the array-of-squares program to also print cubes.

int main()
{
 int i;
 int squares[11]; /* [0..10]; [0] ignored */
 int cubes[11];
 /* fill arrays: */
 for(i = 1; i <= 10; i = i + 1)
  {
  squares[i] = i * i;
  cubes[i] = i * i * i;
  }
 /* print table: */
 printf("n\tsquare\tcube\n");
 for(i = 1; i <= 10; i = i + 1)
  printf("%d\t%d\t%d\n", i, squares[i], cubes[i]);
 return 0;
}

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the dice-rolling program without arrays

int roll2, roll3, roll4, roll5, roll6, roll7, roll8, roll9,
  roll10, roll11, roll12;

 sum = d1 + d2; /* sum two die rolls */

 if(sum == 2)
  roll2 = roll2 + 1;
 else (sum == 3)
  roll3 = roll3 + 1;
 else (sum == 4)
  roll4 = roll4 + 1;
 else (sum == 5)
  roll5 = roll5 + 1;
 ...

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some improvements to the prime number printing program.

int main()
{
int i, j;
double sqrti;

printf("%d\n", 2);

for(i = 3; i <= 100; i = i + 2)
 {
 sqrti = sqrt(i);
 for(j = 2; j < i; j = j + 1)
  {
  if(i % j == 0)
   break;   /* not prime */
  if(j > sqrti)
   {   /* prime */
   printf("%d\n", i);
   break;
   }
  }
 }

return 0;
}

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Program to show a randrange function.

Here is a straightforward implementation of randrange2:

#include 

int randrange2(int m, int n)
{
 return rand() % (n - m + 1) + m;
}

Here is one using the suggested ``better way of reducing the range of the rand function'':

#include 

int randrange2(int m, int n)
{
 return rand() / (RAND_MAX / (n - m + 1) + 1) + m;
}

Notice that I've replaced N in the suggested general form with the expression n - m + 1.

You could implement the simpler randrange function either as

 int randrange(int n)
 {
  return rand() % n + 1;
 }

or, using the improvement,

 int randrange(int n)
 {
  return rand() / (RAND_MAX / n + 1) + 1;
 }

or, by writing it ``on top of'' the more general randrange2 you already wrote,

 int randrange(int n)
 {
  return randrange2(1, n);
 }

The various ``fudge factors'' in these expressions deserve some explanation. The first one is straightforward: The + 1 in (n - m + 1) simply gives us the number of numbers in the range mn, including m and n. (Leaving out the + 1 in this case is the classic example of a fencepost error, named after the old puzzle, ``How many pickets are there in a picket fence ten feet long, with the pickets one foot apart?'') to

The other +1 is a bit trickier. First let's consider the second implementation of randrange. We want to divide rand's output by some number so that the results will come out in the range 0 to n - 1. (Then we'll add in 1 to get numbers in the range 1 through n.) Left to its own devices, randRAND_MAX (where RAND_MAX is a constant defined for us in ). The division, remember, is going to be integer division, which will truncate. So numbers which would have come out in the range 0.0 to 0.99999... (if the division were exact) will all truncate to 0, numbers which would have come out in the range 1.0 to 1.99999... will all truncate to 1, 2.0 to 2.99999... will all truncate to 2, etc. If we were to divide rand's output by the quantity will return numbers in the range 0 to

 RAND_MAX / n

that is, if we were to write

 rand() / (RAND_MAX / n)

then when rand returned RAND_MAX, the division could yield exactly n, which is one too many. (This wouldn't happen too often--only when rand returned that one value, its maximum value--but it would be a bug, and a hard one to find, because it wouldn't show up very often.) So if we add one to the denominator, that is, divide by the quantity

 RAND_MAX / n + 1

then when rand returns RAND_MAX, the division will yield a number just shy of n, which will then be truncated to n - 1, which is just what we want. We add in 1, and we're done.

In the case of the more general randrange2, everything we've said applies, with n replaced by n - m + 1. Dividing by

 RAND_MAX / (n - m + 1)

would occasionally give us a number one too big (n + 1, after adding in m), so we divide by

 RAND_MAX / (n - m + 1) + 1

instead.

Finally, just two lines in the dice-rolling program would need to be changed to make use of the new function:

  d1 = randrange(6);
  d2 = randrange(6);

or

  d1 = randrange2(1, 6);
  d2 = randrange2(1, 6);

The answer to the extra-credit portion of the exercise is that under some compilers, the output of the rand function is not quite as random as you might wish. In particular, it's not uncommon for the rand funciton to produce alternately even and odd numbers, such that if you repeatedly compute rand % 2, you'll get the decidedly non-random sequence 0, 1, 0, 1, 0, 1, 0, 1... . It's for this reason that the slightly more elaborate range-reduction techniques involving the constant RAND_MAX are recommended.

