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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

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Data Structures, Search and Sort Algorithms

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  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

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