Agenda  See schedule  HW5 (mini-programming project) due Next Wed. 16th  Quiz 6 (double quiz- 50 minutes) will be Next Mon. 14th

Chapter 3  Data Structures –Stacks & Queues –Array vs. Linked Lists –Resizable arrays –Binary Search leads to Binary Trees –Priority Queues lead to Binary Heaps

Stacks & Queues  Stacks –FILO (First In – Last Out) –O(1) push –O(1) pop –Ensuring efficient push and pop means that iteration may not be possible.

Stacks & Queues  Queues –FIFO (First In – First Out) –O(1) push or enqueue –O(1) pop or dequeue –Ensuring efficient push and pop means that iteration may not be possible.

Stacks & Queues  Queue q;  Stack s1, s2;  q.push(1)  s1.push(2)  s2.push(3)  q.push(s2.pop())  q.push(4)  s2.push(5)  s1.push(6)  s2.push(q.pop());  s1.push(s2.pop());  s2.pop()  s1.push(s2.pop());

Arrays vs. Linked Lists Arrays  Constant-time access of k th item  Binary search can be implemented on sorted arrays  O(n) insertion  O(n) deletion  O(n) merging and resizing Linked List  O(n)-time to access k th item on average  Binary search can NOT be implemented on sorted linked lists  O(1) insertion  O(1) deletion  O(1) merging

Resizable Arrays  Given an array with a capacity of M  Insert N 1 items  What if N 1 > M?  Resize array to N 1 (stupid)  Resize array to 2*N 1 (smart)  Why?

Resizable Arrays i InsertionsCopies 10 m 11 i Total 1 2 m 12 m 3 i m 13 m 4 mi mmmm mmmm i mi Sum

Resizable Arrays i InsCopies 1 m 11 i Total i m 13 m 4 mi i i Sum

Binary Trees  Tries to combine binary search with the advantages of linked lists. ArrayLinked ListBinary Tree Raw InsertO(n)O(1) Raw DeleteO(n)O(1) Find/SearchO(log n)O(n)O(log n)

Binary Trees  Insertion = Find + Raw Insert –O(log n) + O(1) = O(log n)  Deletion = Find + Raw Delete + Find Replacement –O(log n) + O(1) + O(log n) = O(log n)

Binary Heaps  Arise from priority queues –Enqueue should be as efficient as possible –Dequeue will always remove the minimum/maximum item.

Binary Heap Binary HeapBinary Tree InsertionO(1)O(log n) Delete/Remove Min or Max O(log n) Find/SearchO(n)O(log n)