functions, types, fonts, strings. push(00) PostScript code + move line line line 00 call "move" (takes args from stack) define a path draw the path A simple virtual machine, but a y Perspective stroke 300 Easy specify published page. Easy implement on various specific printers. Revolutionized wld of publishing. Easy add operars of all sts. Can do infix with two stacks (see text). Could output TOY program. Indicative of how Java compiler wks. Aher stack machine: The JVM ( Java Virtual Machine)! 9 20

6 APIs Clients Strawman implementation Linked lists Implementations APIs Clients Strawman implementation Linked lists Implementations Strawman ADT f pushdown stacks Strawman implementation: Instance variables and construcr Warmup: simplify the ADT Implement only f items of type String. Have client provide a stack capacity in the construcr. Data structure choice. Use an array hold the collection. construcr values public class StrawStack private String[] a; private int N = 0; a[0] a[] a[2] items on stack Strawman API public class StrawStack StrawStack(int max) void push(string item) String pop() create a stack of capacity max add item stack return the string most recently pushed public StrawStack(int max) a = new String[max]; N "upside down" representation of boolean isempty() is the stack empty? int size() numr of strings on the stack Rationale. Allows us represent the collection with an array of strings

7 Strawman stack implementation: Test client TEQ on stacks public static void main(string[] args) int max = Integer.parseInt(args[0]); StrawStack stack = new StrawStack(max); String item = StdIn.readString(); if (item.equals("-")) stack.push(item); else StdOut.print(stack.pop()); StdOut.println(); construcrs % me.txt is % java StrawStack 20 <.txt Q. Can we always insert pop() commands make items come out in sted der? Example Example Example What we expect, once the implementation is done TEQ on stacks Strawman implementation: Methods Q. Can we always insert pop() commands make items come out in sted der? Methods define data-type operations (implement APIs). construcrs Example Example Example public class StrawStack public boolean isempty() return (N == 0); public void push(object item) a[n++] = item; N after push() A. No. Example. 6 no way f popped fe 6 public String pop() return a[--n]; public int size() return N; all constant-time one-liners! N N after pop() Note. In a queue, they always come out in the der they came in

8 Strawman pushdown stack implementation Trace of strawman stack implementation (array representation) public class StrawStack private String[] a; private int N = 0; public StrawStack(int max) a = new String[max]; public boolean isempty() return (N == 0); public void push(string item) a[n++] = item; public String pop() return a[--n]; public int size() return N; public static void main(string[] args) int max = Integer.parseInt(args[0]); StrawStack stack = new StrawStack(max); String item = StdIn.readString(); if (item.compareto("-")!= 0) stack.push(item); else StdOut.print(stack.pop()); StdOut.println(); construcr % me.txt is % java StrawStack 20 <.txt 29 stack contents after operation push is pop a[0] a[] a[2] a[3] a[4] a[] a[6] a[7] a[8] a[9] a[0] a[] a[2] a[3] a[4] a[] a[6] a[7] a[8] a[9] N Significant wasted space when stack size is near the capacity (typical). is 30 Benchmarking the strawman stack implementation StrawStack implements a fixed-capacity collection haves like a stack if the data fits. It does implement the stack API meet the perfmance specifications. Stack API StrawStack wks only f strings Perfmance specifications public class Stack<Item> Stack<Item>() void push(item item) Item pop() create a stack of objects, all of type Item add item stack boolean isempty() is the stack empty? int size() remove and return the item most recently pushed # of objects on the stack All operations are constant-time. Memy use is proptional the size of the collection, when it is nonempty. No limits within the code on the collection size. StrawStack requires client provide capacity APIs Clients Strawman implementation Linked lists Implementations Nice try, but need a new data structure. 3

