Introduction to Data Structure and Algorithms

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Introduction to Data Structure and Algorithms

• Chuan-kai Yang

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Data Structures

• Basic Data Types
• Stack
• Queue
• Linked-List
• Array
• Heap, Priority Queue
• Binary Search Tree
• Hash Table

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Basic Data Types

• Character (Byte, Octet)
• Signed or Unsigned
• Boolean
• Integer
• Signed or Unsigned
• Long or short
• Float, double
• String

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Stack

• Interfaces (Allowed Operations)
• Push
• If a stack is not full, this adds one element on
  the top of a stack
• Pop
• If a stack is not empty, this removes one element
  from the top of a stack
• FILO (First In Last Out)

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Queue

• Interfaces
• Enqueue
• If a queue is not full, add one element at the
  tail of a queue
• Dequeue
• If a queue is not empty, remove one element from
  the head of a queue
• FIFO (First In First Out)

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Linked-List

• Singly-linked lists
• Doubly-linked lists
• Circular-linked lists

Search, Insert, Delete
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Array
1
2
3
4
5
6
7
8
9
1
10
9
7
5
3
2
9
6
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Heap
Max_Extract, Insert, Delete
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Binary Search Tree
Search, Insert, Delete, Successor, Predecessor
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Hash Table
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Hash Table Chaining
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Hash Table Open Addressing
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Algorithms

• What is algorithm?
• Time Complexity Space Complexity
• Growth of Functions
• Recurrence relation
• Sorting
• Searching
• Graph Algorithm
• Computational Geometry

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What is Algorithms

• Algorithm Any well-defined computation procedure
  that takes some value, or set of values, as input
  and produces some value, or set of values, as
  output.
• Or tool for solving well specific computational
  problem.
• Example Sorting problem
• Input A sequence of n numbers
• Output A permutation
• of the input sequence such that .

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Time Space Complexity

• Time complexity
• Time to run an algorithm
• Worst-Case, Best-Case, Average-Case
• Space complexity
• (Memory) Capacity to run an algorithm

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Growth of Functions

• Log lt polynomial lt exponential
• Constant time c
• Logarithmic time log(n)
• Linear time cn
• Quadratic time cn2
• Exponential time cn

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Recurrence Relation

• merge_sort(A, p, q) merge_sort(A, p,
  (pq)/2) merge_sort(A, (pq)/21, q)
  merge(A, p, q)
• T(n)2T(n/2)O(n)

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Sorting

• Insertion Sort
• Selection Sort
• Quick Sort
• Counting Sort

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Searching

• Method
• Linear Search
• Binary Search
• Hash Search
• Finding what?
• If a data structure has some element
• Finding the n-th smallest element
• Finding the successor/predecessor

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Graph Algorithm

• Minimal Spanning Tree
• Shortest Path
• Euler Path/Cycle
• Hamiltonian path/Cycle
• Travelling salesman

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Minimal Spanning Tree
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Shortest Path
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Euler Path/Cycle
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Hamiltonian Path/Cycle
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Traveling-Salesman Problem
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Computational Geometry

• Line-segment intersection
• Convex hull
• Voronoi diagram

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Convex Hull
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Voronoi Diagram