Here, type declares the base type of the array, which is the type of each element in the array size defines how many elements the array will hold

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1 Arrays 1. Introduction An array is a consecutive group of memory locations that all have the same name and the same type. A specific element in an array is accessed by an index. The lowest address corresponds to the first element in an array and the highest address to the last element. 2. Declaring and initializing arrays A) Declaring arrays The general form for declaring an array is type array_name[size] Here, type declares the base type of the array, which is the type of each element in the array size defines how many elements the array will hold For example, to declare a 100-element array called balance, and of type double, you can use: double balance[100]; To refer to a particular location or element in the array, we specify the name of the array and the position number of the particular element in the array. All arrays have 0 as the index of their first element. Thus, the first element of array balance is referred to as balance[0], the second element is referred to as balance[1], and in general i-th element is referred to as balance[i-1]. The position number contained within square brackets is called subscript. For example, to print the sum of the values contained in the first three elements of array balance, we would write cout << balance[0] + balance[1] + balance[2]<<endl; B) Initializing arrays To initialize an array you can use the array declaration by following the declaration with an equals sign and a comma-separated list, enclosed in braces, of initializers. For example int n[5] = {30, 30, 30, 30, 30 // initialize the elements of array n to 30 Declaring and initializing one dimensional arrays dynamically If you don t know what the length of the array is going to be you can declare them dynamically It means that you are going to need a pointer to the type of the array that you want. For example, if you

2 want an array of integers you have to declare int *ArrayPtr;// declares a pointer to an integer The length of the array would be entered from the keyboard (cin >> length;) At that point you are free to allocate as many locations as you have entered as the length of the array. To allocate the locations you write: ArrayPtr = new int[length]; At that point ArrayPtr becomes the name of your array and you can use it as any other array before. Example1. a) Write a program that dynamically allocates an array, enters its content from the keyboard and prints its content. #include <iostream> using namespace std; int main(){ int length ; int *ArrayPtr; cout << " Please enter the length of the array " << endl; cin >> length; ArrayPtr = new int[length]; cout << "Please enter the elements of the array " << endl; for (int index = 0; index <= length -1; index++) cin >> ArrayPtr[index]; for (int index = 0; index <= length -1; index++) cout << ArrayPtr[index]<<endl; return 0; b) Write a program that dynamically allocates an array, enters its content from the keyboard and print its content in reverse order c) Write a program that dynamically allocates an array, initializes all the locations with random number s from 1-50 and finds the sum of all the elements of the array Example 2. Write a program that declares two dynamically allocated arrays of integers and appends the second array at the end of the first one to form the third one Dynamically allocating a 2-D array

3 When allocating a 2-dimensional array you will need to declare a pointer to a pointer int **array_ptr; //two * are needed because it is a pointer to a pointer In order to allocate the desired number of rows you will have to create a pointer to The first location in each row array_ptr=new int*[rownumber];//creates an array of pointers to int objects for each row In order to allocate the desired number of locations for each row you will need a for loop for(int i=0; i<rownumber; ++i) array_ptr[i]=new int[columnumber]; //creates new 'column' number of locations After that you can use array_ptr as the name of your 2-dimensional array whose dimension is rownumber by columnumber. Example 1. a) Write program that enters a 2-dimensional array from the keyboard and prints its values row by row #include <iostream> using namespace std; int main() { int row; int column; int **matrix; //two * are needed because it is a pointer to a pointer cout << "please enter the dimension of the matrix" << endl; cin >> row; cin >> column; matrix=new int*[row]; //creates a new array of pointers to int objects for rows for(int i=0; i<row; ++i) matrix[i]= new int[column];//creates new 'column' number of locations cout << "enter the elements of the array " << endl; for ( int i= 0; i<row; i++) for ( int j=0; j<column; j++) cin>>matrix[i][j]; for (int r=0; r<row; r++){ for (int c = 0; c< column; c++) cout << matrix[r][c]<<"\t"; cout << endl; return 0;

