Classification s of Data Structures

Transcription

1 Linear Data Structures using Sequential organization

2 Classification s of Data Structures

3 Types of Data Structures

4 Arrays Declaration of arrays type arrayname [ arraysize ]; Ex-double balance[10];

5 Arrays Initializing Arrays Ex-double balance[5] = {1000.0, 2.0, 3.4, 7.0, 50.0}; If you omit the size of the array, an array just big enough to hold the initialization is created. Therefore, if you write Ex-double balance[] = {1000.0, 2.0, 3.4, 7.0, 50.0};

6 Arrays Initializing Arrays Ex-double balance[5] = {1000.0, 2.0, 3.4, 7.0, 50.0}; If you omit the size of the array, an array just big enough to hold the initialization is created. Therefore, if you write Ex-double balance[] = {1000.0, 2.0, 3.4, 7.0, 50.0};

7 Arrays Initializing Arrays You will create exactly the same array as you did in the previous example. Following is an example to assign a single element of the array Ex-balance[4] = 50.0;

8 Arrays Shown below is the pictorial representation of the array:

9 Accessing Array Elements double salary = balance[4];

10 #include <stdio.h> Ex-Arrays int main () { int a[10],i,size; printf( \nhow many no of elements u want to scan ); scanf( %d,&size); printf( \nenter the elements in the array ); for(i=0;i<size;i++) {

11 Output will be

12 Multi-dimensional Arrays in C type name[size1][size2]...[sizen];

13 Two-dimensional Arrays in C multidimensional array is the two-dimensional array type arrayname [ x ][ y ];

14 Two-dimensional Arrays in C

15 Initializing Two-Dimensional Arrays int a[3][4] = { {0, 1, 2, 3}, /* initializers for {4, 5, 6, 7}, {8, 9, 10, 11} /* initializers for row /* initializers for row indexed by 2 */ };

16 Accessing Two-Dimensional Array Elements int val = a[2][3];

17 Three-dimensional Arrays in C For example, the following declaration creates a three dimensional integer array Ex-int threedim[5][10][4];

18 Passing Arrays as Function Arguments in C void myfunction(int param[10]) {... //Statement Excution }

19 Abstract Data Type ADT is useful tool for specifying the logical properties of a data type. A data type is a collection of values & the set of operations on the values. ADT refers to the mathematical concept that defines the data type. ADT is not concerned with implementation but is useful in making use of data type.

20 ADT for an array Arrays are stored in consecutive set of memory locations. Array can be thought of as set of index and values. For each index which is defined there is a value associated with that index. There are two operations permitted on array data structure.retrieve and store

21 ADT for an array CREATE()-produces empty array. RETRIVE(array,index)->value Takes as input array and index and either returns appropriate value or an error. STORE(array,index,value)-array used to enter new index value pairs.

22 Introduction to arrays Representation and analysis Type variable_name[size] Operations with arrays: Copy Delete Insert Search Sort Merging of sorting arrays.

23 #include <stdio.h> int main() { int a[100],b[100] position, c, n; Copy operation printf("enter number of elements in array\n");

24 Output Enter number of elements in array -4 Enter 4 elements displaying array a 1

25 #include <stdio.h> int main() { int array[100], position, c, n; printf("enter number of elements in array\n"); scanf("%d", &n); printf("enter %d elements\n", n); Delete operation for ( c = 0 ; c < n ; c++ )

26 Delete operation

27 Inserting an element #include <stdio.h> int main() { int array[100], position, c, n, value; printf("enter number of elements in array\n"); scanf("%d", &n); printf("enter %d elements\n", n); for (c = 0; c < n; c++)

28 Inserting an element

29 Sort an array Int a[10]={5,4,3,2,1} for(i=0;i<n;i++) for(j=i+1;j<n-i;j++) { if(a[i]>a[j]) { temp=a[i]; a[i]=a[j]; a[j]=temp; }

30 Reverse array a[6]={11,12,13,14,15,16} J=n-1; For(i=0;i<n/2;i++) { temp=a[i]; a[i]=a[j]; a[j]=temp; j--; }

31 Sort element using array Int a[10]={5,4,3,2,1} for(i=0;i<n;i++) for(j=i+1;j<n;j++) { if(a[i]>a[j]) { temp=a[i]; a[i]=a[j]; a[j]=temp; }

