1. Arrays What is an array… –A data structure that holds a set of homogenous elements (of the same type) –Associate a set of numbers with a single variable name –All of these numbers must be of identical data type Similar to a multi-dimensional vector

2. How to Define Declaration type [size]; Example –To define an integer array called numbers of size int numbers[5]; numbers 0 1 2 3 4

3. How to Use Arrays How to refer to an individual element of an array –Accessed by their position (index) in the array, e.g. numbers[1] = 2; Array elements are always numbered beginning with 0 numbers[0] numbers[1] numbers[2] numbers[3] numbers[4] 2

4. Example – 0 Get a set of numbers from the user int numbers[5]; int i; for( i = 0; i < 5; i++ ) { scanf("%i", &numbers[i]); }

5. Example – I Calculate statistics of a set of numbers –Summation int sum = 0; for( i = 0; i < 5; i++ ) { sum = sum + numbers[i]; } –Finding the maximum value int maxValue = numbers[0]; for( i = 1; i < 5; i++ ) { if (numbers[i] > maxValue) maxValue = numbers[i]; }

6. Fibonacci Numbers in an Array n0123456 F(n)0112358

7. Code #include #define SIZE 15 int main() { int fib[SIZE], i; fib[0] = 0; //set initial values fib[1] = 1; //set initial values for ( i = 2; i < SIZE; i++ ) { fib[i] = fib[i - 2] + fib[i - 1]; } for ( i = 0; i < SIZE; i++ ) { printf(”fibonacci[%i] = %i\n", i, fib[i]); } return 0; }

8. Prime Number Definition (could be you already know this?) –A positive integer that has no positive integer divisors other than 1 and itself. Testing whether a number p is a prime number Is there an integer divisor between 2 and p-1 for p?

9. Approaches – I Base version 1 int d; /* possible divisor */ int p; /* number whose “primeness” we are testing. */ for (d = 2; d < p; d++) { if (p % d == 0) { printf(“%i is not a prime!\n”, p); break; }

10. Approaches – II Version 2 #define TRUE 1 #define FALSE 0 int isPrime = TRUE; int d,p; for (d = 2; d < p; d++) { if (p % d == 0) { isPrime = FALSE; break; } if (isPrime) printf(“%i is prime\n”, p); else printf(“%i is not prime\n”, p);

11. Approaches – III Observation –Only need to test whether there is a integer divisor between 2 and for p for (d = 2; d * d <= p; d++) { if (p % d == 0) { isPrime = FALSE; break; }

12. Approaches – IV Observation –Only need to check whether a prime number between 2 and is a divisor –Need to record which numbers are prime so we only test them once Using arrays!

13. Code Declare variables int p, i; int primes[PRIMES]; // for noting prime numbers int primeIndex; // next place to store a prime int isPrime; // boolean variable Initial setup primes[0] = 2;// we know 2 is prime primes[1] = 3;// we know 3 is prime primeIndex = 2; // the next array slot is [2]

14. Code – cont for (p = 5; p <= PRIMES; p += 2 ) { isPrime = TRUE; // start by assuming p is prime i = 1; // let’s skip the first prime (its 2) while (i < primeIndex) { if ( p % primes[i] == 0 ) { isPrime = FALSE; break;// leave loop, no point to // testing more divisors } i++; } if (isPrime) { primes[primeIndex] = p;// Store prime p ++primeIndex;// advance index if (primeIndex > PRIMES) break; // prime array is full }

15. Initializing arrays Initializing an array using a comma- separated list of constants in { } –int number[] = { 5, 7, 2 }; Size of an array is automatically set as the number of elements within { }

16. Character Arrays and Strings A character array contains characters (naturally) –char word[ ] = {‘H’,’e’,’l’,’l’,’o’,’!’} Strings –A special character ‘\0’ (called a “null” character) at the end of a character array indicates the end of a string. –Use %s in printf to print a string –initialization char word[]="hello"; hello\0

17. The const qualifier When we need the const qualifier –Specify a variable whose value is constant, i.e., value will not be changed How to use –Put const in front of variable definition const double pi = 3.141592654; What if I attempt to change its value –E.g. pi = pi * 2; –I will get a compiler Warning/Error: “Assignment of read-only variable ‘pi’”

18. Multidimensional Arrays Declaration –type name[ nrows][ncols]; e.g. int m[5][10]; Access –m[3][4]; Not m[3,4], or m(3)(4) n columns j changes m–by–n matrix m rows i changes

19. Multidimensional Arrays Initialization int M[2][3] = {{1, 2, 3}, {4, 5,6}}; –Or int M[2][3] = {1, 2, 3, 4, 5, 6}; Numbers will fill up the first row, then the second row,…