Algorithms. Algorithms 1.3 BAGS, QUEUES, AND STACKS. stacks resizing arrays queues generics iterators applications. Is Polleverywhere working?

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1 Is Polleverywhere wking? Algithms ROBERT SEDGEWICK KEVIN WAYNE 1.3 BAGS, QUEUES, AND STACKS Algithms F O U R T H E D I T I O N ROBERT SEDGEWICK KEVIN WAYNE stacks resizing arrays queues generics iterars applications 1 Stacks and queues Client, implementation, interface Fundamental data types. Collections of objects. Operations: insert, remove, iterate, test if empty. Intent is clear when we insert. Which item do we remove? enqueue stack queue push pop dequeue Separate interface and implementation. Ex: stack, queue, bag, priity queue, symbol table, union-find,. Benefits. Client can't know details of implementation client has many implementation from which choose. Implementation can't know details of client needs many clients can re-use the same implementation. Design: creates modular, reusable libraries. Perfmance: use optimized implementation where it matters. Stack. Examine the item most recently added. Queue. Examine the item least recently added. LIFO = "last in first out" FIFO = "first in first out" Client: program using operations defined in interface. Implementation: actual code implementing operations. Interface: description of data type, basic operations. 3 4

2 Stack API Warmup API. Stack of strings data type. push pop 1.3 BAGS, QUEUES, AND STACKS public class StackOfStrings StackOfStrings() create an empty stack Algithms ROBERT SEDGEWICK KEVIN WAYNE stacks resizing arrays queues generics iterars applications void push(string item) insert a new string on stack String pop() remove and return the string most recently added boolean isempty() is the stack empty? int size() numr of strings on the stack Warmup client. Reverse sequence of strings from standard input. 6 Stack test client Read strings from standard input. If string equals "-", pop string from stack and print. Otherwise, push string on stack. push pop pollev.com/jhug text Q: Which of the following inputs the stack test client does NOT produce the output public static void main(string[] args) StackOfStrings stack = new StackOfStrings(); while (!StdIn.isEmpty()) String s = StdIn.readString(); if (s.equals("-")) StdOut.print(stack.pop()); else stack.push(s); % me.txt that is % java StackOfStrings <.txt that A [740669] B [740670] C [740671] D [740672] public static void main(string[] args) StackOfStrings stack = new StackOfStrings(); while (!StdIn.isEmpty()) % java StackOfStrings <.txt String s = StdIn.readString(); if (s.equals("-")) StdOut.print(stack.pop()); else stack.push(s); % me.txt that is that 7 8

Stack: linked-list representation Stack pop: linked-list implementation Maintain pointer first node

item; first insert at front of linked list inner class remove from front - first = first.

implementation in Java public class LinkedStackOfStrings private Node first = ; private inner class

first = new Node(); first.next = oldfirst; first.

3 Stack: linked-list representation Stack pop: linked-list implementation Maintain pointer first node in a linked list; insert/remove from front. StdIn StdOut String item = first.item; first insert at front of linked list inner class remove from front - first = first.next; of linked list Stack push: linked-list implementation Stack: linked-list implementation in Java public class LinkedStackOfStrings private Node first = ; private inner class (access modifiers don't matter) inner class public void push(string item) Node oldfirst = first; first = new Node(); first.next = oldfirst; first.item = item; return first == ; public void push(string item) Node oldfirst = first; first = new Node(); first.item = item; first.next = oldfirst; String item = first.item; first = first.next; 11 12

