Week 4 Stacks & Queues

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1 CPSC 319 Week 4 Stacks & Queues Xiaoyang Liu xiaoyali@ucalgary.ca

2 Stacks and Queues Fundamental data types. Value: collection of objects. Operations: insert, remove, iterate, test if empty. Intent is clear when we insert. Which item do we remove? stack push pop queue enqueue dequeue Stack. Examine the item most recently added. Queue. Examine the item least recently added. LIFO = "last in first out" FIFO = "first in first out"

3 Stacks New trays are put on the top of the stack and taken off the top. The last tray put on the stack is the first tray removed from the stack.

4 Stacks New trays are put on the top of the stack and taken off the top. The last tray put on the stack is the first tray removed from the stack. LIFO structure: last in/first out. push pop

5 Stacks New trays are put on the top of the stack and taken off the top. The last tray put on the stack is the first tray removed from the stack. push pop LIFO structure: last in/first out. clear() Clear the stack. isempty() Check to see if the stack is empty. push(el) Put the element el on the top of the stack. pop() Take the topmost element from the stack. topel() Return the topmost element in the stack without removing it.

6 Stacks How to implement a stack? Singly-linked list Array

7 Linked-list Implementation How to implement a stack with a singly-linked list?

8 Linked-list Implementation How to implement a stack with a singly-linked list? top of stack it was the best of null

9 Linked-list Implementation How to implement a stack with a singly-linked list? top of stack it was the best of null OR top of stack of best the was it null

10 Linked-list Implementation How to implement a stack with a singly-linked list? Maintain pointer first to first node in a singly-linked list. Push new item before first. Pop item from first. top of stack of best the was it null first

11 Linked-list Implementation Push(T data) save a link to the list Node oldfirst = first; oldfirst first or be to null create a new node for the beginning first = new Node(); oldfirst first or be to null set the instance variables in the new node first.item = "not"; first.next = oldfirst; first not or be to null

12 Linked-list Implementation Push(T data) Pop() save a link to the list save item to return Node oldfirst = first; String item = first.item; oldfirst first or be to delete first node null first = first.next; create a new node for the beginning first = new Node(); oldfirst first or be to null first first or or be be to null to set the instance variables in the new node null first.item = "not"; first.next = oldfirst; first not or be to return saved item return item; null

13 Linked-list Implementation Implement your own linked-list stack with the following operations! (5 mins) clear() Clear the stack. isempty() Check to see if the stack is empty. push(el) Put the element el on the top of the stack. pop() Take the topmost element from the stack. topel() Return the topmost element in the stack without removing it. Proposition. Every operation takes constant time in the worst case.

14 Exercise Adding large numbers: 18,274,364,583,929,273,748,459,595,684,373 and 8,129,498,165,026,350,236

15 Exercise Adding large numbers: 18,274,364,583,929,273,748,459,595,684,373 and 8,129,498,165,026,350,236 Integer variables cannot hold such large values, let alone their sum.

16 Exercise Adding large numbers: 18,274,364,583,929,273,748,459,595,684,373 and 8,129,498,165,026,350,236 Integer variables cannot hold such large values, let alone their sum. Can be solved if we treat these numbers as strings of numerals, store the numbers corresponding to these numerals on two stacks, and then perform addition by popping numbers from the stacks.

17 Exercise Adding large numbers: 592 and operand- Stack operand- Stack result- Stack

18 Array Implementation How to implement a stack with an array?

19 Array Implementation How to implement a stack with an array? top of stack it was the best of times null null null null

20 Array Implementation How to implement a stack with an array? top of stack it was the best of times null null null null OR top of stack times of best the was it null null null null

21 Array Implementation How to implement a stack with an array? Use array s[] to store N items on stack. push(): add new item at s[n]. pop(): remove item from s[n-1].

22 Array Implementation How to implement a stack with an array? Use array s[] to store N items on stack. push(): add new item at s[n]. pop(): remove item from s[n-1]. top of stack s[] it was the best of times null null null null N capacity = 10

23 Array Implementation How to implement a stack with an array? Use array s[] to store N items on stack. push(): add new item at s[n]. pop(): remove item from s[n-1]. top of stack s[] it was the best of times null null null null N capacity = 10 Defect. Stack overflows when N exceeds capacity. [stay tuned]

24 Array Implementation Stack considerations Overflow and underflow. Underflow: throw exception if pop from an empty stack. Overflow: use resizing array for array implementation. [stay tuned] Null items. We allow null items to be inserted. Implement your own stack with array!

25 Exercise Adding large numbers: 592 and 3784 (Array Implementation) operand- Stack operand- Stack result- Stack

26 Array Implementation Stack considerations Loitering. Holding a reference to an object when it is no longer needed. public String pop() { return s[--n]; } loitering public String pop() { String item = s[--n]; s[n] = null; return item; } this version avoids "loitering": garbage collector can reclaim memory for an object only if no outstanding references

27 Resizing-Array Implementation Q. How to grow and shrink array? First try. push(): increase size of array s[] by 1. pop(): decrease size of array s[] by 1.

