CSc 120. Introduction to Computer Programming II. 14: Stacks and Queues. Adapted from slides by Dr. Saumya Debray
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1 CSc 120 Introduction to Computer Programming II Adapted from slides by Dr. Saumya Debray 14: Stacks and Queues
2 linear data structures 2
3 Linear data structures A linear data structure is a collec6on of objects with a straight-line ordering among them each object in the collec6on has a posi*on for each object in the collec6on, there is a no6on of the object before it or a-er it 3
4 Data structures we've seen Linear Python lists (aka arrays) Linked lists Not linear Dic6onaries Sets 4
5 Today's topic Linear Not linear Python lists (aka arrays) Linked lists Stacks Queues Dequeues Dic6onaries Sets Key property: the way in which objects are added to, and removed from, the collec6on 5
6 stacks 6
7 Stacks A stack is a linear data structure where objects are inserted or removed only at one end all inser6ons and dele6ons happen at one par6cular end of the data structure this end is called the top of the stack the other end is called the bo1om of the stack inser6ons and dele6ons happen at one end 7
8 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top None stack borom None 8
9 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top stack borom 5 9
10 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top stack borom
11 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top stack borom
12 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top stack borom
13 Stacks: insertion of values Inser6on of a sequence of values into a stack: stack top stack borom
14 Stacks: insertion of values order in which values were inserted stack top stack borom
15 Stacks: removal of values order in which values were inserted Removing values from the stack: stack top stack borom
16 Stacks: removal of values order in which values were inserted Removing values from the stack: 43 stack top stack borom
17 Stacks: removal of values order in which values were inserted Removing values from the stack: 43 9 stack top stack borom
18 Stacks: removal of values order in which values were inserted Removing values from the stack: stack top stack borom
19 Stacks: removal of values order in which values were inserted Removing values from the stack: stack top stack borom
20 Stacks: removal of values order in which values were inserted Removing values from the stack: stack top stack borom None None
21 Stacks: removal of values order in which values were inserted Removing values from the stack: order in which values were removed 21
22 Stacks: LIFO property order in which values were inserted Removing values from the stack: order in which values were removed values are removed in reverse order from the order of inser6on "LIFO order" Last in, First out 22
23 Methods for a Stack class Stack() : creates a new empty stack push(item) : adds item to the top of the stack returns nothing modifies the stack pop() : removes the top item from the stack returns the removed item modifies the stack is_empty() : checks whether the stack is empty returns a Boolean 23
24 Implementing a Stack class class Stack: # the top of the stack is the last item in the list def init (self): self._items = [] def push(self, item): self._items.append(item) def pop(self): return self._items.pop() removes and returns the last item in a list 24
25 EXERCISE >>> s = Stack() >>> s.push(4) >>> s.push(17) >>> s.push(5) >>> x = s.pop() >>> y = s.pop() what does the stack s look like here? what are the values of x and y? 25
26 EXERCISE >>> s = Stack() >>> s.push(4) >>> s.push(17) >>> s.push(5) >>> x = s.pop() >>> y = s.pop() >>> s.push(x) >>> s.push(y) what does the stack s look like here? 26
27 stacks: applications 27
28 An application: balancing parens IDLE (the Python shell) matches up led and right parens ( ), brackets [ ], and braces { } How does it figure out how far back to highlight? 28
29 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] Stack (empty) 29
30 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] push [ Stack ß top 30
31 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] push [ [ Stack ß top ß top 31
32 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] push [ [ [ Stack ß top ß top 32
33 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] matches: pop [ [ [ Stack ß top 33
34 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] [ [ [ Stack ß top 34
35 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] push [ [ [ Stack ß top ß top 35
36 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] matches: pop [ [ [ Stack ß top ß top 36
