The goal is to:

Learn how functions work

Learn more about *if .. else if .. else* statement

Learn more about *while loop*

Learn about variables' scope

=================================================
**Preparations**

Before we begin this lab, please change your current directory to cs1440
or 1440 (whichever you have), and in that directory, create the lab4 directory
and change to that directory. You will do all your work in the lab4
directory. (% **cd cs1440** ... then %**mkdir lab4**, ....
then %**cd lab4**)

**Part 1. Predefined functions**

C++ comes with libraries of defined functions. You can use these
functions in your program by properly making a call to them. A good
example of these type of functions is the *sqrt* function that we
used to solve quadratic equation. For illustration, we look at Program
(4.1) in which we use a new predefined function called *pow*:

// **************************************************************

// Program (4.1)

// This following C++ code illustrates the predefined
functions;

// *pow(x,n), sqrt(x)*

#include<iostream.h>

#include<math.h>

#include<stdlib.h>

int main()

{

double x, z;

cout << "enter
a value for x, and I will compute \n";

cout << "Its square
root in two different ways, and I bet \n";

cout << "I get
it right either way ... \n";

cin >> x;

//Here is the first method

z = pow(x,0.5);

cout << "Square root
of " << x;

cout << " computed using
pow function is " << z << "\n";

//Here is the second
method

z = sqrt(x);

cout << "Square root
of " << x;

cout << " computed using
sqrt function is " << z << "\n";

return 0;

}

// ************************************************************

In the above program you included the math.h library:

#include <math.h>This library allows you to use the following functions:

Name | Description | Type of arguments | Type of Value Returned | Example | Value |

sqrt | square root | double | double | sqrt(4.0) | 2.0 |

pow | powers | double | double | pow(2.0,3.0) | 8.0 |

abs
fabs |
absolute value for integer absolute value for double |
int
double |
int
double |
abs(-7), abs(7)
fabs(-7.5) |
7
7.5 |

ceil | ceiling (round up) | double | double | ceil(3.2) | 4.0 |

floor | floor (round down) | double | double | floor(3.8) | 3.0 |

In addition to the above functions, you can also use, *sin(x), cos(x),
tan(x), asin(x), acos(x), atan(y,x), atan2(x), sinh(x), cosh(x), tanh(x),
exp(x), log(x),log10(x). *There might be some more functions that I
haven't listed.

Please note that type of the parameters and function itself is very important. Without proper type definition, your program will generate errors or wrong answers. Also note that all angles for trigonometric functions are expressed in radians.

In the above code, we used the *pow* and* sqrt *predefined
functions. As you can see in the above table, these two are of type
double and for that is reason we have defined x and z as double.

**Part 2. User Defined Functions**

In this part, we will define our own function. We define a function
to make our program more efficient, better readable, and reusable.
The description of a function has two parts, **function prototype
(function declaration) **and **function definition. **The following
code solve a physics problem. The problem is to find the distance
that a car has traveled after some *t* seconds. The motion is
a non uniform motion, i.e.; the car moves with an acceleration, *a. *As
you may remember, following is the equation for the distance for this type
of motion:
*x = (1/2) at ^{2} + (v0)t + x_{0}*

where, t is time in second, a is acceleration in (m/sec

// ********************************************************

// Program (4.2)

// This program computes the distance traveled
by an object in a non uniform

// motion based on:

//
x = (1/2)a.t^2 + (v0)t + x0

// WITHOUT USING FUNCTION

#include<iostream.h>

#include<math.h>

int main()

{

double t, x0,
v0,a, x;

cout << "Enter
time of travel, t, in (sec) \n";

cin >> t;

cout <<
"Enter acceleration, a, in (m/sec^2) \n";

cin >> a;

cout <<
"Enter initial distance, x0, in (m) \n";

cin >> x0;

cout <<
"Enter initial velocity, v0, in (m/s) \n";

cin >> v0;

x = (0.5) * a * pow(t,2.0) + (v0)*t + x0;

cout << "With
initial distance " << x0 << " (m) \n";

cout <<
"and initial velocity " << v0 << " (m/s) \n";

cout <<
"and acceleration " << a << " (m/s^2) \n";

cout <<
"The object will travel " << x;

cout <<
" (m) after " << t << " (sec) \n";

return 0;

}

// ****************************************************

Now let's write a function to compute the distance:

// ****************************************************

// Program (4.3)

// This program computes the distance traveled
by a car in a non uniform

// motion based on:
x = (1/2)a.t^2 + (v0)t + x0

// USING A FUNCTION

#include<iostream.h>

#include<math.h>

double Distance(double t, double a, double x0,
double v0)

// This function computes the distance traveled
in a non uniform motion.

