Download Introduction to Data Structure and Algorithms

Introduction to Data Structure
and Algorithms
Chuan-kai Yang
Data Structures
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Basic Data Types
Stack
Queue
Linked-List
Array
Heap, Priority Queue
Binary Search Tree
Hash Table
Basic Data Types
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Character (Byte, Octet)
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Boolean
Integer
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Signed or Unsigned
Signed or Unsigned
Long or short
Float, double
String
Stack
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Interfaces (Allowed Operations)
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Push
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Pop
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If a stack is not full, this adds one element on
the top of a stack
If a stack is not empty, this removes one
element from the top of a stack
FILO (First In Last Out)
Queue
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Interfaces
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Enqueue
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Dequeue
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If a queue is not full, add one element at the
tail of a queue
If a queue is not empty, remove one element
from the head of a queue
FIFO (First In First Out)
Linked-List
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Singly-linked lists
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Doubly-linked lists
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Circular-linked lists
Search, Insert, Delete
Array
1
2
3
4
5
6
7
8
9
1
10
9
6
7
5
3
2
9
Heap
Max_Extract, Insert,
Delete
Binary Search Tree
Search, Insert, Delete, Successor, Predecessor
Hash Table
Hash Table – Chaining
Hash Table – Open Addressing
h1 ( k )  k
mod13
h2 ( k )  1  ( k mod11)
Insert
14
Algorithms
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What is algorithm?
Time Complexity & Space Complexity
Growth of Functions
Recurrence relation
Sorting
Searching
Graph Algorithm
Computational Geometry
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  a1 , a2 ,..., a n 
' '
'

a
,
a
,...,
a
 Output: A permutation
1 2
n
of the input sequence such that a1'  a'2 ... a'n .
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Time & Space Complexity
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Time complexity
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Time to run an algorithm
Worst-Case, Best-Case, Average-Case
Space complexity
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(Memory) Capacity to run an algorithm
Growth of Functions
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Log < polynomial < exponential
Constant time: c
Logarithmic time: log(n)
Linear time: cn
Quadratic time: cn2
Exponential time: cn
Recurrence Relation
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merge_sort(A, p, q)
{
merge_sort(A, p, (p+q)/2);
merge_sort(A, (p+q)/2+1, q);
merge(A, p, q);
}
T(n)=2T(n/2)+O(n)
Sorting
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Insertion Sort
Selection Sort
Quick Sort
Counting Sort
Searching
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Method
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Linear Search
Binary Search
Hash Search
Finding what?
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If a data structure has some element
Finding the n-th smallest element
Finding the successor/predecessor
Graph Algorithm
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Minimal Spanning Tree
Shortest Path
Euler Path/Cycle
Hamiltonian path/Cycle
Travelling salesman
Minimal Spanning Tree
Shortest Path
Euler Path/Cycle
Hamiltonian Path/Cycle
Traveling-Salesman Problem
Computational Geometry
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Line-segment intersection
Convex hull
Voronoi diagram
Convex Hull
Voronoi Diagram