37 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] [ [ [ Stack ß top 37
38 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] matches: pop [ [ [ Stack ß top 38
39 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol â Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] [ [ [ ß top Stack 39
40 An application: balancing parens Basic idea: Match each ] with corresponding [ similarly for ( ) and { } pairs Idea: o maintain a stack o on seeing '[' : push o on seeing ']' : pop the matching symbol Example: [ 1, 2, [ 3, [ 4 ], 5, [ 7 ] ] ] Elabora6on: Have each stack element keep track of the posi6on of its [ [ [ [ ß top Stack 40
41 EXERCISE class Stack: def init (self): self._items = [] Write a func*on balanced(s) that returns True if the string s is balanced with respect to [ and ] and False otherwise. def push(self, item): self._items.append(item) def pop(self): return self._items.pop() def is_empty(): return self._items == [] 41
42 Related: Displaying web pages Web page 42
43 Related: Displaying web pages Web page Display considera5ons main header: large font, bold secondary header: medium font, bold bold font italics font Ques5on: how does the web browser figure out how much a given display format should include? E.g., which text is in boldface, how much is in italics, etc. 43
44 Related: Displaying web pages Web page HTML source 44
45 Related: Displaying web pages Web page HTML source 45
46 Related: Displaying web pages Web page HTML source 46
47 Related: Displaying web pages "tags" HTML source <h1> : "open header 1" </h1> : "close header 1" <h2> : "open header 2" </h2> : "close header 2" <i> : "open italics" </i> : "close italics" 47
48 Related: Displaying web pages Web page HTML source Figuring out how to display different parts of the web page requires matching up open- and close- HTML tags. This is essen6ally the same problem as balancing parens. 48
49 >>> s1 = Stack() >>> s1.push(4) >>> s1.push(17) >>> s2 = Stack() >>> s2.push( s1.pop() ) >>> s2.push( s1.pop() ) >>> s1.push( s2.pop() ) >>> s1.push( s2.pop() ) EXERCISE what does the stack s1 look like here? 49
50 Abstract Data Types 50
51 Abstract Data Types An abstract data type (ADT) describes a set of data values and associated opera6ons that are specified independent of any par6cular implementa6on. An ADT is a logical descrip6on of how we view the data and the opera6ons allowed on that data. o describes what the data represents o not how is the data represented The data is encapsulated. 51
52 Abstract Data Types Because the data is encapsulated we can change the underlying implementa6on without affec6ng the way the ADT behaves. o the logical descrip6on remains the same o the opera6ons remain the same 52
53 EXERCISE Hypothe*cal: Python 7 has just been released and built-in lists are inefficient. In fact, all opera*ons are O(n 2 ). Avoid these inefficiencies by implemen*ng the Stack class using LinkedLists. 53
54 queues 54
55 A Queue ADT A queue is a linear data structure where inser6ons and dele6ons happen at different ends inser6ons happen at one end (the queue's "back, or tail ) dele6ons happen at the other end (the queue's "front, or head ) inser6ons occur at this end (tail) dele6ons occur at this end (head) 55
56 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back None queue front None 56
57 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back queue front 57
58 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back queue front 58
59 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back queue front 59
60 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back queue front 60
61 Queues: insertion of values Inser6on of a sequence of values into a queue: queue back queue front 61
62 Queues: insertion of values order of inser*on queue back queue front 62
63 Queues: removal of values order of inser*on Removing values from this queue: queue back queue front 63
64 Queues: removal of values order of inser*on Removing values from this queue: queue back queue front 64
65 Queues: removal of values order of inser*on Removing values from this queue: queue back queue front 65
66 Queues: removal of values order of inser*on Removing values from this queue: queue back queue front 66
67 Queues: removal of values order of inser*on Removing values from this queue: queue back queue front 67
68 Queues: removal of values order of inser*on Removing values from this queue: queue back None queue front None 68
69 Queues: removal of values order of inser*on order of removal
70 Queues: FIFO property order of inser*on order of removal values are removed in order in which they are inserted "FIFO order" First in, First out 70
