Marco Alvarez Department of Computer Science and Statistics University of Rhode Island CSC 212: Data Structures and Abstractions Stacks and Queues Spring 2020 2 Stacks LIFO: Last In First Out Basic Operations ‣ Push ✓ inserts one element onto the stack ‣ Pop ✓ returns the element at the top of the stack (and removes it) ‣ IsEmpty ✓ not necessary, but sometimes useful 3 4 https://en.cppreference.com/w/cpp/container/stack
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Marco AlvarezDepartment of Computer Science and Statistics
University of Rhode Island
CSC 212: Data Structures and AbstractionsStacks and Queues
Spring 2020
2
Stacks
LIFO: Last In First Out
Basic Operations‣ Push
✓ inserts one element onto the stack
‣ Pop✓ returns the element at the top of the stack (and removes it)
‣ IsEmpty✓ not necessary, but sometimes useful
3 4https://en.cppreference.com/w/cpp/container/stack
Implementation‣ Arrays
✓ push and pop at the end of the array (easier and efficient)✓ can be fixed-length✓ can also use a dynamic array (grows over time)
- additional cost for dynamic arrays
5
https://www.cs.usfca.edu/~galles/visualization/StackArray.html
30 1 20 14
top
Implementation‣ Linked Lists
✓ push and pop at front (could use the other end as well)
6https://www.cs.usfca.edu/~galles/visualization/StackLL.html
1 7 3 5
Head
Considerations‣ Underflow
✓ error can be thrown when calling pop on an empty stack
‣ Overflow✓ error can be thrown when calling push on a full stack
(especially in fixed-length implementations)
7
Applications‣ Undo in software applications
‣ Stack in compilers/programming languages
‣ Parsing expressions
‣ …
8
Example‣ Fully parenthesized infix expressions
✓ infix arithmetic expressions: operators are placed between two operands
✓ fully parenthesized infix expression: infix arithmetic expression where every operator and its arguments are contained in parentheses
✓ operator precedence and associativity don't matter
9
((5 + ((10 - 4) * (3+2))) + 25)
Dijkstra’s two stacks algorithm
10
s1 s2
Element Action
operand (value) push it onto the s1
operator push it onto s2
left parenthesis ignore
right parenthesis pop operator from s2 and pop two values from s1, then apply operator to those values and push the result onto s1
((5 + ((10 - 4) * (3+2))) + 25)
11(🗑 #🔝₁ ⊚🔝₂ )🍿₁🍿₁🍿₂🔝₁
12
Queues
FIFO: First In First Out
Basic Operations‣ Enqueue
✓ inserts one element onto the queue
‣ Dequeue✓ returns the next element from the queue (and removes it)
‣ IsEmpty✓ not necessary, but sometimes useful
13 14https://en.cppreference.com/w/cpp/container/queue
Basic Operations (enqueue/dequeue)
15
Implementation‣ Arrays
✓ enqueue and dequeue at different ends of the array✓ can be fixed-length✓ can also use a dynamic array (grows over time)
- additional cost for dynamic arrays
16
https://www.cs.usfca.edu/~galles/visualization/QueueArray.html
20 14 21 3 12
topbase
Implementation‣ Linked Lists
✓ enqueue and dequeue at different ends
17https://www.cs.usfca.edu/~galles/visualization/QueueLL.html
1 7 3 5
Head Tail
Considerations‣ Underflow
✓ error can be thrown when calling dequeue on an empty queue
‣ Overflow✓ error can be thrown when calling enqueue on a full queue
(especially in fixed-length implementations)
18
Applications‣ Media Playlists (Youtube, Spotify, Music, etc.)
‣ Process management in Operating Systems
‣ Simulations
‣ Used in other algorithms
‣ …
19
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