Training

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Data Structures Algorithms
ltShiuh-Sheng Yugt
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What The Course Is About

• Data structures is concerned with the
  representation and manipulation of data.
• All programs manipulate data.
• So, all programs represent data in some way.
• Data manipulation requires an algorithm.

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What The Course Is About

• We shall study ways to represent data and
  algorithms to manipulate these representations.

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Functions of Data Structures

• Add
• Index
• Key
• Position
• Priority
• Get
• Change
• Delete

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Common Data Structures

• Array
• Stack
• Queue
• Linked List
• Tree
• Heap
• Hash Table
• Priority Queue

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How many Algorithms?

• Countless

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Algorithm Strategies

• Greedy
• Divide and Conquer
• Dynamic Programming
• Exhaustive Search
• Approximation Algorithms
• Randomized Algorithms

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Which Data Structure or Algorithm is better?

• Must Meet Requirement
• High Performance
• Low RAM footprint
• Easy to implement
• Encapsulated

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Prerequisites

• C

• Asymptotic Complexity

• Big Oh, Theta, and Omega notations

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Web Site

• programming.im.ncnu.edu.tw

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Assignments

• Assignment guidelines

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Sorting

• Rearrange a0, a1, , an-1 into ascending
  order. When done, a0 lt a1 lt lt an-1
• 8, 6, 9, 4, 3 gt 3, 4, 6, 8, 9

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Sort Methods

• Insertion Sort
• Bubble Sort
• Selection Sort
• Count Sort
• Shaker Sort
• Shell Sort
• Heap Sort
• Merge Sort
• Quick Sort

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Insert An Element

• Given a sorted list/sequence, insert a new
  element
• Given 3, 6, 9, 14
• Insert 5
• Result 3, 5, 6, 9, 14

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Insert an Element

• 3, 6, 9, 14 insert 5
• Compare new element (5) and last one (14)
• Shift 14 right to get 3, 6, 9, , 14
• Shift 9 right to get 3, 6, , 9, 14
• Shift 6 right to get 3, , 6, 9, 14
• Insert 5 to get 3, 5, 6, 9, 14

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Insert An Element

• / insert t into a0i-1 /
• int j
• for (j i - 1 j gt 0 t lt aj j--)
• aj 1 aj
• aj 1 t

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Insertion Sort

• Start with a sequence of size 1
• Repeatedly insert remaining elements

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Insertion Sort

• Sort 7, 3, 5, 6, 1
• Start with 7 and insert 3 gt 3, 7
• Insert 5 gt 3, 5, 7
• Insert 6 gt 3, 5, 6, 7
• Insert 1 gt 1, 3, 5, 6, 7

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Insertion Sort

• for (i 1 i lt n i)
• / insert ai into a0i-1 /
• / code to insert comes here /

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Insertion Sort

• for (i 1 i lt n i)
• / insert ai into a0i-1 /
• int t ai
• int j
• for (j i - 1 j gt 0 t lt aj j--)
• aj 1 aj
• aj 1 t