Data Structure and Algorithm Analysis 2015

About the Course Objective Organize a large amount of data Algorithm: the operation on the organized data Analysis the running time of the algorithms Prerequisite courses: Programming Fundamentals (C/C++ or Java) Discrete Math

About the Course At the end of the course Familiar with the common data structures Internal and external Fundamental algorithms Traverse, sorting, merge etc Time and space complexity of above algorithms Evaluation Final exam Assignment Textbook Mark Allen Weiss, Data Structure and Algorithm Analysis in C

Examination Algorithm complexity analysis Linear data structure Tree and graph Search, sorting [optional] Hash, priority queue

Self Introduction Name: Zhu Huiquan (Nate) Education in China and Singapore Research areas: formal method, data mining and graph algorithm Mobile:

Programming Fundamentals Variables and data types (struct) Control flow: sequential, conditional and loop Function Array and collection Input/output, exceptions

Math

Logarithms

Series

Recursion Base cases Making progress Ensure all recursive calls work Avoid duplicate work on the same instance

Recursion programming An example Questions: Does it follow the four rules in previous slide? int Fibonacci(int n) { if ( n == 0 ) return 0; else if ( n == 1 ) return 1; else return ( Fibonacci(n-1) + Fibonacci(n-2) ); }

Algorithm Analysis How to describe the complexity of the algorithms Typical complexity levels Analysis with an example

Notation

Complexity level FunctionName Constant Logarithmic Log-squared Linear Quadratic Cubic Exponential

Examples int A(int n) { if(n%2==0) return B(n); else return C(n); } int A(int n) { int i = 0, s = 0; while(i<n) { s = s + B(n); i++; } return s; } int B(n) { int s = 0; for(int j = 0; j < n; j++) s = s + j; return s; }

Examples void print_out(int n) { if(n<10) { printf(“%d\n”, n); } else { print_out(n/10); printf(“%d\n”, n%10); }//else }

Examples

int bsearch(int a[], int x, int n) { int low, mid, high; low = 0; high = n - 1; whle(low <= high) { mid = (low + high) / 2; if(a[mid] < x) low = mid + 1; else if (a[mid] < x) high = mid - 1; else return(mid); } //while return(NOT_FOOUND); } low highmid low highmid high'

Assumption The same time cost for all basic operation No complex operation, like hardware acceleration No memory constraint Random access on external storage To measure the complexity Based on the input size n Average running time and worse-case running time, in O(f(n))

Abstract Dada Types An abstract data type (ADT) is a set of operations. Abstract, no implementation defined Modular design Template concept in C++ Example: List: sequential Set/Collection:

List Typical Implementation ArrayList LinkList Typical operations: Insert Append Find Delete Concatenate/join Reverse Sum

ArrayList Allocated N units of space for the list of size n, n <N An integer to store the current size “n” Typical operations: Insert Append Find Delete Concatenate/join Reverse Sum

ArrayList After append 3,7,4, Insert (5, 2) 35743

ArrayList Insert (2, 5) delete (3) 3543