1. Creating and Initializing Arrays, Accessing Elements, Multiple Dimensions Learning & Development Team http://academy.telerik.com Telerik Software Academy

2. 1. What are Arrays? 2. Declaring and Initializing Arrays 3. Accessing Array Elements 4. Array Input and Output 5. Multidimensional Arrays 6. STL vectors 2

3. Compound Data

4.  Arrays are collections of data (variables)  Under the same name  Sequential  All members have an index  i.e. number/position  Each member is accessed through  The array name  Combined with the member's index  "Members" are also called "elements"

5.  What an int array looks like (sort of)  Sequence of int variables, each with a value  Each variable has an index, starting at 0 (zero)  E.g. variable at index 1 has a value of 10  An array can be of any type  char, string, double, etc.  But only one type – cannot mix different types Index 012345 Value 13105100-31000 int a[6] = {13, 10, 5, 100, -3, 1000};

6.  Arrays are essential to programming  Allow group operations (i.e. looping through) on elements  Part of many fundamental algorithms  Easy to manage by just tracking indices  Can represent real life concepts  Queues, Grades of students, Protons per element in the Periodic table, etc.

7. Creating C++ arrays

8.  Array declaration requires  Data type, Identifier  Array size (could be inferred from initialization)  If defined, array size must be constant  Declared arrays assume random values  When they are not initialized  And are local to functions  Memory is always assigned at declaration int numberArray[5]; //"undefined" values char characterArray[2];//"undefined" values

9.  Array initialization  Values provided in braces {}, size can be skipped  If array size is given explicitly  Items in braces less than (or equal to) array size  If number of items is less than array size  Remaining items initialized to default values int numberArray[5] = {42, 13, 7, -1, 5}; int characterArray[] = {'a', 'z'}; //array has size 2 int someDefaults[3] = {1}; //array has values 1, 0, 0 int allDefaults[3] = {}; //array has values 0, 0, 0 int initListArr[] {1, 2, 3}; //using an initializer list //initializer list only available at declaration until C++11

10.  Looping through arrays also a popular method  E.g. initializing with square roots of the indices  Once created, an array cannot be re-assigned  Only way to create an array is declaration  i.e. no way to assign an array to a variable const int N = 100;... double arr[N]; for(int i=0; i<N; i++) { arr[i] = sqrt(i); }

11. Live Demo

12. Reading and Writing the Values of Arrays

13.  Elements are accessed through their index  Index is placed inside brackets []  Indexing starts from 0 to the size of the array  Access is both read and write int numberArray[5] = {42, 13, 7, -1, 5}; cout<numberArray[1]<<endl; //prints 13 numberArray[1] = 9; numberArray[3] += numberArray[1]; cout<<numberArray[1]; //prints 9 cout<<endl; cout<<numberArray[3]; //prints 8

14.  Loops can provide an arbitrary number of executions of a piece of code  Arrays can provide an arbitrary number of elements  Hence, arrays and loops are often used together  i.e. starting a loop going through each index  Often called "iterating" or "traversing" an array

15.  Example: sum of elements of an array const int numElements = 10; int arr[numElements] {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; int sum = 0; for(int i=0; i<numElements; i++) { sum += arr[i]; sum += arr[i];}cout<<sum;

16.  Example: reversing an array const int numElements = 11; int arr[numElements] {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; for(int i=0; i<numElements/2; i++) { int mirrorIndex = numElements - i - 1; int mirrorIndex = numElements - i - 1; int currentIndexValue = arr[i]; int currentIndexValue = arr[i]; arr[i] = arr[mirrorIndex]; arr[i] = arr[mirrorIndex]; arr[mirrorIndex] = currentIndexValue; arr[mirrorIndex] = currentIndexValue; ///or just use the built-in swap method ///or just use the built-in swap method //swap(arr[i], arr[mirrorIndex]); //swap(arr[i], arr[mirrorIndex]);} //arr is now {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

17. Live Demo

18.  When accessing by index in an array of size N  The following bounds for index apply: 0 <= index < N  Arrays are not protected against bad indices  Neither compile-time nor runtime  Exceeding array bounds is not defined in the standard, i.e. unpredictable

19.  Common results of accessing outside the array  You access some part of the program's memory – the access will be successful  Very hard to track this type of error  You access memory outside the program's address space – the OS should deny access  Error 0xC000005 in Windows  Don't rely on that, it could be a fatal error for an unprotected system

