Foundations of Software Design Fall 2002 Marti Hearst

Foundations of Software Design Fall 2002 Marti Hearst Lecture 12: Stacks and Queues 1

Lingering Question • Why is the expected value of accessing an array of length n going to take time n/2? • The expected value is the number of steps you’d expect to take on average. • The average number of steps you’ll have to take walking through an array of length n is: – (1 + 2 + 3 + … + n)/n – This is (n(n+1)/2)/n = (n+1)/2 – This is O(n/2) which is O(n) 2

Lingering Question • Why is O(n/2) equivalent to O(n)? • Recall the definition of O(g(n)): f(n) is (g(n)) if there exist positive constants n 0 and c such that for all n>=n 0, f(n) <= c*g(n) – In the case of n/2 vs. n, there is a constant: 2 – – f(n) = n/2 g(n) = n f(n) <= 2*g(n) Thus f(n) is O(g(n)) 3

Lingering Question • Why is O(n) not equivalent to O( )? • Recall the defintion of O(g(n)): f(n) is (g(n)) if there exist positive constants n 0 and c such that for all n>=n 0, f(n) <= c*g(n) – In the case of n vs. , there is no constant that satisfies the condition for all values of n. – Example: Set c to 100, 000 • Say n =10, 000 • Then = 100, 000 – Thus c is too small. We just can’t pick a large enough c. 4

Definition of Big-Oh A running time is O(g(n)) if there exist constants n 0 > 0 and c > 0 such that for all problem sizes n > n 0, the running time for a problem of size n is at most c(g(n)). In other words, c(g(n)) is an upper bound on the running time for sufficiently large n. http: //www. cs. dartmouth. edu/~farid/teaching/cs 15/cs 5/lectures/0519. html c g(n) 5

What is a Data Structure? • A systematic way of organizing and accessing data. (Goodrich & Tamassia) • An organization of information, usually in memory, for better algorithm efficiency, such as a queue, stack linked list, heap, and tree. It may include redundant information, such as length of the list or number of nodes in a tree. (http: //hissa. nist. gov/dads/terms. html) 6

Stacks 7

Stack • Container of objects that are inserted and removed according to the principle of – Last-in-first-out – LIFO • Objects can be inserted at any time, but only the most recently inserted can be removed at any time. • Operations: – Pop: remove item from stack – Push: enter item onto stack 8

Why Stacks? • The Undo facility in software applications – Is LIFO a good model for this? Why or why not? • The Back button facility in web browsers – Is LIFO a good model? Why or why not • Certain mathematical calculators (operand stack) – Makes it easy to do parenthesized expressions – Example: • • 10 Enter (pushes 10) 30 Enter (pushes 30) 15 Enter (pushes 15) Plus (pops and adds the most recent pair; then pushes the result onto the top of the stack) • Plus (same as above; end up with 55 as only entry) 9

Push notes onto the stack • • • (empty stack) Push do Push re Push mi Push fa Push so Push la Push ti Push do --Pop (8 times) Halt. Top of stack -do re do mi re do fa mi re do so fa mi re do la so fa mi re do ti la so fa mi re do What do the pops sound like? 10

What do the pops sound like? (Sing the note each time you do a pop operation) • • • Push do Push re Push mi Pop Push fa Push so Pop Pop Halt. Top of stack do re do mi re do do fa do so fa do do -- 11

From Goodrich & Tamassia 12

Stack Running Times • What is the running time of each operation? • Push O(1) • Pop O(1) • is. Empty() O(1) 13

More Definitions • What is an ADT? – Abstract data type – A model of a data structure that specifies • The type of data stored • The operations supported • The types of input and output parameters – Specifies what the program does, but not how it does it • What is an API? – Application Programming Interface • The names of the methods supported by an ADT • How those methods are to be declared and used – e. g. , what order the parameters are listed in • The API specifies the programming details of the ADT 14

From Goodrich & Tamassia 15

From Goodrich & Tamassia 16

Stack Example • Backtracking • 8 Queens Example 17

Stacks in the Java VM • Each process running in a java program has a java method stack • Each time a method is called, its state is pushed onto the method stack – The local variables and necessary object references (pointers) are also stored with the method – All this info together is called a stack frame. • This is useful for – Printing error messages (showing the stack trace) – Doing recursive method calls 18

From Goodrich & Tamassia 19

Memory usage in the Java VM Makes memory available for new objects – This is called “the heap” – When the process calls “new”, we allocate the appropriate amount of memory • The heap can be implemented as a queue of blocks of memory Program code Doesn’t grow Java stack Stores method call frames Free Memory Heap Stores objects 20

Queues http: //www. lib. uconn. edu/Dodd. Center/ASC/Wilcox/Students. htm 21

Queue • Container of objects that are inserted and removed according to the principle of – First-in-first-out – FIFO • Objects can be inserted at any time, but only the least recently inserted can be removed at any time. • Operations: – Enqueue: put item onto queue – Dequeue: remove item from queue 22

Queue Running Times • What is the running time of each operation? • Enqueue O(1) • Dequeue O(1) • is. Empty() O(1) 23

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How are Queues Used? • Queues are used extensively in – The OS • For scheduling processes to receive resources – Computer networking • For keeping storing and sending network packets 25

Use of Queues in the OS Processes waiting in a queue http: //courses. cs. vt. edu/~csonline/OS/Lessons/Processes/index. html 26

Use of Queues in Distributed Systems Animation by Remzi Arpaci-Dusseau 27

Sequences, Lists, & Vectors • There are many ways to implement sequences of items • In order of abstractness: – Sequence > List > Vector • Know about Vectors in Java – Can be more intuitive to program with – But can be less efficient – Implements the Enumeration interface 28

Java Vector API 29

Java Vector API 30

Vectors in Java • How do they differ from arrays? – Can grow the length dynamically – Can insert items into any position – Have a different API (set of method calls) • What are the running times of the operations? – boolean is. Empty() • O(1) – void copy. Into(Object[] an. Array) • O(n) – Object first. Element() • O(1) – boolean contains(Object elem) • O(n) – Object element. At(int index) • O(1) 31