// t is traveled time, a is the acceleration,
and x0 is the initial

// distance and v0 is the initial velocity

{

double
x;

x
= (0.5) * a * pow(t,2.0) + (v0)*t + x0;

return
x;

}

int main()

{

double t,
x0, v0, a, x;

cout << "Enter
time of travel, t, in (sec) \n";

cin >> t;

cout <<
"Enter acceleration, a, in (m/sec^2) \n";

cin >> a;

cout <<
"Enter initial distance, x0, in (m) \n";

cin >> x0;

cout <<
"Enter initial velocity, v0, in (m/s) \n";

cin >> v0;

x = Distance(t, a, x0,v0);

cout << "With
initial distance " << x0 << " (m), \n";

cout <<
"initail velocity of " << v0 << " (m/s), \n";

cout <<
"and acceleration " << a << " (m/s^2) \n";

cout <<
"The object will travel " << x;

cout <<
" (m) after " << t << " (sec) \n";

return 0;

}

// ***************************************************************************

In the second program, we used a function, *Distance*, to compute
the distance for us. Note that Distance is a function of type: double.
How do we know that? The function prototype (declaration)

**double** Distance(double t, double a, double
x0, double v0)

will tell us that. This function is taking t, a, x0, and v0 as its arguments. Notice that these variables are defined as double in the main program. Also, they must be received by the function as double, as you can see that is true in the (double t, double a, double x0, double v0) part of the function prototype.

IT IS CRITICALLY IMPORTANT THAT WE CORRECTLY ASSIGN THE FUNCTION TYPE AND IT ARGUMENTS.

As you can see in the main program knows what the Distance(t,a,x0,v0)
is when it gets to the line:

x = Distance(t, a, x0,v0);

How does it know it? We defined the whole function right before the main function. There is another was of telling the main function what to expect when it sees the distance function. Here is how:

// ******************************************************

// Program (4.4)

// This program computes the distance traveled
by a car in a non uniform

// motion based on:
x = (1/2)a.t^2 + (v0)t + x0

// USING A FUNCTION, Function is placed after
the main

#include<iostream.h>

#include<math.h>

// Tell the main what to to expect when it sees
the following function(s)

double Distance(double t, double a, double x0,
double v0);

int main()

{

double t,
x0, v0, a, x;

cout << "Enter
time of travel, t, in (sec) \n";

cin >> t;

cout <<
"Enter acceleration, a, in (m/sec^2) \n";

cin >> a;

cout <<
"Enter initial distance, x0, in (m) \n";

cin >> x0;

cout <<
"Enter initial velocity, v0, in (m/s) \n";

cin >> v0;

x = Distance(t, a, x0,v0);

cout << "With
initial distance " << x0 << " (m), \n";

cout <<
"initial velocity of " << v0 << " (m/s), \n";

cout <<
"and acceleration " << a << " (m/s^2) \n";

cout <<
"The object will travel " << x;

cout <<
"(m) after " << t << " (sec) \n";

return 0;

}

double Distance(double t, double a, double x0,
double v0)

// This function computes the distance traveled
in a non uniform motion.

// t is traveled time, a is the acceleration,
x0 is the initial

// distance, and v0 is the initial velocity

{

double
x;

x
= (0.5) * a * pow(t,2.0) + (v0)*t + x0;

return
x;

}

// ****************************************************************

**Part 3. All Pieces Together**

In the following program, we use while loop, if .. else if ... else,
and function.

// ****************************************************************

// Program (4.5)

// The following program will ask you to enter
5 numbers. Then, it computes the sum

// of those numbers and will compute the average
and also the square root of sum or

// display a message when it cant do it

#include<iostream.h>

#include<math.h>

int Sum(int sum_x, int x)

// This function adds x to the previous sum of
x values and return

// the result

{

return sum_x += x;

}

int main()

{

int x, i;

int N = 5;
// number of values to receive from the keyboard

int sum_x = 0;
// variable to hold the sum of all x values,

//Note: initialized to 0

double z;

i = 0;

while(i < N){

cout << "Input a integer \n";

cin >> x;

sum_x = Sum(sum_x, x);

cout << "The sum so far is " << sum_x << " \n";

i++;

}

if( (sum_x >= 0)
&& (sum_x <10) ){

cout << "Sum of input values is between 0 to 10 \n";

cout << "I will multiply it by 10";

cout << "and will compute the square root \n";

z = sqrt(double(sum_x));

cout << "The sum is " << sum_x;

cout << " and the square root is " << z << "\n";

}

else if(sum_x
>= 10){

cout << "Sum of input values is larger than or equal to 10 \n";

z = sqrt(double(sum_x));

cout << "The sum is " << sum_x;

cout << " and the square root is " << z << "\n";

}

else{

cout << "Sum is a negative value \n";

cout << "I can't compute a square root \n";

cout << "The sum is " << sum_x << "\n";

}

return 0;

}

// ******************************************************************

Modify Program (4.3) given above to solve the following physics problem:

x = (v^{2}-v_{0}^{2})/(2a)

This time we compute the distance traveled without using time.
Instead we use the initial velocity, v_{0}, and the final velocity,
v, and the acceleration, a, as the input. Please note that *a*
is in the denominator. take proper precaution to avoid dividing by
zero.

Call your program lab4.C and submit using the submit command:

~rt/bin/submit1440_10? lab4 lab4.C (**replace ? with
correct number for your section**)