4 b) Write a program that initializes a 2-dim array using random numbers from and finds the average of all the values c) Write a program that initializes an n by n (square) 2-dim array and prints the elements on its main diagonal Example 2. Write a program that declares two dynamically allocated 2-dim arrays of integers and appends the second array at the end of the first one to form the third 2-dim array. C) Passing arrays to functions To pass an array to a function, specify the name of the array without any brackets. For example, if array hourlytemperatures has been declared as int hourlytemperatures[24]; the function call modifyarray( hourlytemperatures, 24); passes array hourlytemperature and its size to the function modifyarray. Entire arrays are passed by call-by-reference, but individual array elements are passed call-by-value. For a function that receives an array, the function s parameter list must specify that an array will be received. For example the function header for the function modifyarray could be written as: void modifyarray(int b[], int arraysize) Similarly corresponding function prototype could be written void modifyarray(int[], int); Example 1. Declare and initialize an array of length 5. Send the array to the function modifyarray that doubles each of the original values of elements of the array. Now, print the new values of the array. Also, send a single element of the array to the function modifyelement that doubles the element received and prints it out. Now, print the value of the element one more time after returning to the main function. #include <iostream> using namespace std; void modifyarray (int[], int); void modifyelement(int); int main() { int element[5]; for (int index =0; index <= 4; index++) element[index] = index; cout << "Effects of passing entire array call by reference\n\n"; cout << "Value of the original array is \n";

5 return 0; for (int x = 0; x <= 4; x++) cout << element[x] << " "; cout << endl; modifyarray (element, 5); cout << endl << endl; cout << "Effects of passing array element call-by-value\n\n"; cout << "The value of element[3] is " << element[3] << endl; modifyelement(element[3]); cout << "The value of element[3] is " << element[3] << endl; void modifyarray(int b[], int ArraySize){ // add the body of the function void modifyelement(int a) { // add the body of the function Example 2. a) Write a function printarray to print an array b) Write a function printarrayrecursive to print an array recursively void print_array_rec(int a[], int length){ if (length == 0) cout << "\t"; else print_array_rec( a, length-1); cout << a[length ] << "\t"; Example 3. Write a recursive function that initializes elements of the array called twopower to 1, 2, 4, 8, and so on. Example 4. a) Write a function sum that finds the sum of the elements of an array. b) Write a function recursive_sum that finds the sum of the elements of an array. int sum_array_rec (int a[], int length){ if (length == 0) return a[0]; else return a[length-1]+sum_array_rec( a, length-1);

6 Example 5. a) Write a function init_array that initializes an array of length 10 to random numbers between 1 and 50 b) Write a function printarray to print the array c) Write a function printarrayrecursive to print the array recursively d)) Write a function sum that finds the sum of the elements of the array. e) Write a function recursive_sum that finds the sum of the elements of the array. f) Write a function largest that finds the largest element in the array g) Write a function recuursive_largest that finds the largest element in the array recursively Example 6. Write a program that solves the problem known as The Birthday Paradox. The problem goes like this: Find the probability that at least 2 people in the class are born on the same day if the class has a) 1 student b) 2 students... z) 26 students General concept to find the probability of an event: 1) find the total number of samples that include all possibility. (sample space) 2) find the total number of samples that match the event. (event space) 3) (event space)/(sample space) is the answer. a) Write an iterative function that solves the problem b) Write a recursive function that solves the problem The Birthday Paradox Solution 1. Assume that there are 365 days in a year. a) What is the probability that a person that you meet on street has a birthday different than yours? P(A) = 364 / 365 b) A 3 rd person appears. What is the probability that all 3 birthdays are different? P(A) = (363 / 365)*(364 / 365) c) What is the probability that at least 2 students in your class of 26 students have the same birthday? Indirect Solution: P(at least 2 have birthdays on same day) = 1 P(you all have different birthdays) = 1 (364 / 365)(363 / 365)(362 / 365)*...*(340 / 365) = 1 P(365, 26) / = = 0.6