Iterations Exercises

Warm Up Question

Determine the output of the code below:

print(list(range(5)))
print(list(range(3,8)))
print(list(range(5, 43, 10)))

Warm Up Question

Write a program that displays the following list of numbers using a range() function. \( [3, 7, 11, 15, 19]\)

Warm Up Question

Determine the output of the code below:

for i in range(3):
    print(2*i)

Warm Up Question

Determine the output of the code below:

n = 5 
while n <= 8:
    print(2*n)
    n += 1

Warm Up Question

Write a program that calculates the sum of the first 50 positive integers.

Warm Up Question

Determine the output of the code below:

n = 5

while True:
    print(n)
    n += 2
    if n > 9:
        break

Question-1

Print the letters with negative even indexes (-2, -4, …) from the given text using:

• a for loop

• a while loop

• slicing with a step. (use join method())

text = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'  

Print the letters in a single line and comma separated.

Sample Output:
text : abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ
for loop : Y,W,U,S,Q,O,M,K,I,G,E,C,A,y,w,u,s,q,o,m,k,i,g,e,c,a
while loop: Y,W,U,S,Q,O,M,K,I,G,E,C,A,y,w,u,s,q,o,m,k,i,g,e,c,a
slicing : Y,W,U,S,Q,O,M,K,I,G,E,C,A,y,w,u,s,q,o,m,k,i,g,e,c,a

Question-2

Find the sum of the first \(100\) terms of the following sequence:

\(\displaystyle \frac{1}{1^3+1^2}, \frac{1}{2^3+2^2}, \frac{1}{3^3+3^2}, \frac{1}{4^3+4^2}, ...\)

• Use a for loop.

• Use a while loop.

Question-3

Ask the user to input a name and then insert a random punctuation mark between each character of the name.

• Ensure that the output does not have a punctuation mark at the end.

Sample Output
Please enter a name : ashley
Randomly generated name: a&s#h”l#e”y

Question-4

Ask the user to input a number and print the consecutive pairs of digits within this number.

• Example: The consecutive digits in 156319672 are 56 and 67.

Sample Output
Please enter a number: 156319672
Consecutive pairs are: 56,67

Question-5: Secret Number Game

This is another version of the Guess the Secret Number Game.

• The user selects a secret 3-digit number.

• The computer randomly selects a 3-digit number to find the secret number.

• You can use random.randint or numpy.randint.

• Count the number of attempts by the computer.

• If the computer can find the secret number in fewer than 100 attempts, it wins; otherwise, it loses the game.

• After each attempt, print the computer’s guess.

• After each attempt, provide a hint to the computer whether the secret number is larger or smaller than the guess. The computer makes the next guess based on the hint

Sample Output
Choose a 3 digit secret number: 123
Try Number: 0 Guess: 654 is LARGE. Try Again!
Try Number: 1 Guess: 638 is LARGE. Try Again!
Try Number: 2 Guess: 467 is LARGE. Try Again!
COMPUTER WINS!
Number of tries: 3

Question-6: Scatter Plot

Use a for loop to randomly select 100 points on a coordinate plane and plot them individually as a scatter plot. For each point:

• The x and y coordinates are randomly chosen between 0 and 1.

• The size of the point is a random number between 10 and 500.

• The color is chosen from the characters of he following string: color_str = ‘rgbky’.

  • ‘r’ represents red, ‘g’ represents green,’b’ represents blue, ‘k’ represents black,’y’ represents yellow

• The transparancey is represented by a random number between 0 and 1.

Refer to the scatterplot section in Appendix: Visualization for implementation guidance.

Question-7: Empirical Probability

Flip a coin 100 times and count the number of heads.

• Use the string ‘TH’ to randomly select either ‘T’ (tail) or ‘H’ (head).

  • Randomly choose 0 or 1 as the index of the character that will be selected randomly.

Question-8: Rotating Stick

Use a for loop and the sleep method from the time library to sequentially display the rotation of ‘’, ‘–’, and ‘/’ characters 20 times.