20. Live Demo

21. Reading and Printing Arrays on the Console

22.  Need to know the max size the array can be  Usually known in algorithmic problems  Further on, we will discuss how to do it even without knowing the max size in advance  Create an array with the max size  Read the actual number of elements  Start a loop and input each of the elements  Using the loop's "control variable"  for loops are good for this 22

23.  Example of Reading an Array from the Console const int MAX_SIZE = 100; //asume we know it //need to initialize array with constant expression int arr[MAX_SIZE]; int actualSize = 0; cin>>actualSize; for (int i=0; i<actualSize; i++) { cin>>arr[i]; cin>>arr[i];}

24.  Assume we know the array size  Probably stored it on creation  Loop through each element index in the array  Print each element to the console const int numElements = 5;... int arr[numElements] =... for (int index = 0; index < numElements; index++) { // Print each element on a separate line // Print each element on a separate line cout << arr[index] << endl; cout << arr[index] << endl;} 24

25. Live Demo

26. Arrays of arrays, Representing Tabular Data

27.  Multidimensional arrays are arrays of arrays  Every element of the array is an array itself  Nesting can be as deep as needed (3D, 4D …)  Useful for multi-dimensional data, e.g. tables IndexValue 042 19 2101 3121 4-11 5-101 IndexValue 0index01234 value20141983194219811945 1index01234 value429101121-11 2index01234 value43210 int array 2D int array

28.  2D arrays  Represent tables, mathematical matrices, etc.  A 2D array is usually called a "matrix"  Usually perceived as tables/spreadsheets 01234 020141983194219811945 1429101121-11 243210 Second dimension (columns) First dimension (rows)

29. Live Demo

30.  3D arrays  Represent matrices with more than one value per cell (e.g. an RGB image)  Some representations of objects in 3D space  Sometimes called "cubes" 012 0012012012 255 15030100 12 1012012012 341777634177763417776 2012012012 237255362372553623725536 Note: blurred by magnification

31.  Declaring multidimensional arrays  Just like normal arrays, with an extra pair of []  Initializing multidimensional arrays  The {} are filled with initializations of arrays  If provided arrays are less, default values are assigned int matrix[10][15]; //creates a 2D int array containing //10 one-dimensional int arrays, //10 one-dimensional int arrays, //each 15 elements long //each 15 elements long //Simply said a 2D array with 10 rows and 15 cols int m[2][3] = { {1, 2, 3}, {1, 2, 3}, {4, 5, 6} {4, 5, 6}} m 012 0123 1456

32.  Accessing elements of multidimensional arrays  Multidimensional arrays contain other arrays  Additional [] for each additional dimension  E.g. mat[5][3] accesses the 3 rd element of the 5 th array in mat  In other words, the cell at 5 th row and 3 rd column int m[2][3] = { {1, 2, 3}, {4, 5, 6} } cout<<m[0][0]; //prints 1 cout<<m[1][2]; //prints 6 cout<<m[1]; //prints the memory address of the second //array ({4,5,6}) in m //array ({4,5,6}) in m

33.  Traversing multidimensional arrays  Extra nested loop for traversing each dimension  Reading a matrix from the console  Printing matrices is similar (consider new lines) const int ROWS =..., COLS =...; int matrix[ROWS][COLS]; for(int row = 0; row < ROWS; row++) { for(int col = 0; col < COLS; col++) for(int col = 0; col < COLS; col++) { cin>>matrix[row][col]; cin>>matrix[row][col]; }}

34. Syntax, How it Works

35.  Arrays can be parameters for functions  Array data itself is not passed  Instead, a "reference" is passed  Much faster than copying the entire array  A reference points to the original object  Modifying a reference in the function leads to modifying the object  i.e. changing array elements effects the array in the caller

36.  Syntax for passing an array as a parameter  Much like declaration syntax  Size of first dimension can be omitted  i.e. normal (1D) arrays can have empty [] int Sum(int arr[], int numElements) { int sum = 0; int sum = 0; for(int i=0; i<numElements; i++) for(int i=0; i<numElements; i++) { sum += arr[i]; sum += arr[i]; } return sum; return sum;} int main() { int numbers[] = {1,2,3}; int numbers[] = {1,2,3}; cout<<Sum(numbers, 3); //prints 6 cout<<Sum(numbers, 3); //prints 6}