4 Stack: linked-list implementation perfmance Stack: array implementation Proposition. Every operation takes constant time in the wst case. Proposition. A stack with N items uses ~ 40 N bytes. public class LinkedStackOfStrings private Node first = ; inner class object overhead extra overhead item next references 16 bytes (object overhead) 8 bytes (inner class extra overhead) 8 bytes (reference String) 8 bytes (reference Node) 40 bytes per stack node Array implementation of a stack. Use array s[] sre N items on stack. push(): add new item at s[n]. s[] pop(): remove item from s[n-1] N capacity = 10 Remark. This accounts f the memy f the stack (but the memy f strings themselves, which the client owns). Defect. Stack overflows when N exceeds capacity. [stay tuned] Stack: array implementation Stack considerations public class FixedCapacityStackOfStrings private String[] s; private int N = 0; //# items on stack public FixedCapacityStackOfStrings(int capacity) s = new String[capacity]; return N == 0; a cheat (stay tuned) Overflow and underflow. Underflow: might want throw exception if pop from an empty stack. Overflow: use resizing array f array implementation. [stay tuned] Null items. We allow items inserted. Loitering. Holding a reference an object when it is no longer needed. public void push(string item) s[n++] = item; //some consider this bad style N--; String item = S[N]; s[n] = ; //these two lines //prevent loitering //so do something similar 15 return s[--n]; loitering String item = s[--n]; s[n] = ; this version avoids "loitering": garbage collecr can reclaim memy only if no outstanding references 16

Stack: resizing-array implementation Problem. Requiring client provide capacity does implement API! Q. How grow and shrink array? Algithms ROBERT SEDGEWICK KEVIN WAYNE http://algs4.cs.princen.edu 1.

5 Stack: resizing-array implementation Problem. Requiring client provide capacity does implement API! Q. How grow and shrink array? Algithms ROBERT SEDGEWICK KEVIN WAYNE BAGS, QUEUES, AND STACKS stacks resizing arrays queues generics iterars applications First try. push(): increase size of array s[] by 1. pop(): decrease size of array s[] by 1. Too expensive. Need copy all items a new array. Inserting first N items takes time proptional N ~ N 2 / 2. infeasible f large N Challenge. Ensure that array resizing happens infrequently. 18 Stack: resizing-array implementation Q. How grow array? A. If array is full, create a new array of twice the size, and copy items. public ResizingArrayStackOfStrings() s = new String[1]; "repeated doubling" Stack: amtized cost of adding a stack Cost of inserting first N items. N + ( N) ~ 3N. 1 array access per push k array accesses double size k (igning cost create new array) public void push(string item) if (N == s.length) resize(2 * s.length); s[n++] = item; private void resize(int capacity) String[] copy = new String[capacity]; f (int i = 0; i < N; i++) copy[i] = s[i]; s = copy; see next slide 128 cost (array accesses) 0 one gray dot f each operation red dots give cumulative average 3 0 numr of push() operations 128 Consequence. Inserting first N items takes time proptional N ( N 2 )

Stack: resizing-array implementation Stack: resizing-array implementation Q. How shrink array? Q. How shrink array? First try. push(): double size of array s[] when array is full.

6 Stack: resizing-array implementation Stack: resizing-array implementation Q. How shrink array? Q. How shrink array? First try. push(): double size of array s[] when array is full. pop(): halve size of array s[] when array is one-half full. Efficient solution. push(): double size of array s[] when array is full. pop(): halve size of array s[] when array is one-quarter full. Too expensive in wst case. Consider push-pop-push-pop- sequence when array is full. Each operation takes time proptional N. N = 5 String item = s[--n]; s[n] = ; if (N > 0 && N == s.length/4) resize(s.length/2); N = 4 N = 5 N = 4 Invariant. Array is tween 25% and 100% full Stack: resizing-array implementation trace Stack resizing-array implementation: perfmance push() pop() N a.length a[] that 4 8 that - that is 2 2 is Trace of array resizing during a sequence of push() and pop() operations Amtized analysis. Starting from an empty data structure, average running time per operation over a wst-case sequence of operations. Proposition. Starting from an empty stack, any sequence of M push and pop operations takes time proptional M. construct push pop size st wst amtized N 1 1 N der of growth of running time f resizing stack with N items doubling and halving operations 23 24