32 Merging of two arrays int main() { int arr1[30], arr2[30], res[60]; int i, j, k, n1, n2; printf("\nenter no of

33 Merging of two arrays // Merging starts while (i < n1 && j < n2) { if (arr1[i] <= arr2[j]) { res[k] = arr1[i]; i++;

34 Merging of two arrays /* Some elements in array 'arr1' are still remaining where as the array 'arr2' is exhausted */ while (i < n1) { res[k] = arr1[i]; i++; k++; }

35 Merging of two arrays /* Some elements in array 'arr2' are still remaining where as the array 'arr1' is exhausted */ while (j < n2) { res[k] = arr2[j]; k++; j++; }

36 Merging of two arrays //Displaying elements of array 'res' printf("\nmerged array is :"); for (i = 0; i < n1 + n2; i++) printf("%d ", res[i]); return (0); }

37 Merging of two arrays /* Some elements in array 'arr2' are still remaining where as the array 'arr2' is exhausted */ while (i < n2) { res[k] = arr2[i]; i++; k++; } for(i=0;i<k;i++) { printf( %d,res[i]); }

38 Merging of two arrays Output: Enter no of elements in 1st array : Enter no of elements in 2nd array : Merged array is :

39 Merging of two arrays

40 Two-dimensional Arrays in C multidimensional array is the two-dimensional array type arrayname [ x ][ y ];

41 Two-dimensional Arrays in C

42 m-no of rows n-no of columns Printf( \n Enter the rows and columns ); Scanf(%d %d,&m,&n); for(i=0;i<m;i++) { for(j=0;j<n;j++) { Printf( \n Enter the value of(%d)(%d)=,i,j); Scanf( %d,&a[i][j]); }

43 For(i=0;i<m;i++) { Printf( \n ); For(j=0;j<n;j++) { printf( %d,&a[i][j]); } }

44 int main () { /* an array with 5 rows and 2 columns*/ int a[5][2] = { {0,0}, {1,2}, {2,4}, {3,6},{4,8}}; int i, j; /* output each array element's value */ for ( i = 0; i < 5; i++ ) { for ( j = 0; j < 2; j++ ) { printf("a[%d][%d] = %d\n", i,j, a[i][j] ); } } return 0; }

45 Address Calculation in single (one) Dimension Array:

46 Address Calculation

47 Address Calculation Array of an element of an array say A[ I ] is calculated using the following formula: Address of A [ I ] = B + W * ( I LB ) Where, B = Base address W = Storage Size of one element stored in the array (in byte) I = Subscript of element whose address is to be found LB = Lower limit / Lower Bound of subscript, if not specified assume 0 (zero)

48 Address Calculation Ex-Given the base address of an array B[ ] as 1020 and size of each element is 2 bytes in the memory. Find the address of B[1700]. Solution: The given values are: B = 1020, LB = 1300, W = 2, I = 1700 Address of A [ I ] = B + W * ( I LB ) = * ( ) = * 400 =

49 Address Calculation in Double (Two) Dimensional Array: While storing the elements of a 2-D array in memory, these are allocated contiguous memory locations. Therefore, a 2-D array must be liberalized so as to enable their storage. There are two alternatives to achieve linearization: Row-Major and Column-Major.

50 Address Calculation in Double (Two) Dimensional Array:

51 Address Calculation in Double (Two) Dimensional Array:

52 Address Calculation in Double (Two) Dimensional Array: Address of an element of any array say A[ I ][ J ] is calculated in two forms as given: (1) Row Major System (2) Column Major System

53 Address Calculation in Double (Two) Dimensional Array: The address of a location in Row Major System is calculated using the following formula: Address of A [ I ][ J ] = B + W * [ N * ( I Lr ) + ( J Lc ) B = Base address I = Row subscript of element whose address is to be found J = Column subscript of element whose address is to be found W = Storage Size of one element stored in the array (in byte) Lr = Lower limit of row/start row index of matrix, if not given assume 0 (zero) Lc = Lower limit of column/start column index of matrix, if not given assume 0 (zero) M = Number of row of the given matrix N = Number of column of the given matrix

