1 / 20

Data Structures, Search and Sort Algorithms

Data Structures, Search and Sort Algorithms. Kar-Hai Chu karhai@hawaii.edu. Data structures. Storage Insertion, deletion Searching Sorting Big O. Stacks. LIFO Push, pop O(1) operations. Linked lists v. Arrays. Linked lists: Resizable Insertion/deletion Arrays: Faster index

fidelio
Download Presentation

Data Structures, Search and Sort Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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(n2) • Algorithm: • Find the minimum value • Swap with 1st position value • Repeat with 2nd position down

  7. Insertion sort :-) • O(n2) • O(1) space • Great with small number of elements (becomes relevant later) • Algorithm: • Move element from unsorted to sorted list

  8. Bubble sort :-( • O(n2) • 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(n2) • O(n) extra space (can optimized for O(logn)) • Algorithm: • pick a pivot • put all x < pivot in less, 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 and node.right_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

  20. Useful • http://www.cs.pitt.edu/~kirk/cs1501/animations/Sort3.html

More Related