1.

Write a program which prints information on the screen when variables a and b fulfills the condition \(a \in (-\infty,0) \cup (10,+\infty)\) and \(b \in (0,+\infty)\). Check if the following code is working correctly and apply modifications if necessary:

int a = -1;
int b = -1;
if (a < 0 || a > 10 && b > 0)
{
  printf("Put here a message\n");
}

2.

Write a program which generates random 2D points. The points should lay inside a rectangle shown on the figure. Keep on generating the points until there will be \(N\) points laying inside a circle placed inside the rectangle. Coordinates of the rectangle and the circle should be hardcoded (do not read them from the keyboard) and value of \(N\) should be read from the keyboard. Use function rand for generating the pseudorandom numbers. The function returns a pseudorandom integer in the range 0 to RAND_MAX. In order to get values in the range \((v_{min}, v_{max})\) use a scaling formula:

v = rand() * (v_max - v_min) / (double)RAND_MAX + v_min;

Pseudorandom numbers means that every time the generator is started it will produce the same series of numbers. To improve that behavior every time the generator is started it should initialized with different value. It can be done with function srand which is called once at the begining of a program:

srand(time(NULL));

Execute the program for \(N\) = 7.

3.

Modify the program above in such a way that the coordinates of the points will be written to a file. Coordinates of the points laying inside the circle and outside the circle should be written in different columns. Writing data to the file can be done in the following way:

FILE *f;                              // declaration of a pointer to a file
f = fopen("data.dat", "wt");          // open the file with a name "data.dat"
                                      // w - write
                                      // r - read
                                      // a - append
                                      // t - text file
                                      // b - binary file
if (f == NULL)
{
  printf("Error opening a file.\n");
  exit(-1);                           // exit the program
}

fprintf(f, "write to the file");      // here place the code to write your data
fclose(f);                            // close the file

Show the results using the point graph from Excel. Use different color for points laying inside the circle. Do this for \(N \in \{7,50,500 \}\).