Introduction to Data Structure and Algorithms Chuan-kai Yang

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

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

Stack Interfaces (Allowed Operations) Push Pop 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)

Queue Interfaces Enqueue Dequeue FIFO (First In First Out) 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)

Linked-List Singly-linked lists Doubly-linked lists 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

Algorithms 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 Output: A permutation of the input sequence such that .

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

Growth of Functions Log < polynomial < exponential Constant time: c Logarithmic time: log(n) Linear time: cn Quadratic time: cn2 Exponential time: cn

Recurrence Relation 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 Insertion Sort Selection Sort Quick Sort Counting Sort

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

Graph Algorithm 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 Line-segment intersection Convex hull Voronoi diagram

Convex Hull

Voronoi Diagram