How to Win Coding Competitions: Secrets of Champions. Week 2: Computational complexity. Linear data structures Lecture 5: Stack. Queue.

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1 How to Win Coding Competitions: Secrets of Champions Week 2: Computational complexity. Linear data structures Lecture 5: Stack. Queue. Deque Pavel Krotkov Saint Petersburg 2016

2 General overview Stack, Queue and Deque are just interfaces. 2 / 10

3 General overview Stack, Queue and Deque are just interfaces. sometimes it s reasonable to limit set of possible operations on data structure 2 / 10

4 General overview Stack, Queue and Deque are just interfaces. sometimes it s reasonable to limit set of possible operations on data structure implementation of Stack and Queue can be based on Vector or Array 2 / 10

5 General overview Stack, Queue and Deque are just interfaces. sometimes it s reasonable to limit set of possible operations on data structure implementation of Stack and Queue can be based on Vector or Array different implementations will have different properties 2 / 10

6 Stack overview Stack has only two possible operations. push inserting element to the end of structure 3 / 10

7 Stack overview Stack has only two possible operations. push inserting element to the end of structure pop removing element from the end of structure and returning its value 3 / 10

8 Stack overview Stack has only two possible operations. push inserting element to the end of structure pop removing element from the end of structure and returning its value Push operation / 10

9 Stack overview Pop operation / 10

10 Stack overview Pop operation The end of the structure is called top of the stack. 4 / 10

11 Stack analysis Stack can be implemented with vector or with list. both this data structures support inserting elements to and removing elements from the end of the structure in constant time 5 / 10

12 Stack analysis Stack can be implemented with vector or with list. both this data structures support inserting elements to and removing elements from the end of the structure in constant time Stack has numerous applications in different areas. various graph algorithms (DFS) 5 / 10

13 Stack analysis Stack can be implemented with vector or with list. both this data structures support inserting elements to and removing elements from the end of the structure in constant time Stack has numerous applications in different areas. various graph algorithms (DFS) local variables and function calls during execution of yor program are stored in stack 5 / 10

14 Stack analysis Stack can be implemented with vector or with list. both this data structures support inserting elements to and removing elements from the end of the structure in constant time Stack has numerous applications in different areas. various graph algorithms (DFS) local variables and function calls during execution of yor program are stored in stack during calculation of expressions written in Reverse Polish notation 5 / 10

15 Stack analysis Stack can be implemented with vector or with list. both this data structures support inserting elements to and removing elements from the end of the structure in constant time Stack has numerous applications in different areas. various graph algorithms (DFS) local variables and function calls during execution of yor program are stored in stack during calculation of expressions written in Reverse Polish notation etc. 5 / 10

16 Queue overview Queue is a list organized by FIFO (first in - first out) rule. 6 / 10

17 Queue overview Queue is a list organized by FIFO (first in - first out) rule. It supports two operations: enqueue inserting element to the end of structure dequeue removing element from the beginning of structure 6 / 10

18 Queue overview Queue is a list organized by FIFO (first in - first out) rule. It supports two operations: enqueue inserting element to the end of structure dequeue removing element from the beginning of structure Enqueue operation / 10

19 Queue overview Dequeue operation / 10

20 Queue overview Dequeue operation the end of queue is called tail 7 / 10

21 Queue overview Dequeue operation the end of queue is called tail the beginning of queue is called head 7 / 10

22 Queue analysis Queue implementation 8 / 10

23 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list 8 / 10

24 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list queue can be implemented with array, if maximum possible size of queue is known beforehand we can reuse free elements at the beginning of array for storing new elements of queue 8 / 10

25 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list queue can be implemented with array, if maximum possible size of queue is known beforehand we can reuse free elements at the beginning of array for storing new elements of queue queue can be implemented with vector some additional techniques of removing from the beginning of vector required 8 / 10

26 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list queue can be implemented with array, if maximum possible size of queue is known beforehand we can reuse free elements at the beginning of array for storing new elements of queue queue can be implemented with vector some additional techniques of removing from the beginning of vector required queue with amortized constant time of operations can be implemented with two stacks details of implementation can be considered as a home work 8 / 10

27 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list queue can be implemented with array, if maximum possible size of queue is known beforehand we can reuse free elements at the beginning of array for storing new elements of queue queue can be implemented with vector some additional techniques of removing from the beginning of vector required queue with amortized constant time of operations can be implemented with two stacks details of implementation can be considered as a home work Queue usage. graph algorithms (BFS) 8 / 10

28 Queue analysis Queue implementation the easiest way to implement queue is based on list we just need to store links to the first and last elements of list queue can be implemented with array, if maximum possible size of queue is known beforehand we can reuse free elements at the beginning of array for storing new elements of queue queue can be implemented with vector some additional techniques of removing from the beginning of vector required queue with amortized constant time of operations can be implemented with two stacks details of implementation can be considered as a home work Queue usage. graph algorithms (BFS) processing some queries in order of their arrival 8 / 10

29 Deque overview Deque is a queue with allowed operations of removing element from the end and inserting element to the beginning. implementation details are very similar to queue implementation details doubly linked list cycled array (if fixed maximum size) vector 9 / 10

30 Deque overview Deque is a queue with allowed operations of removing element from the end and inserting element to the beginning. implementation details are very similar to queue implementation details doubly linked list cycled array (if fixed maximum size) vector can be used as stack and as queue at the same time 9 / 10

31 Thank you for your attention! 10 / 10

How to Win Coding Competitions: Secrets of Champions. Week 2: Computational complexity. Linear data structures Lecture 4: List

How to Win Coding Competitions: Secrets of Champions Week 2: Computational complexity. Linear data structures Lecture 4: List Pavel Krotkov Saint Petersburg 2016 Operations on list Let s define operations