1. Data Structures, Search and Sort Algorithms Kar-Hai Chu karhai@hawaii.edu

2. Data structures Storage Insertion, deletion Searching Sorting Big O

3. Stacks LIFO Push, pop O(1) operations

4. Linked lists v. Arrays Linked lists: –Resizable –Insertion/deletion Arrays: –Faster index –O(1) lookup –Preset size

5. Hash tables Keys and values O(1) lookup Hash function –Good v fast Clustering Databases

6. Selection sort :-( O(n 2 ) Algorithm: –Find the minimum value –Swap with 1st position value –Repeat with 2nd position down

7. Insertion sort :-) O(n 2 ) O(1) space Great with small number of elements (becomes relevant later) Algorithm: –Move element from unsorted to sorted list

8. Bubble sort :-( O(n 2 ) Algorithm: –Iterate through each n, and sort with n+1 element Maybe go n-1 steps every iteration? Great for big numbers, bad for small Totally useless?

9. Merge sort :-) O(nlogn) Requires O(n) extra space Parallelizable Algorithm: –Break list into 2 sublists –Sort sublist –Merge

10. Quick sort :-) Average O(nlogn), worst O(n 2 ) O(n) extra space (can optimized for O(logn)) Algorithm: –pick a pivot –put all x pivot in more –Concat and recurse through less, pivot, and more Advantages also based on caching, registry (single pivot comparison) Variations: use fat pivot

11. Linear search :-( O(n) Examines every item

12. Binary search :-) Requires a sorted list O(log n) Divide and conquer

13. Trees Almost like linked lists! Traverse: Pre-order v. Post-order v. In- order Node, edge, sibling/parent/child, leaf

14. Binary trees 0, 1, or 2 children per node Binary Search Tree: a binary tree where node.left_child = node.value

15. Balanced binary trees Minimizes the level of nodes Compared with “bad” binary tree? Advantages: –Lookup, insertion, removal: O(log n) Disadvantages: –Overhead to maintain balance

16. Heaps (binary) Complete: all leafs are at n or n-1, toward the left Node.value >= child.value In binary min/max heap –Insert = O(logn).. add to bottom, bubble-up –deleteMax = O(logn).. Move last to root and bubble-down

17. Heapsort O(nlogn) Algorithm: –Build a heap –deleteMax (or Min) repeatedly O(1) overhead

18. Why bother? Tries (say trees) –Position determines the key –Great for lots of short words –Prefix matching But.. –Long strings.. –Complex algorithms

19. Chess! Minimax: Alpha-beta pruning - pick a bag! –ordering B: B1B: B2B: B3 A: A1+3-2+2 A: A20+4 A: A3-4-3+1

20. Useful http://www.cs.pitt.edu/~kirk/cs1501/ani mations/Sort3.html