7 Stack resizing-array implementation: memy Stack resizing-array implementation: memy Invariant. Array is tween 25% and 100% full. Invariant. Array is tween 25% and 100% full. public class ResizingArrayStackOfStrings private String[] s; private int N = 0; 8 bytes (reference array) 24 bytes (array overhead) 8 bytes array size 4 bytes (int) 4 bytes (padding) public class ResizingArrayStackOfStrings private String[] s; private int N = 0; 8 bytes (reference array) 24 bytes (array overhead) 8 bytes array size 4 bytes (int) 4 bytes (padding) pollev.com/jhug text pollev.com/jhug text Q: If the array is completely full, how many bytes does the stack use sre N strings? Give your answer in Tilde ation. A. ~N bytes [740928] D. ~16N bytes [740931] B. ~4N bytes [740929] E. ~32N bytes [740932] C. ~8N bytes [740930] F. ~16N + 40 bytes [740933] Do count the memy used sre the actual strings, only count the references. Q: If N is the numr of strings in the stack, how much memy does a ResizingArrayStackOfStrings use in the wst case as a function of N? Give your answer in Tilde ation. A. ~N bytes [740966] D. ~16N bytes [740969] B. ~4N bytes [740967] E. ~32N bytes [740970] C. ~8N bytes [740968] F. ~16N + 40 bytes [740971] As fe, don t count the memy of the actual strings, just references Stack resizing-array implementation: memy usage Stack implementations: resizing array vs. linked list Proposition. Uses tween ~ 8 N and ~ 32 N bytes represent a stack with N items. ~ 8 N when full. ~ 32 N when one-quarter full. public class ResizingArrayStackOfStrings private String[] s; private int N = 0; 8 bytes (reference array) 24 bytes (array overhead) 8 bytes array size 4 bytes (int) 4 bytes (padding) Tradeoffs. Can implement a stack with either resizing array linked list; client can use interchangeably. Which one is tter? Linked-list implementation. Every operation takes constant time in the wst case. Uses extra time and space deal with the links. Resizing-array implementation. Every operation takes constant amtized time. Less wasted space. Invariant. Array is tween 25% and 100% full. N = 4 Remark. This accounts f the memy f the stack (but the memy f strings themselves, which the client owns). first 27 28

8 Queue API enqueue public class QueueOfStrings 1.3 BAGS, QUEUES, AND STACKS QueueOfStrings() create an empty queue void enqueue(string item) insert a new string on queue Algithms stacks resizing arrays queues generics String dequeue() remove and return the string least recently added boolean isempty() is the queue empty? int size() numr of strings on the queue ROBERT SEDGEWICK KEVIN WAYNE iterars applications dequeue 30 Queue: linked-list representation Queue dequeue: linked-list implementation Maintain pointer first and last nodes in a linked list; insert/remove from opposite ends. StdIn StdOut first last inner class remove from front of linked list - - insert at end of linked list public String dequeue() String item = first.item; first = first.next; 31 32

9 Queue dequeue: linked-list implementation Queue enqueue: linked-list implementation inner class inner class public String dequeue() String item = first.item; first = first.next; if (first == ) last = ; public void enqueue(string item) Node oldlast = last; last = new Node(); last.item = item; oldlast.next = last; Queue enqueue: linked-list implementation Queue: linked-list implementation in Java public class LinkedQueueOfStrings private Node first, last; /* same as in LinkedStackOfStrings */ return first == ; inner class public void enqueue(string item) Node oldlast = last; last = new Node(); last.item = item; if (first == ) first = last; else // avoid pointer oldlast.next = last; public void enqueue(string item) Node oldlast = last; last = new Node(); last.item = item; last.next = ; if (isempty()) first = last; else oldlast.next = last; public String dequeue() String item = first.item; first = first.next; if (isempty()) last = ; special cases f empty queue 35 36

