perfect

Write a program, perfect.c, that

1. takes one integer parameter p
2. checks whether p is perfect by adding up all the (positive) numbers less than p which divide it exactly
3. returns 1 if p is perfect and 0 otherwise

Create perfect.c by adding a main() function that computes all the perfect numbers less than 64,000. Compile and test your program.

fun1

Create a text file called fun1.c that contains the following C program:

#include <stdio.h>

int sqr (int x)
{
    return x*x;
}

int main()
{
    int k;
    for (k=0; k<10; k++)
        printf("sqr(%i) = %3i\n",k, sqr(k));
    return 0;
}

1. The program uses a function to calculate the square of an (integer) number. When the program is run it prints out a table of squares of the numbers from zero to nine. Save the file and then compile and run the program.
2. Modify the program so that it prints out the squares of the numbers from zero to 99.

fun2

In a similar way to the program fun1 write a program, fun2.c, that prints a table of the numbers from zero to 31 along with their cubes. You should write and use a function called cube that calculates the cubes of integer numbers.

fun3

In a similar way to the program fun1 write a program, fun3.c, that prints a table of the numbers starting at zero along with their squares, cubes, and fourth powers. The table will therefore begin like this:

0       0       0       0
1       1       1       1
2       4       8      16
3       9      27      81

To compute the fourth-powers you should use the sqr function (twice) - do not write a new fourth-power function. You should extend the table until the results become unreliable. (The previous question has already demonstrated how this can happen.)

gcd

The greatest common divisor of two integer numbers is the largest integer that can be divided exactly into both of them. Note, the answer may be one of the numbers themselves if the other is a multiple of it. For example, the greatest common divisor of 32 and 12 is 4 whereas the greatest common divisor of 36 and 12 is 12 itself. An algorithm for calculating the greatest common divisor of two numbers (x and y) is given here:

Repeat
      While x is less than y,
            subtract x from y
      While y is less than x,
            subtract y from x
Until x is equal to y
Return x  (or y, since they are the same)

calc

Create a text file called calc.c that contains the following C program:

#include <stdio.h>

float add (float x, float y)
{
    return x + y;
}

int main()
{
    float a, b, r;
    char op;
    do {
       printf("number  op  number?  ");
       scanf(" %f %c %f", &a, &op, &b);
       switch (op)
       {
           case '+' : r = add(a,b);
                      break;
           case 'q' : break;
           default  : op='?';
       }
       if (op=='?')
          printf("Unknown operator\n");
       else if (op=='q')
          printf("Bye\n");
       else
          printf("%f %c %f = %f\n", a, op, b, r);
    }
    while (op != 'q');
    
    return 0;
}

1. The program behaves like a calculator asking the user to type in binary expressions (like 2.5 + 3.7) and printing out the results. If the user enters 'q' for the operator (e.g. 0 q 0) then this is taken as a signal to stop the program.
2. Add a new function to the program that multiplies its two arguments together and returns their product. Then modify the switch statement so that the operator '*' causes this new product function to be called. Test the program by using a mixture of '+' and '*' calculations.
3. Add operators for subtraction ('-') and division ('/') and test your program again.
4. We introduce some special operators. Write functions to implement each of these (adding one at a time and testing after each new operator is incorporated into your calculator).

   Symbol	Description	Example
   m	Minimum	2.3 m 1.7 = 1.7
   M	Maximum	2.3 M 1.7 = 2.3