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a function celsius() to convert degrees Fahrenheit to degrees Celsius. Use it to print a Fahrenheit-to-Centigrade table for -40 to 220 degrees Fahrenh

Here is the function:

double celsius(double f)
{
 return 5. / 9. * (f - 32);
}

Here is the driver program:

#include 

double celsius(double);

int main()
{
 double f;

 for(f = -40; f <= 220; f = f + 10)
  printf("%f\t%f\n", f, celsius(f));

 return 0;
}

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a function to compute the factorial of a number, and use it to print the factorials of the numbers 1-7.

Here is the function:

int factorial(int x)
{
 int i;
 int fact = 1;
 for(i = 2; i <= x; i = i + 1)
  fact = fact * i;
 return fact;
}

Here is a driver program:

#include 

int factorial(int);

int main()
{
 int i;

 for(i = 1; i <= 7; i = i + 1)
  printf("%d   %d\n", i, factorial(i));

 return 0;
}

The answer to the ``extra credit'' problem is that to portably compute factorials beyond factorial(7), it would be necessary to declare the factorial() function as returning long int (and to declare its local fact variable as long int as well, and to use %ld in the call to printf). 8! (``eight factorial'') is 40320, but remember, type int is only guaranteed to hold integers up to 32767.

(Some machines, but not all, have ints that can hold more than 32767, so computing larger factorials on those machines would happen to work, but not portably. Some textbooks would tell you to ``use long int if your machine has 16-bit ints,'' but why write code two different ways depending on what kind of machine you happen to be using today? I prefer to say, ``Use long int if you would like results greater than 32767.'')

Related Links :

printnchars function, and use it to rewrite the triangle-printing program.

void printnchars(int ch, int n)
{
 int i;

 for(i = 0; i < n; i++)
  printf("%c", ch);
}

Here is the rewritten triangle-printing program:

#include 

int main()
{
 int i;

 for(i = 1; i <= 10; i = i + 1)
  {
  printnchars('*', i);
  printf("\n");
  }

 return 0;
}

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Program to find square() function and use it to print the squares of the numbers 1-10.

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

Here is a loop and main program to call it:



int square(int);

int main()
{
int i;

for(i = 1; i <= 10; i = i + 1) printf("%d %d\n", i, square(i)); return 0; }

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Program to sum the elements of an array of int.

int sumnum(int a[], int n)

{

	int i;

	int sum = 0;

	for(i = 0; i < i =" i">

		sum = sum + a[i];

	return sum;

}

Here is a test program to call it:

#include 



int a[] = {1, 2, 3, 4, 5, 6};



int sumnum(int [], int);



int main()

{

	printf("%d\n", sumnum(a, 6));

	return 0;

}

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write the simple graphics program to print ``open'' boxes.

int printbox(int n)
{
 int i, j;
 for(j = 0; j < n; j = j + 1)
  printf("*");
 printf("\n");
 for(i = 0; i < n-2; i = i + 1)
  {
  printf("*");
  for(j = 0; j < n-2; j = j + 1)
   printf(" ");
  printf("*\n");
  }
 for(j = 0; j < n; j = j + 1)
  printf("*");
 printf("\n");
 return 0;
}

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Modify the array-of-squares program to also print cubes.

int main()
{
 int i;
 int squares[11]; /* [0..10]; [0] ignored */
 int cubes[11];
 /* fill arrays: */
 for(i = 1; i <= 10; i = i + 1)
  {
  squares[i] = i * i;
  cubes[i] = i * i * i;
  }
 /* print table: */
 printf("n\tsquare\tcube\n");
 for(i = 1; i <= 10; i = i + 1)
  printf("%d\t%d\t%d\n", i, squares[i], cubes[i]);
 return 0;
}

Related Links :

What is the difference between a defining instance and an external declaration?

A defining instance is a declaration of a variable or function that actually defines and allocates space for that variable or function. In the case of a variable, the defining instance may also supply an initial value, using an initializer in the declaration. In the case of a function, the defining instance supplies the body of the function.

An external declaration is a declaration which mentions the name and type of a variable or function which is defined elsewhere. An external declaration does not allocate space; it cannot supply the initial value of a variable; it does not need to supply the size of an array; it does not supply the body of a function. (In the case of functions, however, an external declaration may include argument type information; in this case it is an external prototype declaration.)

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a program to print the first 10 Fibonacci numbers.

#include 

int main()
{
 int i;
 int fibonacci = 1;
 int prevfib = 0;
 int tmp;

 for(i = 1; i <= 10; i = i + 1)   
{   
printf("%d   %d\n", i, fibonacci);   
tmp = fibonacci;   
fibonacci = fibonacci + prevfib;   
prevfib = tmp;   
}   
return 0;
} 

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a program to print the first 7 positive integers and their factorials.

#include "stdio.h"

int main()
{
 int i;
 int factorial = 1;

 for(i = 1; i <= 7; i = i + 1)
  {
  factorial = factorial * i;
  printf("%d   %d\n", i, factorial);
  }

 return 0;
}

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Print out the 8 points of the compass, based on the x and y components of the direction of travel.

