Algorithm 1
//We will adopt the standard algorithm writing
//conventions as per Donald Knuth's book, The Art of Computer
Programming
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Answer to 1)
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algorithm find_area
input:
shaded_box_length, shaded_box_width,
white_box_length, white_box_width
Integers shaded_box_x, shaded_box_y,
white_box_x, white_box_y: shaded_box_x is the number of shaded
boxes in horizontal direction, white_box_y is the number of white
boxes in verticial direction. Other definitions follow
similarly.
output:
area: the area of shaded boxes in total
number_of_shaded_boxes <- shaded_box_x * shaded_box_y
number_of_white_boxes <- white_box_x * white_box_y
area_of_shaded_box <- shaded_box_length * shaded_box_width
area_of_white_box <- white_box_length * white_box_width
area <- (number_of_shaded_boxes * area_of_shaded_box) -
(number_of_white_boxes * area_of_white_box)
if area < 0
print 'Area cannot be negative'
else
print(area)
Explanation:
The algorithm simply calculates the area of shaded region by
subtracting the total area of bigger box from the white boxes. The
boundary conditions for values input to the program are not checked
based on the assumption that a input function is doing the
constraint checking. It should check for positive real values for
dimensions entered and the dimensions of white box should not
exceed the outer shaded box dimensions.
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Answer to 2)
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algorithm calculate_interest
input:
interest_rate: the rate of interest
principal: original loan amount
payment: payment made in this year
amount: outstanding amount before the start of
the year
year: current year number in which payments were
made. eg. 2017 or 2018.
year_of_loan: year in which loan was taken
output:
interest: total interest on the loan in this
year
balance: outstanding amount at the end of this
year
balance <- amount - payment
interest <- interest_rate*balance/100
amount <- balance + interest //amount for next
year
Explanation:
The algorithm takes in the the remaining balance prior to this year
and then calculates the balance that will remain at the end of this
year.
Interest is calculated using the formula I = PRT/100 where P is the
principal amount, R is rate of interest and T is time. Here, T is 1
since we are calculating for each year.
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Answer to 3)
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algorithm medical_payments
input:
total_charges: total charges overdue
prescription_charge: charge per
prescription
prescription_quantitiy: number of
prescriptions
output:
customer_pay: amount paid by the patient
insurance_company_pay: amount paid by the
insurance company
assumption:
presciption charges are excluded from total
charges
variables:
customer_deductible_amount: It is set to $1000
amount that each customer pays in the beginning.
assumption: total charges is greater than the deductible
amount
co_pay: fixed amount to be paid by the
customer
prescription_pay: total prescription
charge
prescription_co_pay: co pay for each
prescription by customer
prescription_insurance_pay: amount paid by
insurance company for the presciption
if customer_deductible_amount > total_charges
customer_deductible_amount <-
customer_deductible_amount - total charges
co_pay <- total_charges
insurance_company_pay <- 0
else
co_pay <- 0.2 * (total_charges -
customer_deductible_amount)
insurance_company_pay <- total_charges -
co_pay
prescription_pay <- prescription_quantity *
prescription_charge
prescription_co_pay <- prescription_quantity * 40
prescription_insurance_pay <- prescription_pay -
prescription_co_pay
customer_pay <- co_pay + prescription_co_pay
insurance_company_pay <- insurance_company_pay +
prescription_insurance_pay
Explanation:
The algorithm checks if the total charge is less than the
deductible amount that customer has. If it is true than the amount
is deducted from the deductible and insurance company doesn't pay
anything other than the prescription fees. Otherwise, the 20% of
the amount is paid by the customer and rest by insurance company.
For presciptions, $40 is paid per prescription by the customer and
rest by the insurance company. Prescription charges are not
included in the deductible and insurance company pays for them.
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