Linear Data Structures using Sequential

organization

Classification s of Data Structures

Types of Data Structures

Arrays

Declaration of arrays

type arrayName [ arraySize ];

Ex-double balance[10];

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};

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};

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;

Arrays

Shown below is the pictorial representation of the array:

Accessing Array Elements

double salary = balance[4];

Ex-Arrays#include <stdio.h> 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++)

{ scanf(“%d”,&a[i]);

} //end for

for(i=0;i<size;i++) {

printf(“The array is %d”,a[i]); //Displaying Array

}//end for

return 0;}

Output will be

12345

Multi-dimensional Arrays in C

type name[size1][size2]...[sizeN];

Two-dimensional Arrays in C

multidimensional array is the two-dimensional array

type arrayName [ x ][ y ];

Two-dimensional Arrays in C

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 */ };

Accessing Two-Dimensional Array Elements

int val = a[2][3];

Three-dimensional Arrays in C

For example, the following declaration creates a three dimensional integer array −

Ex-int threedim[5][10][4];

void myFunction(int param[10]) { . . . //Statement Excution }

Passing Arrays as Function Arguments in C

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.

Abstract Data Type

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

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.

ADT for an array

Representation and analysisType variable_name[size]

Operations with arrays:CopyDeleteInsertSearchSortMerging of sorting arrays.

Introduction to arrays

#include <stdio.h> int main() { int a[100],b[100] position, c, n;

printf("Enter number of elements in array\n");

scanf("%d", &n); printf("Enter %d elements\n", n);

for ( c = 0 ; c < n ; c++ ) scanf("%d", &a[c]);

printf("Enter %d elements\n", n);

for( c = 0 ; c < n - 1 ; c++ )

printf("%d\n", a[c]);

//Coping the element of array a to b

for( c = 0 ; c < n - 1 ; c++ )

{ b[c]=a[c]; }

} return 0; }

Copy operation

Output

Enter number of elements in array -4

Enter 4 elements 1 2 3 4

displaying array a 1 2 3 4 displaying array b 1 2 3 4

#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); for ( c = 0 ; c < n ; c++ ) scanf("%d", &array[c]); printf("Enter the location where you wish to delete element\n");

scanf("%d", &position); if ( position >= n+1 ) printf("Deletion not possible.\n"); else { for ( c = position - 1 ; c < n - 1 ; c++ ) array[c] = array[c+1]; printf("Resultant array is\n"); for( c = 0 ; c < n - 1 ; c++ ) printf("%d\n", array[c]); } return 0; }

Delete operation

Delete operation

#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++) scanf("%d", &array[c]); printf("Enter the location where you wish to insert an element\n"); scanf("%d", &position); printf("Enter the value to insert\n"); scanf("%d", &value); for (c = n - 1; c >= position - 1; c--) array[c+1] = array[c]; array[position-1] = value; printf("Resultant array is\n"); for (c = 0; c <= n; c++) printf("%d\n", array[c]); return 0;}

Inserting an element

Inserting an element

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; }

}

Sort an 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--;}

Reverse 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; }

}

Sort element using array

int main(){ int arr1[30], arr2[30], res[60];

int i, j, k, n1, n2;  printf("\nEnter no of elements in 1st array :");

scanf("%d", &n1);

for (i = 0; i < n1; i++) {scanf("%d", &arr1[i]);}  printf("\nEnter no of elements in 2nd array :");

scanf("%d", &n2);

for (i = 0; i < n2; i++) {scanf("%d", &arr2[i]);}   i = 0; j = 0;k = 0;  

Merging of two arrays

// Merging startswhile (i < n1 && j < n2) { if (arr1[i] <= arr2[j]) { res[k] = arr1[i]; i++; k++; } else { res[k] = arr2[j]; k++; j++; }}  

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++; } 

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++; }

Merging of two arrays

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); }

/* 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]); }

Merging of two arrays

Output:

Enter no of elements in 1st array : 411 22 33 44 Enter no of elements in 2nd array : 310 40 80 Merged array is : 10 11 22 33 40 44 80

Merging of two arrays

Merging of two arrays

Two-dimensional Arrays in C

multidimensional array is the two-dimensional array

type arrayName [ x ][ y ];

Two-dimensional Arrays in C

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]);

}

For(i=0;i<m;i++) {

Printf(“\n”); For(j=0;j<n;j++) {

printf(“%d”,&a[i][j]); }

}

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; }

Address Calculation in single (one) Dimension Array:

Address Calculation

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)

Address Calculation Ex-Given the base address of an array B[1300…..1900] 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 ) = 1020 + 2 * (1700 – 1300) = 1020 + 2 * 400 = 1020 + 800 = 1820 [Ans]

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.

Address Calculation in Double (Two) Dimensional

Array:

Address Calculation in Double (Two) Dimensional

Array:

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

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 addressI = Row subscript of element whose address is to be foundJ = Column subscript of element whose address is to be foundW = 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 matrixN = Number of column of the given matrix

Address Calculation in Double (Two) Dimensional

Array:

Address of A [ I ][ J ] Column Major Wise = B + W * [( I – Lr ) + M * ( J – Lc )]

Column Major System:The address of a location in Column Major System is calculated using the following formula:

B = Base addressI = Row subscript of element whose address is to be foundJ = Column subscript of element whose address is to be foundW = 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 matrixN = Number of column of the given matrix

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) + 1Number of columns (N) will be calculated as = (Uc – Lc) + 1And rest of the process will remain same as per requirement (Row Major Wise or Column Major Wise).

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 = 26Number or columns say N = (Uc – Lc) + 1 = [40 – 15)] +1 = 26

Address Calculation in Double (Two) Dimensional

Array:

(i) Column Major Wise Calculation of above equationThe given values are: B = 1500, W = 1 byte, I = 15, J = 20, Lr = -15, Lc = 15, M = 26Address of A [ I ][ J ] =B + W * [ ( I – Lr ) + M * ( J – Lc ) ]= 1500 + 1 * [(15 – (-15)) + 26 * (20 – 15)] = 1500 + 1 * [30 + 26 * 5] = 1500 + 1 * [160] = 1660 [Ans]

= 1500 + 1* [26 * (15 – (-15))) + (20 – 15)] = 1500 + 1 * [26 * 30 + 5] = 1500 + 1 * [780 + 5] = 1500 + 785 = 2285 [Ans]

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

Addition of Two 2-D Matrices:

If we add two matrices am*n & bm*n producing Cm*n 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]; } }

Upper Triangular Matrix   A triangular matrix  of the form

Written explicitly,

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]); } } printf("\nThe entered matrix is:\n"); for(i=0;i<3;i++) { for(j=0;j<3;j++) { printf("%d\t",a[i][j]); } printf("\n"); } printf("\nUpper triangular matrix is:\n"); for(i=0;i<3;i++) { for(j=0;j<3;j++) { if(i<=j) { printf("%d\t",a[i][j]); } else { printf("%d\t",0); } } printf("\n"); } getch(); }

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,

Lower Triangular Matrix A triangular matrix  L of the form

Written explicitly,

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,

Assignment on

Strictly Upper Triangular Matrix Strictly Lower Triangular Matrix

For example:Suppose two matrixes A and B of size of 2 x 2 and 2 x 3 respectively:

MULTIPLICATION OF TWO MATRICES

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.

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)

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

Example of ordered list

Polynomial Operations

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.

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.