Print out the 8 points of the compass, based on the x and y components of the direction of travel.

if(x > 0)
 {
 if(y > 0)
  printf("Northeast.\n");
 else if(y < 0)
  printf("Southeast.\n");
 else printf("East.\n");
 }
else if(x < 0)
 {
 if(y > 0)
  printf("Northwest.\n");
 else if(y < 0)
  printf("Southwest.\n");
 else printf("West.\n");
 }
else {
 if(y > 0)
  printf("North.\n");
 else if(y < 0)
  printf("South.\n");
 else printf("Nowhere.\n");
 }

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a program to compute the average of the ten numbers 1, 4, 9, ..., 81, 100.

int main()
{
int i;
float sum = 0;
int n = 0;

for(i = 1; i <= 10; i = i + 1)
 {
 sum = sum + i * i;
 n = n + 1;
 }

printf("the average is %f\n", sum / n);

return 0;
}

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What are the definitions of the ``Boolean'' values true and false in C?

False is always represented by a zero value. Any nonzero value is considered true. The built-in operators <, <=, >, >=, ==, !=, &&, ||, and ! always generate 0 for false and 1 for true.

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A program to print the numbers from 1 to 10 and their squares.

#include 

int main()
{
 int i;

 for(i = 1; i <= 10; i = i + 1)
  printf("%d  %d\n", i, i * i);

 return 0;
}

Exercise 4. Write a program to print a simple triangle of asterisks.

#include "stdio.h"

int main()
{
 int i, j;

 for(i = 1; i <= 10; i = i + 1)
  {
  for(j = 1; j <= i; j = j + 1)
   printf("*");
  printf("\n");
  }

 return 0;
}

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What is the function of the semicolon in a C statement?

It is the statement terminator.

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What is the difference between the constants 7, '7', and "7"?

The constant 7 is the integer 7 (the number you get when you add 3 and 4). The constant '7' is a character constant consisting of the character `7' (the key between `6' and `8' on the keyboard, which also has a `&' on it on mine). The constant "7" is a string constant consisting of one character, the character `7'.

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What is the difference between the constants 7, '7', and "7"?

The constant 7 is the integer 7 (the number you get when you add 3 and 4). The constant '7' is a character constant consisting of the character `7' (the key between `6' and `8' on the keyboard, which also has a `&' on it on mine). The constant "7" is a string constant consisting of one character, the character `7'.

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Why is the line #include "stdio.h" at the top of a C source file for?

In the case of our first few programs, it lets the compiler know some important information about the library function, printf. It also lets the compiler know similar information about other functions in the ``Standard I/O library,'' some of which we'll be learning about later. (It also provides a few I/O-related definitions which we'll be using later.) We'll learn more about the #include directive when we cover the C Preprocessor in a few weeks.

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a short program to read two lines of text, and concatenate them using strcat.

#include "stdio.h"
#include "string.h" 
/* for strcpy and strcat */

#define MAXLINE 100

extern int getline(char [], int);

int main()
{
 char string1[MAXLINE], string2[MAXLINE];
 int len1, len2;
 char newstring[MAXLINE*2];

 printf("enter first string:\n");
 len1 = getline(string1, 100);
 printf("enter second string:\n");
 len2 = getline(string2, 100);

 if(len1 == EOF || len2 == EOF)
  exit(1);

 strcpy(newstring, string1);
 strcat(newstring, string2);

 printf("%s\n", newstring);

 return 0;
}

Exercise 5. Write a function to find a substring in a larger string and replace it with a different substring.

Here is one way. (Since the function doesn't return anything, I've defined it with a return type of void.)

void replace(char string[], char from[], char to[])
{
 int start, i1, i2;
 for(start = 0; string[start] != '\0'; start++)
  {
  i1 = 0;
  i2 = start;
  while(from[i1] != '\0')
   {
   if(from[i1] != string[i2])
    break;
   i1++;
   i2++;
   }
  if(from[i1] == '\0')
   {
   for(i1 = 0; to[i1] != '\0'; i1++)
    string[start++] = to[i1];
   return;
   }
  }
}

This code is very similar to the mystrstr function in the notes, chapter 10, section 10.4, p. 8. (Since strstr's job is to find one string within another, it's a natural for the first half of replace.)

Extra credit: Think about what replace() should do if the from string appears multiple times in the input string.

Our first implementation replaced only the first occurrence (if any) of the from string. It happens, though, that it's trivial to rewrite our first version to make it replace all occurrences--just omit the return after the first string has been replaced:

void replace(char string[], char from[], char to[])
{
 int start, i1, i2;
 for(start = 0; string[start] != '\0'; start++)
  {
  i1 = 0;
  i2 = start;
  while(from[i1] != '\0')
   {
   if(from[i1] != string[i2])
    break;
   i1++;
   i2++;
   }
  if(from[i1] == '\0')
   {
   for(i1 = 0; to[i1] != '\0'; i1++)
    string[start++] = to[i1];
   }
  }
}

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