71 Methods for a queue class Queue(): creates a new empty queue enqueue(item): adds item to the back of the queue modifies the queue returns nothing dequeue(): removes and returns the item at the front of the queue returns the removed item modifies the queue is_empty(): checks whether the queue is empty returns a Boolean size(): returns the size of the queue returns an integer 71
72 Implementing a queue class Use a built-in list for the internal representa6on Python lists can be added at to the front or at the end First implementa6on: the head is the 0 th element the tail is the nth element Second implementa6on the head is the nth element the tail is the 0 th element 72
73 Implementing a Queue class I class Queue: # the front of the queue is the first item in the list def init (self): self._items = [] head tail def enqueue(self, item): self._items.append(item) def dequeue(self): return self._items.pop(0) removes and returns item 0 from the list 73
74 Implementing a Queue class II class Queue: # the front of the queue is the last item in the list def init (self): self._items = [] tail head def enqueue(self, item): self._items.insert(0, item) def dequeue(self): return self._items.pop() removes and returns the last item in the list 74
75 >>> q = Queue() >>> q.enqueue(4) >>> q.enqueue(17) >>> x = q.dequeue() >>> q.enqueue(5) >>> y = q.dequeue() EXERCISE what are the values of x and y? 75
76 >>> q = Queue() >>> q.enqueue(4) >>> q.enqueue(17) >>> x = q.dequeue() >>> y = q.dequeue() >>> q.enqueue(y) >>> q.enqueue(x) >>> q.enqueue(y) EXERCISE what does the queue q look like here? 76
77 queues: applications 77
78 Application 1: Simulation Typical applica6ons simulate problems that require data to be managed in a FIFO manner Hot potato o Kids stand in a circle and pass a hot potato around un6l told to stop. The person holding the potato is taken out of the circle. The process is repeated un6l only one person remains. Generalized: Given n elements, eliminate every kth element repeatedly un6l only 1 element is led. What was the original posi6on of the remaining element? Use a simula*on to determine which element remains. 78
79 EXERCISE Problem: Given n elements, eliminate every kth element repeatedly un6l only 1 element is led. What was the original posi6on of the remaining element? use a queue to simulate the circle n is the number of elements to put into the queue while there is more than one element in the queue eliminate every kth element What opera6ons take an element from the front of the queue and place it at the back of the queue? 79
80 General solution for k=2 Given n elements, eliminate every kth element repeatedly un6l only 1 element is led. What was the original posi6on of the remaining element? When k = 2, the original posi6on can be derived from the binary representa6on of n. Take the first digit of the binary representa6on. Move it to the end The result is the original posi6on. Ex: n = 41, k=2 In binary n = Therefore, the original posi6on (in binary) is and = = 19 hrps://en.wikipedia.org/wiki/josephus_problem#citerefdowdymays
81 Application 2 : Simulation Suppose we are opening a grocery store. How many checkout lines should we put in? too few long wait 6mes, unhappy customers too many wasted money, space Use simula*ons of the checkout process to guide the decision study exis6ng stores to figure out typical shopping and checkout 6mes es6mate no. of customers expected at the new loca6on run simula6ons to determine customer wait 6me and checkout line u6liza6on under different scenarios 81
82 Discrete event simulation departures queue arrivals servers departure rate distribu6on By varying the parameters of the simula6on (arrival and departure rates, no. of servers) we can try out different scenarios customers arrival rate distribu6on 82
83 Summary Stacks and queues are abstract data types (ADTs) similar in that they are both linear data structures items can be thought of as arranged in a line each item has a posi6on and a before/ader rela6onship with the other items They differ in the way items are added and removed stacks: items added and removed at one end o results in LIFO behavior queues: items added at one end, removed at the other o results in FIFO behavior They find a wide range of applica6ons in computer science 83
84 A Deque ADT A deque is a linear data structure where inser6ons and dele6ons happen at both ends inser6ons and dele6ons occur at this end (tail) inser6ons and dele6ons occur at this end (head) 84
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