Understanding Arrays: Structure, Declaration, and Usage in Programming

1. 1-d Arrays

2. Array • Many applications require multiple data items that have common characteristics • In mathematics, we often express such groups of data items in indexed form: • x1, x2, x3, …, xn • Array is a data structure which can represent a collection of data items which have the same data type (float/int/char/…)

3. Example: Printing Numbers in Reverse 4 numbers 3 numbers int a, b, c, d; scanf(“%d”, &a); scanf(“%d”, &b); scanf(“%d”, &c); scanf(“%d”, &d); printf(“%d ”, d); printf(“%d ”, c); printf(“%d ”, b); printf(“%d \n”, a); int a, b, c; scanf(“%d”, &a); scanf(“%d”, &b); scanf(“%d”, &c); printf(“%d ”, c); printf(“%d ”, b); printf(“%d \n”, a);

4. The Problem • Suppose we have 10 numbers to handle • Or 20 • Or 100 • Where do we store the numbers ? Use 100 variables ?? • How to tackle this problem? • Solution: • Use arrays

5. Printing in Reverse Using Arrays void main() { int n, A[100], i; printf(“How many numbers to read? “); scanf(“%d”, &n); for (i = 0; i < n; ++i) scanf(“%d”, &A[i]); for (i = n -1; i >= 0; --i) printf(“%d ”, A[i]); printf(“\n”); }

6. x[0] x[1] x[2] x[9] X is a 10-element one dimensional array Using Arrays • All the data items constituting the group share the same name int x[10]; • Individual elements are accessed by specifying the index

7. Declaring Arrays • Like variables, the arrays used in a program must be declared before they are used • General syntax: type array-name [size]; • type specifies the type of element that will be contained in the array (int, float, char, etc.) • size is an integer constant which indicates the maximum number of elements that can be stored inside the array • marks is an array that can store a maximum of 5 integers int marks[5];

8. Examples: int x[10]; char line[80]; float points[150]; char name[35]; • If we are not sure of the exact size of the array, we can define an array of a large size int marks[50]; though in a particular run we may only be using, say, 10 elements

9. Accessing Array Elements • A particular element of the array can be accessed by specifying two things: • Name of the array • Index (relative position) of the element in the array • In C, the index of an array starts from zero • Example: • An array is defined as int x[10]; • The first element of the array x can be accessed as x[0], fourth element as x[3], tenth element as x[9], etc.

10. Contd. • The array index must evaluate to an integer between 0 and n-1 where n is the maximum number of elements possible in the array a[x+2] = 25; b[3*x-y] = a[10-x] + 5; • Remember that each array element is a variable in itself, and can be used anywhere a variable can be used (in expressions, assignments, conditions,…)

11. A first example “data refers to a block of 10 integer variables, data[0], data[1], …, data[9] void main() { int i; int data[10]; for (i=0; i<10; i++) data[i]= i; i=0; while (i<10) { printf("Data[%d] = %d\n", i, data[i]); i++; } }

12. The result Array size should be a constant void main() { int i; int data[10]; for (i=0; i<10; i++) data[i]= i; i=0; while (i<10) { printf("Data[%d] = %d\n", i, data[i]); i++; } } Output Data[0] = 0 Data[1] = 1 Data[2] = 2 Data[3] = 3 Data[4] = 4 Data[5] = 5 Data[6] = 6 Data[7] = 7 Data[8] = 8 Data[9] = 9

13. How is an array stored in memory? • Starting from a given memory location, the successive array elements are allocated space in consecutive memory locations • x: starting address of the array in memory • k: number of bytes allocated per array element • a[i]  is allocated memory location at address x + i*k Array a

14. Storage Output &Data[0] = 3221224480 &Data[1] = 3221224484 &Data[2] = 3221224488 &Data[3] = 3221224492 &Data[4] = 3221224496 &Data[5] = 3221224500 &Data[6] = 3221224504 &Data[7] = 3221224508 &Data[8] = 3221224512 &Data[9] = 3221224516 void main() { int i; int data[10]; for(i=0; i<10; i++) printf("&Data[%d] = %u\n", i, &data[i]); }

15. Initialization of Arrays • General form: type array_name[size] = { list of values }; • Examples: int marks[5] = {72, 83, 65, 80, 76}; char name[4] = {‘A’, ‘m’, ‘i’, ‘t’}; • The size may be omitted. In such cases the compiler automatically allocates enough space for all initialized elements int flag[ ] = {1, 1, 1, 0}; char name[ ] = {‘A’, ‘m’, ‘i’, ‘t’};

16. How to read the elements of an array? • By reading them one element at a time for (j=0; j<25; j++) scanf (“%f”, &a[j]); • The ampersand (&) is necessary • The elements can be entered all in one line or in different lines

17. Passing Arrays to Function • Array element can be passed to functions as ordinary arguments • IsFactor (x[i], x[0]) • sin (x[5])

18. Passing Entire Array to a Function • An array name can be used as an argument to a function • Permits the entire array to be passed to the function • The way it is passed differs from that for ordinary variables • Rules: • The array name must appear by itself as argument, without brackets or subscripts • The corresponding formal argument is written in the same manner • Declared by writing the array name with a pair of empty brackets

19. Whole Array as Parameters Only Array Name/address passed. [ ] mentioned to indicate that is an array. const int ASIZE = 5; float average (int B[ ]) { int i, total=0; for (i=0; i<ASIZE; i++) total = total + B[i]; return ((float) total / (float) ASIZE); } void main ( ) { int x[ASIZE] ; float x_avg; x [] = {10, 20, 30, 40, 50}; x_avg = average (x) ; } Called only with actual array name

20. Contd. void main() { int n; float list[100], avg; : avg = average (n, list); : } float average (int a, float x[]) { : sum = sum + x[i]; } We don’t need to write the array size. It works with arrays of any size.