10 Sentinel nodes Sentinel nodes Annoying Cases. Enqueueing on an empty list. Dequeuing an empty list. Solutions Write special case code. Create a node that can never removed (sentinel node). Always first in line. Never gets leave the line. The queue is considered empty if sentinel is the only item. Annoying Cases. Going /from empty list. Solutions Use an if statement. Never allow an empty list. Create a single dummy node. Null pointer if dequeue on empty list. Never allow a pointer. Create two dummy nodes. Have back dummy node point backwards. dummy node returned if dequeue on empty list. public class LinkedQueueOfStrings private Node sentinel, last; public LinkedQueueOfStrings sentinel = new Node(); sentinel.item = dummy node ; last = sentinel; return sentinel == last; public void enqueue(string item) Node oldlast = last; last = new Node(); last.item = item; oldlast.next = last; public String dequeue() String item = sentinel.next.item; sentinel.next = sentinel.next.next; 37 Single dummy node example. Two nodes is arguably tter. 38 Queue: resizing array implementation Array implementation of a queue. Use array q[] sre items in queue. enqueue(): add new item at q[tail]. q[] dequeue(): remove item from q[head]. Update head and tail modulo the capacity. Add resizing array. the st of times head tail capacity = 10 Algithms ROBERT SEDGEWICK KEVIN WAYNE BAGS, QUEUES, AND STACKS stacks resizing arrays queues generics iterars applications Q. How resize? 39

11 Parameterized stack Parameterized stack We implemented: StackOfStrings. We implemented: StackOfStrings. We also want: StackOfURLs, StackOfInts, StackOfVans,. We also want: StackOfURLs, StackOfInts, StackOfVans,. Attempt 1. Implement a separate stack class f each type. Attempt 2. Implement a stack with items of type Object. Maintaining cut-and-pasted code is tedious and err-prone. Casting is required in client. Casting is err-prone: run-time err if types mismatch. Rewriting code is tedious and err-prone. StackOfObjects s = new most reasonable approach until Java 1.5. Apple a = new Apple(); Orange b = new Orange(); s.push(a); s.push(b); a = (Apple) (s.pop()); run-time err 41 Parameterized stack 42 Generic stack: linked-list implementation We implemented: StackOfStrings. public class LinkedStackOfStrings private Node first = ; We also want: StackOfURLs, StackOfInts, StackOfVans,. Attempt 3. Java generics. Avoid casting in client. Discover type mismatch errs at compile-time instead of run-time. return first == ; type parameter Stack<Apple> s = new Stack<Apple>(); Apple a = new Apple(); Orange b = new Orange(); s.push(a); s.push(b); public class Stack<Item> private Node first = ; compile-time err a = s.pop(); Item item; return first == ; generic type name public void push(string item) Node oldfirst = first; first = new Node(); first.item = item; first.next = oldfirst; public void push(item item) Node oldfirst = first; first = new Node(); first.item = item; first.next = oldfirst; String item = first.item; first = first.next; public Item pop() Item item = first.item; first = first.next; Guiding principles. Welcome compile-time errs; avoid run-time errs

12 Generic stack: array implementation Generic stack: array implementation the way it should the way it is public class FixedCapacityStackOfStrings private String[] s; private int N = 0; public class FixedCapacityStack<Item> private Item[] s; private int N = 0; public class FixedCapacityStackOfStrings private String[] s; private int N = 0; public class FixedCapacityStack<Item> private Item[] s; private int N = 0; public..stackofstrings(int capacity) s = new String[capacity]; public FixedCapacityStack(int capacity) s = new Item[capacity]; public..stackofstrings(int capacity) s = new String[capacity]; public FixedCapacityStack(int capacity) s = (Item[]) new Object[capacity]; return N == 0; return N == 0; return N == 0; return N == 0; public void push(string item) s[n++] = item; public void push(item item) s[n++] = item; public void push(string item) s[n++] = item; public void push(item item) s[n++] = item; return s[--n]; public Item pop() return s[--n]; return s[--n]; public Item pop() return generic array creation allowed in Java the ugly cast Unchecked cast Generic data types: auboxing Q. What do about primitive types? % javac FixedCapacityStack.java Note: FixedCapacityStack.java uses unchecked unsafe operations. Note: Recompile with -Xlint:unchecked f details. % javac -Xlint:unchecked FixedCapacityStack.java FixedCapacityStack.java:26: warning: [unchecked] unchecked cast found : java.lang.object[] required: Item[] 1 warning a = (Item[]) new Object[capacity]; ^ Wrapper type. Each primitive type has a wrapper object type. Ex: Integer is wrapper type f int. Auboxing. Aumatic cast tween a primitive type and its wrapper. Stack<Integer> s = new Stack<Integer>(); s.push(17); // s.push(integer.valueof(17)); int a = s.pop(); // int a = s.pop().intvalue(); Botm line. Client code can use generic stack f any type of data

