## Implementation of algorithm for the calculating of prefix expressions.

To calculate a prefix expression, we either convert a number from ASCII to decimal (in the loop ‘while’ at the end of the program) or implement the operation indicated by the first character of the expressions to the two terms, with a recursive calculation. This function is recursive, but it uses a global array containing the expression and an index number for the current character of the expression. The index number goes beyond each sub-expression calculated.

## Implementation of an application for the sorting of an array of strings.

The following program demonstrates a significant processing operation on arrays of strings. More precisely, we present the re-sorting of a set of strings in order to classify them. So, we read the strings and place them in a temporary storage area (buffer) large enough to be able to store all, keeping in an array a pointer to each string. Then we re-sort the pointers (only pointers and not strings to increase the performance) to place the pointer to the “smallest” string at the first position of the array, the pointer to the next “largest” string at the second position of the array, and so on.

## Implementation of graph representation with an adjacency matrix.

The following program reads a set of edges that define an undirected graph and creates a representation of this graph with an adjacency matrix, giving a[i][j] and a[j][i] the value of 1 if there is an edge from i to j or from j to i in the graph, or the value of 0 if it does not exist. Also, we assume that the number of vertices V is a constant known at compilation time. Otherwise, there should be dynamic memory allocation for the array that represents the adjacency matrix.

## Implementation of string search algorithm.

The following program finds all the occurrences of a word in a text string. We set the text string as an array of characters of fixed size (although we could, instead, use the operator ‘new’) and read it from the standard input using the function cin.get(). The memory allocation for the word entered in the command line and passed on as argument is done by the system before this program is called and we find the pointer to the string in argv[1]. For every starting position i in the array a, tries to associate the substring starting from this position with the p, checking character by character for equality. Each time we reach the end of p successfully, we display the starting position (i) of the word in the text on the screen.

## Implementation of closest point calculation.

This program demonstrates the use of an array and is representative of the usual situation in which we store data in one array to process them later. It counts the number of pairs of N randomly generated points of the unit square, which can be connected to a line segment of length less than ‘d’, using the point data type. Because the execution time of this program is O(n^{2}), it can’t be used for large N.

## Implementation of algorithm for finding primes with the sieve of Eratosthenes.

The aim of this program is to assign to a[i] the value 1 if i is a prime number and the value 0 if not. Initially, all elements of the array take the value 1 to indicate that there are no numbers which are known not to be prime. Then all elements of the array corresponding to indexes that are known not to be primes (multiples of known primes) take the value 0. If a[i] has the value 1 even after all multiples of smaller primes have taken the value 0, we know that i is a prime number.