54 Address Calculation in Double (Two) Dimensional Array: Column Major System: The address of a location in Column Major System is calculated using the following formula: Address of A [ I ][ J ] Column Major Wise = B + W * [( I Lr ) + M * ( J Lc )] B = Base address I = Row subscript of element whose address is to be found J = Column subscript of element whose address is to be found W = Storage Size of one element stored in the array (in byte) Lr = Lower limit of row/start row index of matrix, if not given assume 0 (zero) Lc = Lower limit of column/start column index of matrix, if not given assume 0 (zero)

55 Address Calculation in Double (Two) Dimensional Array: Important : Usually number of rows and columns of a matrix are given ( like A[20][30] or A[40][60] ) but if it is given as A[Lr- Ur, Lc- Uc]. In this case number of rows and columns are calculated using the following methods: Number of rows (M) will be calculated as = (Ur Lr) + 1 Number of columns (N) will be calculated as = (Uc Lc) + 1 And rest of the process will remain same as per requirement (Row Major Wise or Column Major Wise).

56 Address Calculation in Double (Two) Dimensional Array: Examples: Q 1. An array X [-15.10, 15 40] requires one byte of storage. If beginning location is 1500 determine the location of X [15][20]. Solution: As you see here the number of rows and columns are not given in the question. So they are calculated as: Number or rows say M = (Ur Lr) + 1 = [10 (- 15)] +1 = 26 Number or columns say N = (Uc Lc) + 1 = [40 15)] +1 = 26

57 Address Calculation in Double (Two) Dimensional Array: (i) Column Major Wise Calculation of above equation The given values are: B = 1500, W = 1 byte, I = 15, J = 20, Lr = -15, Lc = 15, M = 26 Address of A [ I ][ J ] =B + W * [ ( I Lr ) + M * ( J Lc ) ] = * [(15 (-15)) + 26 * (20 15)] = * [ * 5] = * [160] = 1660 [Ans]

58 (ii) Row Major Wise Calculation of above equation The given values are: B = 1500, W = 1 byte, I = 15, J = 20, Lr = -15, Lc = 15, N = 26 Address of A [ I ][ J ] = B + W * [ N * ( I Lr ) + ( J Lc ) ] = * [26 * (15 (-15))) + (20 15)] = * [26 * ] = * [ ] = = 2285 [Ans]

59 Addition of Two 2-D Matrices: If we add two matrices am*n & bm*n Cm*n producing for(i=0;i<m;i++) //for row { for(j=0;j<n;j++) //for column { c[i][j]=a[i][j]+b[i][j]; } }

60 Upper Triangular Matrix A triangular matrix of the form Written explicitly,

61 Example #include<stdio.h> #include<conio.h> void main() { int a[3][3],i,j; clrscr(); printf("enter the elements of 3x3 matrix:\n"); for(i=0;i<3;i++) { { for(j=0;j<3;j++) scanf("%d",&a[i][j]); } }

62 Strictly Upper Triangular Matrix A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well as the lower portion, i.e., a matrix such that for. Written explicitly,

63 Lower Triangular Matrix A triangular matrix L of the form Written explicitly,

64 Strictly Lower Triangular Matrix A lower triangular matrix having 0s along the diagonal as well as the upper portion, i.e., a matrix such that for. Written explicitly,

65 Assignment on Strictly Upper Triangular Matrix Strictly Lower Triangular Matrix

66 MULTIPLICATION OF TWO MATRICES For example: Suppose two matrixes A and B of size of 2 x 2 and 2 x 3 respectively:

67

68 Transpose of a Matrix A matrix which is formed by turning all the rows of a given matrix into columns and vice-versa. The transpose of matrix A is written AT.

69 Concept of Ordered List It is a set of elements.such a list sometimes called as linear list. Definition- EX-1.List of one one digit numbers. (0,1,2,3,4,5,6,7,8,9) Ex-2 Days in a week. (Sunday, Monday Tuesday, Wednesday, Thursday,Friday,Saturday)

70 Operations on ordered list Create an ordered list Dispay of list Searching particular element from the list Insertion of any element in the list Deletion of any element from the list

71 Example of ordered list Polynomial Operations

72 While scanning the string doesn t required scanf( %s,str1) ; scanf needs the address of the variable to read into, and string buffers are already represented as addresses (pointer to a location in memory, or an array that decomposes into a pointer). printf does the same, treating %s as a pointer-to-string.

73 Scanning string scanf needs the address of the variable to read into, and string buffers are already represented as addresses (pointer to a location in memory, or an array that decomposes into a pointer). printf does the same, treating %s as a pointer-to-string.