(C++) Arrays. Basics

Error

Referencing an array element

Much of the usefulness of arrays comes from the fact that its elements can be accessed individually.
The way to do this is to use an index to number the elements.

REMEMBER!
NUMBERING OF ARRAYS IN C STARTS FROM ZERO.
(This is mandatory — you must start from scratch. This is especially important to remember)

Examples of accessing array A:

x = (A[3] + 5)*A[1]; // read the values ​​of A[3] and A[1]
A[0] = x + 6; // write new value to A[0]

Let's analyze the program for working with array elements.

#include <iostream>
using namespace std;
main()
 {
   int i=1, A[5];
   A[0] = 23; //to each of the 5 elements of the array (indices from 0 to 4)
   A[1] = 12; //write a specific value
   A[2] = 7;
   A[3] = 43;
   A[4] = 51;
   A[2] = A[i] + 2*A[i-1] + A[2*i]; //change the value of the element with index 2 to the result of the expression
                                    //because i=1, then substituting the value of the variable i into the expression we get
                                    //next expression A[2] = A[i] + 2*A[0] + A[2];
   cout << A[2]+A[4];
}

As a result of the execution of this program, the value of the array element with index 2 equal to 116 will appear on the screen. As you can see from the example, we can access any element of the array. And also calculate the required number of the element using various formulas (for example, as in the program A[i-1] or A[2*i], in these cases, the indexes of the elements will be calculated and depend on the value of i.)

Let's look at an example program

#include<iostream>
using namespace std;
main()
{
 const int N = 5;
  int A[N];
  x = 1;
  cout << A[x-3]; //reference to element A[-2]
  A[x+4]=A[x]+A[2*(x+1)]; //after substituting x into expressions and calculations, we get the following line: A[5] = A[1]+A[4];
  ...
}

Because the array is declared with 5 elements, which means the elements will be numbered from 0 to 4. We see that the program accesses non-existent elements: A[-2] and A[5]
It turns out that the program went beyond the bounds of the array

Array out of bounds is accessing an element with an index that does not exist in the array.

In such cases, programs usually crash with run-time error

Let's try to work with array elements on our own. Complete the task
 

Iterating over array elements

When working with arrays, you usually have to work with all the elements of the array at once.
 
To do this, most often a loop with a variable is used, which changes from 0 to N-1 (N the number of array elements). ... const int N = 10; int A[N]; for (i = 0; i < N; i++) { // action on element A[i] } ... In the specified loop, the variable i will take on the values ​​0, 1, 2, ..., N-1.  That is, at each step of the loop, we access a specific array element with index i.
Thus, it is enough to write down what needs to be done with one element of the A[i] array and place these actions inside such a loop.
 

Task

Fill the array with the first N natural numbers. Those. at the end of the program, the elements of the array should become equal: A[0] = 1;  A[1] = 2; A[2] = 3; ... A[N-1] = N;
It is easy to see the pattern: the value of an array element must be greater by 1 than the index of the element.
The cycle will look like this: for (i=0; i<N; i++) { A[i] = i+1; }