Data Structures, Search and Sort Algorithms

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Data Structures, Search and Sort Algorithms

• Kar-Hai Chu
• karhai_at_hawaii.edu

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Data structures

• Storage
• Insertion, deletion
• Searching
• Sorting
• Big O

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Stacks

• LIFO
• Push, pop
• O(1) operations

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Linked lists v. Arrays

• Linked lists
• Resizable
• Insertion/deletion
• Arrays
• Faster index
• O(1) lookup
• Preset size

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Hash tables

• Keys and values
• O(1) lookup
• Hash function
• Good v fast
• Clustering
• Databases

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Selection sort -(

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

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Insertion sort -)

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

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Bubble sort -(

• O(n2)
• Algorithm
• Iterate through each n, and sort with n1 element
• Maybe go n-1 steps every iteration?
• Great for big numbers, bad for small
• Totally useless?

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Merge sort -)

• O(nlogn)
• Requires O(n) extra space
• Parallelizable
• Algorithm
• Break list into 2 sublists
• Sort sublist
• Merge

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Quick sort -)

• Average O(nlogn), worst O(n2)
• O(n) extra space (can optimized for O(logn))
• Algorithm
• pick a pivot
• put all x lt pivot in less, all x gt pivot in more
• Concat and recurse through less, pivot, and more
• Advantages also based on caching, registry
  (single pivot comparison)
• Variations use fat pivot

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Linear search -(

• O(n)
• Examines every item

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Binary search -)

• Requires a sorted list
• O(log n)
• Divide and conquer

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Trees

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

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Binary trees

• 0, 1, or 2 children per node
• Binary Search Tree a binary tree where
  node.left_child lt node.value and node.right_child
  gt node.value

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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

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Heaps (binary)

• Complete all leafs are at n or n-1, toward the
  left
• Node.value gt 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

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Heapsort

• O(nlogn)
• Algorithm
• Build a heap
• deleteMax (or Min) repeatedly
• O(1) overhead

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Why bother?

• Tries (say trees)
• Position determines the key
• Great for lots of short words
• Prefix matching
• But..
• Long strings..
• Complex algorithms

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Chess!

• Minimax
• Alpha-beta pruning - pick a bag!
• ordering

B B1 B B2 B B3
A A1 3 -2 2
A A2 -1 0 4
A A3 -4 -3 1
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Useful

• http//www.cs.pitt.edu/kirk/cs1501/animations/Sor
  t3.html