1.1 Exercises

Exercise 1

1. Design an algorithm in flowchart to find the smallest number in a group of three real numbers.

2. Design an algorithm in flowchart to solve the quadratic equation: ax^2 + bx + c =0 with the inputs a, b, and c.

3. A set of linear equations:

aX + bY = c

dX + eY = f

can be solved using Cramer’s rule as:

X = (ce – bf)/(ae – bd)

Y = (af – cd)/(ae – bd)

Design an algorithm in flowchart to read in a, b, c, d, e and f and then solve for X and Y.

4. Design an algorithm in flowchart to read in a group of N numbers and compute the average of them, where N is also an input.

5. Design an algorithm in flowchart to read in a group of N numbers and compute the sum of them, where N is also an input.

Exercise 2

1. Read the following C++ program for understanding. Add some suitable declarations to complete the program and run it.

#<include<iostream.h>

void main(){

...

units = 5;

price = 12.5;

idnumber = 12583;

cost = price*units;

cout<<idnumber<<“ “<<units<<“ “<<price<<“ “<<cost<<endl;

tax = cost*0.06;

total = cost + tax;

cout<<tax<<“ “<<total<<endl;

}

2. Write and run a program to print your first name on the first line, your middle name on the second line and your last name on the third line using only cout statement.

3. Write and run a program that performs the following steps:

• Assigning value to the radius r.
• Calculating the circumference using the formula: C = 2*pi*r.
• Displaying the circumference.

4. Given an initial deposit of money, denoted as P, in a bank that pays interest annually, the amount of money at a time N years later is given by the formula:

Amount = P*(1 + R)^N

where R is the interest rate as a decimal number (e.g., 6.5% is 0.065). Using this formula, design, write and run a program that determines the amount of money that will be available in 4 years if $10.000 is deposited in a bank that pays 7% interest annually.

5. Write and run a program that performs the following steps:

• Assigning value to a Fahrenheit temperature f.
• Calculating the equivalent Celsius temperature C using the formula:

C = (5/9)(f –32).

• Displaying the Celsius temperature C.

Exercise 3

1. Write and run a program that performs the following steps:

• Reading the radius r from the keyboard.
• Calculating the circumference using the formula: C = 2*pi*r.
• Displaying the circumference C.

2. Write and run a program that performs the following steps:

• Reading a Fahrenheit temperature f from the keyboard.
• Calculating the equivalent Celsius temperature C using the formula:

C = (5/9)(f –32).

• Displaying the Celsius temperature C.

3. Write and run a program that reads two integers through the keyboard and performs simple arithmetic operations (i.e., addition, subtraction, multiplication and division) and displays the results.

4. Write and run a program that reads a floating-point number through the keyboard and performs its square root and displays the result with 4 digits of precision to the right of the decimal point.

5. Given an initial deposit of money, denoted as P, in a bank that pays interest annually, the amount of money at a time N years later is given by the formula: