1.1 Basic Concepts 1

Transcription

1 1.1 Basic Concepts 1

2 What is Data Structure? (1) Data Structure How do we store (input/output) data in a (mostly) main memory? Ex) How to store a Matrix in a memory? We need to specify a data structure to organize them. Data Structure + Algorithm UNIT Choice of different data structures gives us different algorithms. Good data structures are essential for constructing efficient algorithms. 2

3 What is Data Structure? (2) 1-dimensional memory Types of data structures view implement 3

4 What is Algorithm? Definition Algorithm is a step-by-step procedure for solving a problem in a finite amount of time. It consists of : Instructions Input data Output data Representation Flow chart Pseudo Code Programming language (e.g., C Language) 4

5 Algorithm: Searching Problem : Find an integer X among n ( > 1 ) integers Algorithm 1 Data Structure : Store unsorted n integers in array. Method : Sequential Search Algorithm 2 n array X 4 7 Data Structure : Store sorted n integers in array. Method : Binary Search n array 1 4 X Which algorithm is better? It depends on many criteria such as Searching Cost? Insertion Cost? Deletion Cost? X>4 X=5 X<6 5

6 Algorithm Example [Binary search]: Finds out if an integer searchnum is in a sorted list. List[0] list[1]... list[n-1] If list[i]=searchnum then return the index i Else return -1 Initially left=0, right=n-1 Middle position in the list : middle=(left+right)/2 Compare List[middle] with searchnum 1) searchnum < list[middle] : list[0] searchnum list[middle-1] right = middle-1 2) searchnum = list[middle] : return middle 3) searchnum > list[middle] : list[middle+1] searchnum list[n-1] left = middle+1 6

7 Algorithm int compare(int x, int y) { /* compare x and y, return -1 for less than, 0 for equal, 1 for greater */ if (x<y) return -1; else if (x = = y) return 0; else return 1; } Comparison of two integers int binsearch(int list[], int searchnum, int left, int right) { */ search list [0] <= list[1] <= <= list[n-1] for searchnum. Return its position if found. Otherwise return -1 */ int middle; while (left <=right) { middle = (left + right) / 2; switch (COMPARE(list[middle], searchnum)) { case -1: left = middle + 1 break; case 0 : return middle; case 1 : right = middle -1;} } return -1; } Searching an ordered list 7

8 System Life Cycle (1) Requirements set of specifications that defines the purpose of the project description of input and output information Analysis break the problem down into manageable pieces bottom-up/top-down approach Design creation of abstract data types specification of algorithms 8

9 System Life Cycle (2) Refinement and Coding choose representations for data objects write algorithms for each operation on them Verification correctness proof mathematical techniques for the proof (before or during coding) testing requires the working code and sets of test data consideration of the estimates of running time error removal debugging autonomous units that interact through parameters is desirable 9

10 System Life Cycle (2) Refinement and Coding choose representations for data objects write algorithms for each operation on them Verification correctness proof mathematical techniques for the proof (before or during coding) testing requires the working code and sets of test data consideration of the estimates of running time error removal debugging autonomous units that interact through parameters is desirable 10

11 Pointers and Memory Allocation (1) Pointers For any type T in C there is corresponding type pointer-to-t. Actual value of a pointer type is an address of memory. Operators used with the pointer type are: & : address operator * : dereferencing (or indirection) operator Ex) i (integer variable), pi (pointer to an integer) int i, *pi pi = &i; assigns the address of i as the value of pi i = 10; or *pi = 10; assigns a value to i Null pointer points to no object or function represented by the integer 0 test for the null pointer int (pi == null) or if(!pi) 11

12 Pointers and Memory Allocation (2) Dynamic memory allocation may not know how much space is needed at coding time int *pi; float *pf; pi = (int *) malloc(sizeof(int)); pf = (float *) malloc(sizeof(float)); *pi = 1024; *pf = 3.14; printf( an integer = %d, a float = %f\n, *pi, *pf); free(pi); free(pf); Allocation and deallocation of memory 12

13 Recursive Algorithms Recursive function: A function which calls itself. int binsearch(int list[], int searchnum, int left, int right) { */ search list [0] <= list[1] <= <= list[n-1] for searchnum. Return its position if found. Otherwise return -1 */ int middle; if (left <=right) { middle = (left + right) / 2; switch (COMPARE(list[middle], searchnum)) { case -1: return binsearch(list, searchnum, middle+1, right); case 0 : return middle; case 1 : return binsearch(list, searchnum, left, middle-1); } } return -1; } Recursive implementation of binary search 13

14 Data Abstraction The basic data types of C : char, int, float, double, Grouping data : array, structure Int list[5] : integer array structure struct student { } char lastname; int studentid; char grade; User defined data type 14

15 Data Abstraction definition : abstract data type (ADT) A data type organized in such a way that the specification of the objects and operations on the objects is separated from the implementation. e.g.) C++ : Class Specification of the operations of an ADT: This consists of the names of every function, the type of arguments, type of result, description of what the function does, without the implementation details. ADT is implementation-independent. 15

16 Data Abstraction Example [abstract data type NaturalNumber] ADT NaturalNnumber is objects: an ordered subrange of the integers starting at zero and ending at the maximum interger (INT_MAX) on the compute functions: for all x, y NaturalNumber, TRUE, FALSE Boolean and where +, -, <, and == are the integer operations NaturalNumber Zero() ::= 0 Boolean IsZero(x) ::= if(x) return FALSE else return TRUE Boolean Equal(x, y) ::= if(x= =y) return TRUE else return FALSE NaturalNumber Successor ::= if(x = = INT_MAX) return x else return x+1 NaturalNumber Add(x,y) ::= if((x+y)<= INT_MAX) return x+y else return INT_MAX NaturalNumber Subtract(x,y) ::= if(x<y) return 0 else return x-y end NaturalNumber 16