37.  Syntax for passing 2D array as a parameter  Multi-dimensional arrays need to specify size in each dimension, except the first int Print3ColMatrix(int matrix[][3], int rows) { for(int row = 0; row < rows; row++) { for(int row = 0; row < rows; row++) { for(int col = 0; col < 3; col++) { for(int col = 0; col < 3; col++) { cout<<matrix[row][col] cout<<matrix[row][col] } cout << endl; //new line for each row cout << endl; //new line for each row }} int main() { int matrix[2][3] = {{1,2,3},{4,5,6}}; int matrix[2][3] = {{1,2,3},{4,5,6}}; Print3ColMatrix(matrix, 2); Print3ColMatrix(matrix, 2);}

38. Live Demo

39. Using the STL vector, Array vs. Vector

40.  The typical C++ array has a very big problem  Declared and allocated with a constant size  i.e. cannot instantiate an array based on input  Dynamic Array  Concept in programming as a whole  Can change its size – grow, shrink (fast)  And knows its size  Can have elements added and removed (fast)  Has all functionality of a normal array

41.  The Standard Template Library has a template for a dynamic array  vector, where T can be any type  Can grow indefinitely (depends on RAM)  Initialized dynamically (E.g. based on input)  Declaring and initializing a vector #include //required header … vector numbers; numbers.push_back(42); //numbers is now {42} numbers.push_back(13); //numbers is now {42, 13} int consoleNumber; cin>>consoleNumber; numbers.push_back(consoleNumber)

42. Live Demo

43.  Accessing vector elements  Done the same way as with arrays, i.e. []  Vector size and can be obtained by calling size() vector numbers; numbers.push_back(42);numbers.push_back(13); cout<<numbers[1]; //prints 13 cout<<endl; numbers[1] = numbers[0]; cout<<numbers[1]; //prints 42 vector numbers; numbers.push_back(42);numbers.push_back(13); cout<<numbers.size(); //prints 2

44.  Vectors vs. Arrays  Vectors are dynamic, with fast resize  Vector parameters are copied (slow)  Except when parameter is a reference (fast)  Vectors allocate in dynamic memory (default)  Arrays are allocated on the stack – much smaller  Large arrays can cause a Stack overflow, vectors are safe in this manner  Vectors allocate twice the memory needed  Not all of the time, can be manually "fixed"

45. Live Demo

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47. 1. Write a program that allocates array of 20 integers and initializes each element by its index multiplied by 5. Print the obtained array on the console. 2. Write a program that reads two arrays from the console and compares them element by element. 3. Write a program that compares two char arrays lexicographically (letter by letter). 4. Write a program that finds the maximal sequence of equal elements in an array. Example: {2, 1, 1, 2, 3, 3, 2, 2, 2, 1}  {2, 2, 2}. 47

48. 5. Write a program that finds the maximal increasing sequence in an array. Example: {3, 2, 3, 4, 2, 2, 4}  {2, 3, 4}. 6. Write a program that reads two integer numbers N and K and an array of N elements from the console. Find in the array those K elements that have maximal sum. 7. Sorting an array means to arrange its elements in increasing order. Write a program to sort an array. Use the "selection sort" algorithm: Find the smallest element, move it at the first position, find the smallest from the rest, move it at the second position, etc. 48

49. 8. Write a program that finds the sequence of maximal sum in given array. Example: {2, 3, -6, -1, 2, -1, 6, 4, -8, 8}  {2, -1, 6, 4} Can you do it with only one loop (with single scan through the elements of the array)? 9. Write a program that finds the most frequent number in an array. Example: {4, 1, 1, 4, 2, 3, 4, 4, 1, 2, 4, 9, 3}  4 (5 times) 10. Write a program that finds in given array of integers a sequence of given sum S (if present). Example: {4, 3, 1, 4, 2, 5, 8}, S=11  {4, 2, 5} 49

50. 11. Write a program that finds the index of given element in a sorted array of integers by using the binary search algorithm (find it in Wikipedia). binary search binary search 12. Write a program that finds all prime numbers in the range [1...10 000 000]. Use the sieve of Eratosthenes algorithm (find it in Wikipedia). sieve of Eratosthenessieve of Eratosthenes 50