28 Resizing-Array Implementation Q. How to grow and shrink array? First try. push(): increase size of array s[] by 1. pop(): decrease size of array s[] by 1. Too expensive. infeasible for large N Need to copy all items to a new array, for each operation. Array accesses to insert first N items = N + ( (N 1)) ~ N 2. 1 array access per push 2(k 1) array accesses to expand to size k (ignoring cost to create new array)

29 Resizing-Array Implementation Q. How to grow and shrink array? First try. push(): increase size of array s[] by 1. pop(): decrease size of array s[] by 1. Too expensive. infeasible for large N Need to copy all items to a new array, for each operation. Array accesses to insert first N items = N + ( (N 1)) ~ N 2. 1 array access per push 2(k 1) array accesses to expand to size k (ignoring cost to create new array) Challenge. Ensure that array resizing happens infrequently.

30 Resizing-Array Implementation Q. How to grow array? "repeated doubling" A. If array is full, create a new array of twice the size, and copy items. Array accesses to insert first N = 2 i items. N + ( N) ~ 3N. 1 array access per push k array accesses to double to size k (ignoring cost to create new array) Q. How to shrink array? First try. push(): double size of array s[] when array is full. halve size of array s[] when array is one-half full. pop():

31 Resizing-Array Implementation Too expensive in worst case. Consider push-pop-push-pop- sequence when array is full. Each operation takes time proportional to N. N = 5 to be or not to null null null N = 4 to be or not N = 5 to be or not to null null null N = 4 to be or not

32 Resizing-Array Implementation Q. How to shrink array? Efficient solution. push(): double size of array s[] when array is full. halve size of array s[] when array is one-quarter full. pop(): Invariant. Array is between 25% and 100% full.

33 Resizing-Array Implementation Amortized analysis. Starting from an empty data structure, average running time per operation over a worst-case sequence of operations. Proposition. Starting from an empty stack, any sequence of M push and pop operations takes time proportional to M. best worst amortized construct push 1 N 1 pop size 1 N doubling and halving operations order of growth of running time for resizing stack with N items

34 Resizing-Array Vs. Linked-list Tradeoffs. Can implement a stack with either resizing array or linked list; client can use interchangeably. Which one is better? Linked-list implementation. Every operation takes constant time in the worst case. Uses extra time and space to deal with the links. Resizing-array implementation. Every operation takes constant amortized time. Less wasted space. N = 4 to be or not null null null null first not or be to null

35 Queues A queue is simply a waiting line that grows by adding elements to its end and shrinks by taking elements from its front.

36 Queues A queue is simply a waiting line that grows by adding elements to its end and shrinks by taking elements from its front. enqueue FIFO structure: first in/first out. dequeue

Queues A queue is simply a waiting line that grows by adding elements to its end and shrinks by taking elements from its front. enqueue FIFO structure: first in/first out. clear() Clear the queue.

37 Queues A queue is simply a waiting line that grows by adding elements to its end and shrinks by taking elements from its front. enqueue FIFO structure: first in/first out. clear() Clear the queue. isempty() Check to see if the queue is empty. enqueue(el) Put the element el at the end of the queue. dequeue() Take the first element from the queue. firstel() Return the first element in the queue without removing it. dequeue

38 Linked-list Implementation How to implement a queue with a singly-linked list?

39 Linked-list Implementation How to implement a queue with a singly-linked list? back of queue front of queue times of best the was it null

40 Linked-list Implementation How to implement a queue with a singly-linked list? back of queue front of queue times of best the was it null OR front of queue back of queue it was the best of times null

41 Linked-list Implementation enqueue(t data) dequeue() save a link to the last node Node oldlast = last; save item to return String item = first.item; oldlast last first to be or null delete first node first = first.next; create a new node for the end last = new Node(); last.item = "not"; first to be link the new node to the end of the list oldlast or null last not null first first to to be be last last or null or null oldlast.next = last; first to be oldlast or last not null return saved item return item;

42 Linked-list Implementation Implement your own linked-list queue with the following operations! (5 mins) clear() Clear the queue. isempty() Check to see if the queue is empty. enqueue(el) Put the element el at the end of the queue. dequeue() Take the first element from the queue. firstel() Return the first element in the queue without removing it. Queue can be implemented with resizing arrays as well. Refer to Figure 4.9 in your text book for more information.

43 Exercise Acrostic Checker: Round the wondrous globe I wander wild, Up and down-hill Age succeeds to youth Toiling all in vain to find a child Half so loving, half so dear as Ruth. The poem is dedicated to Ruth Dymes, which is indicated not only by the last word of the poem, but also by reading in sequence the first letter of each line, which also spells Ruth. This type of poem is called an acrostic, and it is characterized by initial letters that form a word or phrase when taken in order.

44 Exercise Acrostic Checker: The algorithm: acrosticindicator() while not finished read a line of poem; enqueue the first letter of the line; output the line; while queue is not empty dequeue and print a letter; Save the poem to a text file and read it line by line Implement this with your own queue data structure.

45 Exercise Acrostic Checker: The algorithm: acrosticindicator() while not finished read a line of poem; enqueue the first letter of the line; output the line; while queue is not empty dequeue and print a letter; For more significant example, refer to Figure 4.12 in your text book. Save the poem to a text file and read it line by line Implement this with your own queue data structure.

46 References 1. Algorithms, fourth edition 2. Algorithm, Book site: 3. Data Structures and Algorithms in Java, 2013, fourth edition

CSE 214 Computer Science II Stack

CSE 214 Computer Science II Stack Spring 2018 Stony Brook University Instructor: Shebuti Rayana shebuti.rayana@stonybrook.edu http://www3.cs.stonybrook.edu/~cse214/sec02/ Random and Sequential Access Random