9 Data structures: sequential vs. linked Sequential data structure Put objects next one aher. TOY: consecutive memy cells. Java: array of objects. Fixed size, arbitrary access. i th element Array at C0 addr value C0 "Alice" C "Bob" C2 "Carol" C3 Linked list at C4 addr value C0 "Carol" C null C2 C3 APIs Clients Strawman implementation Linked lists Implementations Linked data structure Associate with each object a link aher one. TOY: link is memy address of next object. Java: link is reference next object. Variable size, sequential access. next element Overlooked by novice programmers. Flexible, widely used method f ganizing data. C4 C C6 C7 C8 C9 CA CB C4 C C6 C7 C8 C9 CA CB "Alice" CA "Bob" C0 34 Simplest singly-linked data structure: linked list Singly-linked data structures Linked list A recursive data structure. Def. A linked list is null a reference a node. Def. A node is a data type contains a reference a node. Unwind recursion: A linked list is a sequence of nodes. private class Node private String item; private Node next; Even with just one link ( Linked list (this lecture) ) a wide variety of data structures are possible. Tree Rho Representation Use a private nested class Node implement the node abstraction. F simplicity, start with nodes having two values: a String and a Node. Circular list (TSP) General case A linked list "Alice" "Bob" "Carol" item next null Multiply linked structures: many me possibilities! From the point of view of a particular object, all of these structures look the same. 3 36

10 Building a linked list List processing code Node third = new Node(); third.item = "Carol"; third.next = null; Node second = new Node(); second.item = "Bob"; second.next = third; Node = new Node();.item = "Alice";.next = second; third C0 second CA C4 addr C0 C C2 C3 C4 C C6 C7 C8 value "Carol" null "Alice" CA Standard operations f processing data structured as a singly-linked list Add a node at the ginning. Remove and return the node at the ginning. Add a node at the end (requires a reference the last node). Traverse the list (visit every node, in sequence). An operation calls f a doubly-linked list (slightly yond our scope) Remove and return the node at the end. second third C9 CA "Bob" "Alice" "Bob" "Carol" CB C0 null List processing code: Remove and return the item List processing code: Add a new node at the ginning Goal. Remove and return the item in a linked list. Goal. Add item a linked list. item "Dave" "Alice" "Bob" "Carol" "Alice" "Bob" "Carol" item =.item; item "Alice" "Alice" "Bob" "Carol" Node second = ; second "Alice" "Bob" "Carol" second =.next; item "Alice" "Alice" "Bob" "Carol" = new Node(); "Alice" "Bob" "Carol" available f garbage collection second return item; item "Alice" "Bob" "Carol".item = item;.next = second; "Dave" "Alice" "Bob" "Carol" 39 40

11 List processing code: Traverse a list Goal. Visit every node on a linked list. TEQ on linked lists Q. What is the effect of the following code (-so-easy question)? Node x = ; while (x!= null) StdOut.println(x.item); x = x.next; x "Alice" "Bob" "Carol" StdOut Alice Bob Carol Node list = null; Node old = list; list = new Node(); list.item = StdIn.readString(); list.next = old; f (Node t = list; t!= null; t = t.next) StdOut.println(t.item); 4 42 TEQ on linked lists Q. What is the effect of the following code (-so-easy question)? TEQ 2 on stacks Q. Give code uses a stack print the strings from StdIn on StdOut, in reverse der. Node list = null; Node old = list; list = new Node(); list.item = StdIn.readString(); list.next = old; f (Node t = list; t!= null; t = t.next) StdOut.println(t.item); list old list old list A. Prints the strings from StdIn on StdOut, in reverse der. Note. Better use a stack

12 TEQ 2 on stacks TEQ 2 on linked lists Q. Give code uses a stack print the strings from StdIn on StdOut, in reverse der. Q. What is the effect of the following code (-so-easy question)? A. Stack<String> stack = new Stack<String>(); stack.push(stdin.readstring()); while (!stack.isempty()) StdOut.println(stack.pop()); Node list = new Node(); list.item = StdIn.readString(); Node last = list; last.next = new Node(); last = last.next; last.item = StdIn.readString(); 4 46 TEQ 2 on linked lists Q. What is the effect of the following code (-so-easy question)? Node list = new Node(); list.item = StdIn.readString(); Node last = list; last.next = new Node(); last = last.next; last.item = StdIn.readString(); A. Puts the strings from StdIn on a linked list, in the der they are read (assuming at least one string). Note. Better use a queue, in most applications. list list list last last last APIs Clients Strawman implementation Linked lists Implementations In this course, we restrict use of linked lists data-type implementations 47