• Add a waiting time between each character to simulate the rotation of a stick.

• Ensure that after printing each character, it is deleted before the next one is printed to maintain the rotating effect.

Question-9: Counter

Use a for loop and the sleep method from the time library to display a counter counting from 0 to 999.

• Ensure that one-digit numbers have two zeros added to the left, and two-digit numbers have one zero added to the left.

• After printing each number, delete it before the next one is printed to maintain the rotating effect.

• Numbers: 001, 002,…,010,011,…,999

Business Applications

Question: Max of Revenue

Revenue (R) is the product of the number (n) of items sold and the price (p) of the item.

• \(R = p\cdot n\)

The number of item sold is given by the following equation: \(n = -1.5p+30\)

Write a program which finds the \(p\) which maximize the revenue for \(0\le p \le 20\)

• Plot the graph of revenue for \(0\le p \le 20\)

Question: Profit

Profit (P) is the difference between Revenue and Cost

• \(Profit = Revenue - Cost\)

The monthly fixed cost of a cable factory is 1500 dollars. Each cable costs 13 dollars and sells for 25 dollars.

• Find the profit of producing 400 cables.

• For what number of cables produced profit is zero.

  • Hint: Calculate the profit for \(n\) between 1 and 400.

Question: Linear Depreciation

The value of a new machine is \(100,000\) dollars and its values is depreciated by \(7500\) dollars per year. After how many years the value of the machine will be 2,500 dollars.

• Hint: Calculate the value for years between 1 and 100.

Question: Equilibrium Point

An equilibrium point is where the demand and supply curves intersect.

For the given demand and the supply functions find the equilibrium point.

Demand: \(p(q) = -0.03q + 1000\)

Supply: \(p(q) = 0.02q + 400\)

• Hint: Calculate the demand and supply for \(q\) between 1 and 20,000.

Question: Linear Programming

Linear programming involves finding the highest or lowest possible outcome of a linear function, while satisfying specific constraints.

The store sells three items labeled (a, b, c) priced at 2, 3, and 4 dollars respectively. The following conditions are known:

• The store can sell up to 100 units of each item.

• The combined sales of items b and c exceed 90 units.

• The total sales of items a and b do not surpass 50 units.

• The sales of items a and c are more than 80 units.

What is the highest revenue achievable, and at what quantities of items is this maximum revenue attained?

Question: Home Mortgage

Amortization is paying off a loan by making equal payments.

The present value of an amortized loan is given by the following formula: \(\displaystyle P = R \left( \frac{1-(1+\frac{r}{m})^{-mt}}{\frac{r}{m}} \right)\) where,

• \(P\): Present value

• \(R\): regular payment

• \(r\): annual interest rate

• \(m\): number of payments in a year

• \(t\): number of years

If you take out an 449,000 dollars loan to buy a house with an annual interest rate of 2.75%, to be paid off over 30 years, what is the monthly payment?

• Sketch the graph of monthly payments for annual interest rates of 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, and 10%.

Hint:

• Use the variables \(P, r, m, t\) for the given values.

• Calculate the value of the variable \(R\).

Question: Amortization Schedule-1

If you take out a 449,000 dollars loan to buy a house with an annual interest rate of 2.75%, to be paid off over 30 years with a monthly payment of $1,833, construct an amortization schedule for the first 5 payments.

For each month, a fixed monthly payment is deducted from the balance. Additionally, simple interest is added to the loan based on that month’s remaining balance.

Hint:

• Use the variables \(P, r, m, t, R\) for the given values.

• Calculate the monthly simple interest for each monthly balance.

Question: Amortization Schedule-2

If you take out a 449,000 dollars loan to buy a house with an annual interest rate of 2.75%, to be paid off over 30 years with a monthly payment of 1,833 dollars, construct an amortization schedule for the last 5 payments.

For each month, a fixed monthly payment is deducted from the balance. Additionally, simple interest is added to the loan based on that month’s remaining balance.