13 Iteration Question. How would you print out the contents of the stack without destroying it? Algithms ROBERT SEDGEWICK KEVIN WAYNE BAGS, QUEUES, AND STACKS stacks resizing arrays queues generics iterars applications public class StackOfStrings public void push() public void printstackofstrings(stackofstrings sos) 50 Iteration Question. How would you print out the contents of the stack without destroying it? public class StackOfStrings public void push() Iteration Question. How would you print out the contents of the stack without destroying it? public class StackOfStrings public void push() public void printstackofstrings(stackofstrings sos) StackOfStrings sos2; while (sos.isempty() == false) String s = sos.pop(); StdOut.println(s); sos2.push(s); while (sos2.isempty() == false) String s = sos2.pop(); sos.push(s); Alternate Approach. Extend the API suppt iteration. public class StackOfStrings public void push() public int startiterating() public String getnextstring() public boolean hasnextstring() StackOfStrings sos =...; sos.startiterating(); while (sos.hastnextstring()) System.out.println( sos.getnextstring()); 51 API above doesn t allow nested iteration! 52

14 Iteration Question. How would you print out the contents of the stack without destroying it? Iteration Design challenge. Suppt iteration over stack items by client, without revealing the internal representation of the stack. public class StackOfStrings public void push() s[] i N it was the st of times Java Approach. Extend the API suppt iteration using Iterable interface. first current public class StackOfStrings public void push() public Iterar<String> iterar() feach statement (shthand) f (String s : stack) StdOut.println(s); times of st the was it feach statement (shthand) f (String s : stack) StdOut.println(s); Java solution. Make stack implement the java.lang.iterable interface Iterars Q. What is an Iterable? A. Has a method called iterar() that returns an Iterar. Iterable interface public interface Iterable<Item> Iterar<Item> iterar(); Stack iterar: linked-list implementation impt java.util.iterar; public class Stack<Item> implements Iterable<Item>... public Iterar<Item> iterar() return new ListIterar(); Q. What is an Iterar? A. Has methods hasnext(), next() (and remove()). Q. Why make data structures Iterable? A. Java suppts elegant client code. feach statement (shthand) f (String s : stack) StdOut.println(s); Iterar interface public interface Iterar<Item> boolean hasnext(); Item next(); void remove(); equivalent code (longhand) optional; use at your own risk Iterar<String> i = stack.iterar(); while (i.hasnext()) String s = i.next(); StdOut.println(s); 55 private class ListIterar implements Iterar<Item> private Node current; first public ListIterar() current = first; public boolean hasnext() return current!= ; public void remove() /* suppted */ public Item next() throw NoSuchElementException Item item = current.item; if no me items in iteration current = current.next; current throw UnsupptedOperationException times of st the was it 56

