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Queues

Queues. Queue Q = x 0 x 1 x 2 x 3 … x n-1 n = # elements A queue is a list but the nodes are only accessed first-in-first-out (FIFO). Functions: createEmptyQueue() returns a newly created empty queue front(Q) returns the first node of Q

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Queues

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  1. Queues Queue Q = x0 x1 x2 x3 … xn-1 n = # elements A queue is a list but the nodes are only accessed first-in-first-out (FIFO). Functions: createEmptyQueue()returns a newly created empty queue front(Q) returns the first node of Q dequeue(Q) returns and removes the first node of Q enqueue(Q, x) returns Q with x added as the last element isEmptyQueue(Q) returns true if Q is empty and false if it is not

  2. Homework 3a • Describe how to implement a queue using an array (assume it will never have more than 100 elements). • Do the five queue functions. • Describe how to implement a queue using an set of nodes (this queue will have no number of element limit). • Do the five queue functions.

  3. Queue – Array NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 0 1 2 3 4 5 6 int front = the front of the queue int n = the number of elements in the queue in this case front = 1 n = 4

  4. createEmptyQueue() declare an array of max size array q[100] int front = 0 int n = 0

  5. front(Q) return q[front]

  6. dequeue(Q) temp = front front = (front + 1) modulo 100 n = n - 1 return q[temp]

  7. enqueue(Q, x) int end = (front + n) modulo 100 q[end] = x n = n + 1

  8. isEmptyQueue(Q) return n == 0

  9. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 Queue – Linked Nodes q null

  10. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 Queue – Linked Nodes f e null

  11. createEmptyQueue() Declare pointers to type node called f and e f null e null

  12. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 front(Q) f e return node pointed to by f null

  13. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 dequeue(Q) f e null

  14. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 dequeue(Q) f e temp temp = f null

  15. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 dequeue(Q) f e temp f = f.next null

  16. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 dequeue(Q) f e temp null temp.next = null return temp null

  17. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x)single pointer q x null null

  18. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x)- sp temp q x temp = q temp = temp.next until temp.next = null null null

  19. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x)- sp temp q x null null

  20. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x)- sp temp q x temp.next = x null

  21. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x) f e x null null

  22. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x) f e x e.next = x null

  23. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 enqueue(Q, x) f e x e = x null

  24. isEmptyQueue(Q) return f == null

  25. NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 NameLast: Smart FirstName: Joe StudentNumber: 8 SSN: 123-34-1112 Grade: 95 Linked List Search head null

  26. Speed of List Search • O(n) for when implemented as a linked-list • O(lg n) possible if implemented as an array • How?

  27. Speed of List Search 1

  28. Speed of List Search 2

  29. Speed of List Search 3

  30. Speed of List Search 4

  31. Speed of List Search 5

  32. Speed of List Search -- Array • It took 5 compares • There were 29 elements • lg(16) < lg(29) < lg(32) • 4 < lg(29) < 5 • What if there were 1,000,000 elements? • How many compares would it take?

  33. Speed of List Search -- Array • lg(1000000) = 20 • In 20 compares we can search a list of 1,000,000 elements. • But we can’t always use an array to hold the data because we may not know the size limit of the database. • How can we dynamically represent the data in such a way that we can still get searches in lg(n)?

  34. Trees

  35. Trees • Root • Nodes • Edges • Leaves • Parent / Child • Depth of a Node • Height of a Tree

  36. Binary Tree

  37. Binary Search Tree 54 21 72 5 30 60 84 10 25 35 79 86 44 93

  38. Binary Search Tree Tree T is a binary search tree made up of n elements: x0 x1 x2 x3 … xn-1 Functions: createEmptyTree() returns a newly created empty binary tree delete(T, p) removes the node pointed to by p from the tree T insert(T, p) returns T with the node pointed to by p added in the proper location search(T, key) returns a pointer to the node in T that has a key that matched key returns null if key is not found traverse(T) prints the contents of T in order isEmptyTree(T) returns true if T is empty and false if it is not

  39. Homework 4 • Describe how to implement a binary search tree using a set of nodes (this tree will have no number of element limit). • Do the six BST functions. • Can you determine how to implement a binary search tree using an array (assume it will never have more than 100 elements)? • Consider the six BST functions.

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