21. Arrays used as Output Parameters void VectorSum (int a[ ], int b[ ], int vsum[ ], int length) { int i; for (i=0; i<length; i=i+1) vsum[i] = a[i] + b[i] ; } void PrintVector (int a[ ], int length) { int i; for (i=0; i<length; i++) printf (“%d “, a[i]); } void main () { int x[3] = {1,2,3}, y[3] = {4,5,6}, z[3]; VectorSum (x, y, z, 3) ; PrintVector (z, 3) ; } vector-sum.c

22. Reading into an array void main() { const int MAX_SIZE = 100; int i, size; float marks[MAX_SIZE]; float total=0; scanf("%d",&size); for (i=0; i<size; i++) { scanf("%f",&marks[i]); total = total + marks[i]; } printf("Total = %f \n Avg = %f\n", total, total/size); } Output 4 2.5 3.5 4.5 5 Total = 15.500000 Avg = 3.875000

23. A Warning • In C, while accessing array elements, array bounds are not checked • Example: int marks[5]; : : marks[8] = 75; • The above assignment would not necessarily cause an error • Rather, it may result in unpredictable program results

24. How to copy the elements of one array to another? • By copying individual elements for (j=0; j<25; j++) a[j] = b[j]; • The element assignments will follow the rules of assignment expressions • Destination array must have sufficient size

25. Example 1: Find the minimum of a set of 10 numbers void main() { int a[10], i, min; for (i=0; i<10; i++) scanf (“%d”, &a[i]); min = a[0]; for (i=1; i<10; i++) { if (a[i] < min) min = a[i]; } printf (“\n Minimum is %d”, min); }

26. Example 2:Computing cgpa const int nsub = 6; void main() { int grade_pt[nsub], cred[nsub], i, gp_sum=0, cred_sum=0; double gpa; for (i=0; i<nsub; i++) scanf (“%d %d”, &grade_pt[i], &cred[i]); for (i=0; i<nsub; i++) { gp_sum += grade_pt[i] * cred[i]; cred_sum += cred[i]; } gpa = ((float) gp_sum) / cred_sum; printf (“\n Grade point average: is %.2lf”, gpa); } Handling two arrays at the same time

27. Things you cannot do • You cannot • use = to assign one array variable to another a = b; /* a and b are arrays */ • use == to directly compare array variables if (a = = b) ……….. • directly scanf or printf arrays printf (“……”, a);

28. Recall

29. Recall

30. Recall

31. x=a++ - ++a; Right to left evaluation of the expression. First update (rightmost) a to 11. Leftmost a =>11 x=0 a=12

32. Revisit loops

33. SUM = 12 + 22 + 32 + …+ N2

34. SUM = 12 + 22 + 32 + …+ N2 void main() { int N, count, sum; scanf (“%d”, &N) ; sum = 0; count = 1; while (count <= N) { sum = sum + count  count; count = count + 1; } printf (“Sum = %d\n”, sum) ; return 0; }

35. Maximum of positive Numbers

36. Maximum of positive Numbers void main() { double max = 0.0, next; printf (“Enter positive numbers, end with 0 or a negative number\n”); scanf(“%lf”, &next); while (next > 0) { if (next > max) max = next; scanf(“%lf”, &next); } printf (“The maximum number is %lf\n”, max) ; }

37. Find the sum of digits of a number digit-sum.c

38. Find the sum of digits of a number void main() { int n, sum=0; scanf (“%d”, &n); while (n != 0) { sum = sum + (n % 10); n = n / 10; } printf (“The sum of digits of the number is %d \n”, sum); } digit-sum.c

39. Test if a number is prime or not void main() { int n, i=2; scanf (“%d”, &n); while (i < n) { if (n % i == 0) { printf (“%d is not a prime \n”, n); break; } ++i; } if (i == n) printf (“%d is a prime \n”, n); }

40. More efficient?? void main() { int n, i = 2, flag = 0; double limit; scanf (“%d”, &n); limit = sqrt(n); while (i <= limit) { if (n % i == 0) { printf (“%d is not a prime \n”, n); flag = 1; break; } i = i + 1; } if (flag == 0) printf (“%d is a prime \n”, n); }

41. Some Loop Pitfalls while (sum <= NUM) ; sum = sum+2; for (i=0; i<=NUM; ++i); sum = sum+i; for (i=1; i!=10; i=i+2) sum = sum+i; double x; for (x=0.0; x<2.0; x=x+0.2) printf(“%f\n”, x);

42. Some observations on for • Initialization, loop-continuation test, and update can contain arithmetic expressions for ( k = x; k <= 4 * x * y; k += y / x ) • Update may be negative (decrement) for (digit = 9; digit >= 0; --digit) • If loop continuation test is initially 0 (false) • Body of for structure not performed • No statement executed • Program proceeds with statement after for structure

43. Example • We can give several expressions separated by commas in place of expr1 and expr3 in a for loop to do multiple assignments for example for (fact=1, i=1; i<=10;++ i) fact = fact * i; for (sum=0, i=1; i<=N; ++i) sum = sum + i * i;