15 Stack iterar: array implementation impt java.util.iterar; public class Stack<Item> implements Iterable<Item> public Iterar<Item> iterar() return new ReverseArrayIterar(); private class ReverseArrayIterar implements Iterar<Item> private int i; public ReverseArrayIterar() public boolean hasnext() public void remove() /* suppted */ public Item next() i N Algithms ROBERT SEDGEWICK KEVIN WAYNE BAGS, QUEUES, AND STACKS stacks resizing arrays queues generics iterars applications s[] it was the st of times Java collections library Java collections library List interface. java.util.list is API f an sequence of items. public interface List<Item> implements Iterable<Item> List() create an empty list boolean isempty() is the list empty? java.util.stack. Suppts push(), pop(), and and iteration. Extends java.util.vecr, which implements java.util.list interface from previous slide, including get() and remove(). Bloated and poly-designed API (why?) int size() numr of items void add(item item) append item the end Item get(int index) return item at given index Item remove(int index) return and delete item at given index boolean contains(item item) does the list contain the given item? Java 1.3 bug rept (June 27, 2001) The iterar method on java.util.stack iterates through a Stack from the botm up. One would think that it should iterate as if it were popping off the p of the Stack. Itearr<Item> iterar() iterar over all items in the list... status (closed, will fix) Implementations. java.util.arraylist uses resizing array; java.util.linkedlist uses linked list. caveat: only some It was an increct design decision have Stack extend Vecr ("is-a" rather than "has-a"). We sympathize with the submitter but can fix this cause of compatibility. operations are efficient 59 60

Java collections library War sry (from Assignment 1) java.util.stack. Generate random open sites in an N-by-N percolation system.

percolates blocked pick (i, j) at random; if already open, repeat. Takes ~ c1 N 2 seconds.

arraylist of N 2 closed sites. Pick an index at random and delete. open Takes ~ c2 N 4 seconds.

An interface, an implementation of a queue. Lesson. Don't use a library until you understand its API! Best practices.

61 Stack applications 62 Function calls Parsing in a compiler. Java virtual machine. Undo in a wd process. Back butn in a Web browser.

Function call: push local environment and return address. Return: pop return address and local environment. Recursive function.

16 Java collections library War sry (from Assignment 1) java.util.stack. Generate random open sites in an N-by-N percolation system. Extends java.util.vecr, which implements java.util.list interface Jenny: Suppts push(), pop(), and and iteration. percolates blocked pick (i, j) at random; if already open, repeat. Takes ~ c1 N 2 seconds. Kenny: from previous slide, including get() and remove(). Bloated and poly-designed API (why?) does percolate site create a java.util.arraylist of N 2 closed sites. Pick an index at random and delete. open Takes ~ c2 N 4 seconds. site open site connected p no open site connected p Why is my program so slow? Kenny java.util.queue. An interface, an implementation of a queue. Lesson. Don't use a library until you understand its API! Best practices. Use our implementations of Stack, Queue, and Bag. This course. Can't use a library until we've implemented it in class. 61 Stack applications 62 Function calls Parsing in a compiler. Java virtual machine. Undo in a wd process. Back butn in a Web browser. PostScript language f printers. Implementing function calls in a compiler.... How a compiler implements a function. Function call: push local environment and return address. Return: pop return address and local environment. Recursive function. Function that calls itself. Note. Can always use an explicit stack remove recursion. gcd (216, 192) static int gcd(int p, int q) if (q == 0) return p; else return gcd(q,gcd p %(192, q); 24) static int gcd(int p, int q) p = 192, q = 24 if (q == 0) return p; gcd else return gcd(q, p % (24, q); 0) static int gcd(int p, int q) if (q == 0) return p; p = 24, q = 0 else return gcd(q, p % q); p = 216, q =

17 Assignment 2 Implementation of two data types Randomized queue. Deque (double-ended queue). Imptant choice made Linked list vs. resizing array. Think carefully about whether your choice allows you oy timing constraints! Extra credit Complete the checkout line simular. Rept anything interesting you discover. OK do alone, even if you had a partner. Tiny amount of extra credit (1 point). No suppt in office hours. OK ask questions on Piazza me directly by . 65

Algorithms. Algorithms. Algorithms 1.3 BAGS, QUEUES, AND STACKS. stacks resizing arrays queues generics iterators applications

Algorithms. Algorithms. Algorithms 1.3 BAGS, QUEUES, AND STACKS. stacks resizing arrays queues generics iterators applications Algithms Stacks and queues 1.3 BAGS, QUEUES, AND STACKS Fundamental data types. Value: collection of objects. Operations: insert, remove, iterate, test if empty. Intent is clear when we insert. Which item