13 ADT f pushdown stacks: review A pushdown stack is an idealized model of a LIFO srage mechanism. An ADT allows us write Java programs use and manipulate pushdown stacks. APIs Clients Strawman implementation Linked lists Implementations API Perfmance specifications public class Stack<Item> Stack<Item>() void push(item item) add item stack Item pop() boolean isempty() is the stack empty? int size() create a stack of objects, all of type Item remove and return the item most recently pushed # of objects on the stack All operations are constant-time. Memy use is proptional the size of the collection, when it is nonempty. No limits within the code on the collection size. 0 Pushdown stack implementation: Instance variables and construcr Stack implementation: Test client Data structure choice. Use a linked list hold the collection. public class Stack<Item> private Node = null; private int N = 0; private class Node private Item item; private Node next; use in place of concrete type objects on stack construcr construcrs public static void main(string[] args) Stack<String> stack = new Stack<String>(); String item = StdIn.readString(); if (item.equals("-")) stack.push(item); else System.out.print(stack.pop()); StdOut.println(); % me.txt is Annoying exception ( a problem here). Can't declare an array of Item objects (don't ask why). Need cast: Item[] a = (Item[]) new Object[N] What we expect, once the implementation is done. % java Stack <.txt 2

14 Stack implementation: Methods Stack implementation Methods define data-type operations (implement the API). public class Stack<Item> public boolean isempty() return == null; public void push(item item) Node second = ; = new Node();.item = item;.next = second; N++; public Item pop() Item item =.item; =.next; N--; return item; public int size() return N; add a new node the ginning of the list remove and return item on list instance variable second construcrs local variable in push() 3 public class Stack<Item> private Node = null; private int N = 0; private class Node private Item item; private Node next; public boolean isempty() return == null; public void push(item item) Node second = ; = new Node();.item = item;.next = second; N++; public Item pop() Item item =.item; =.next; N--; return item; public int size() return N; public static void main(string[] args) // See earlier slide nested class % me.txt is % java Stack <.txt 4 Trace of stack implementation (linked list representation) Benchmarking the stack implementation push is pop Pop from the ginning Push the ginning is Stack implements the stack abstraction. It does implement the API and meet the perfmance specifications. Stack API Perfmance specifications public class Stack<Item> Stack<Item>() void push(item item) Item pop() All operations are constant-time. Memy use is proptional the size of the collection, when it is nonempty. No limits within the code on the collection size. Made possible by linked data structure. create a stack of objects, all of type Item add item stack boolean isempty() is the stack empty? int size() remove and return the item most recently pushed # of objects on the stack dequeue(): same code as pop() enqueue(): slightly me complicated, like TEQ 2 Also possible implement the queue abstraction with a singly-linked list (see text). 6

15 Summary push the pop from the ginning ginning Stacks and queues Fundamental collection abstractions. Differ only in der in which items are removed. Perfmance specifications: Constant-time f all operations and space proptional numr of objects. stack Last In Out dequeue from the ginning In queue Out enqueue at the end Linked structures APIs Clients Strawman implementation Linked lists Implementations Fundamental alternative sequential structures. Enable implementations of the stack/queue abstractions meet perfmance specifications. Next: Symbol tables 7 Section 4.3

14. Stacks and Queues

1 COMPUTER SCIENCE S E D G E W I C K / W A Y N E 14. Stacks and Queues Section 4.3 http://introcs.cs.princen.edu COMPUTER SCIENCE S E D G E W I C K / W A Y N E 14. Stacks and Queues APIs Clients Strawman