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Part 1: Geometry and rain!

This problem is a warm up of the use of functions. You will be asked to write a few simple functions.

Did you know that Panama Canal runs on rain water? Every time a ship passes through a lock,

the canal is filled from a lake in the middle of the Panama canal, and then this water is released

to the ocean and lost forever. Basically, this man-made lake is filled with rain water. Yes, it rains

a lot in Panama. We will compute the change in the depth of the lake during the dry season, i.e.

the three months in the year when it rains a bit less.

We will make some simplifying assumptions: locks are rectangular prisms and the lake is a cylinder.

We will ask to the user the dimensions of the rectangular prism (length, width, height) and

the radius of the cylinder. You will then compute and output the following:

• Total amount of water needed to fill the rectangular prism 70 times a day for 3 months,

assuming a month is 30 days (basically, about 35 ships pass through two locks every day.)

Remember the volume of a rectangular prism is given by length * width * height. Write

a function volume_prism(length, width, height) to compute this and use it in your computation.

• Then, you will find the height of a cylinder with the given radius needed to hold this much

water. Remember, the volume of a cylinder given by pi* radius**2 * height.

Write a function find_length(radius, volume) that finds and returns the depth of a cylinder needed to hold the computed amount of water. You must use the math module for

the value of pi.

Here is an expected output of your program (how it will look on Wing IDE):

Length of rectangular prism (m) ==> 12.5

12.5

Width of rectangular prism (m) ==> 15.8

15.8

Height of rectangular prism (m) ==> 18.1

18.1

Water needed for (12.5m,15.8m,18.1m) locks is 22520925.0m^3.

Radius of cylinder (m) ==> 1150

1150

Lake with radius 1150.0m will loose 5.4m depth in three months.

Remember, using formatted strings will be very useful in this homework.

When you have tested your code, please submit it as hw2_part1.py.

Part 2: Find the hidden message!

Write a program that asks the user for a sentence written in a cipher using (raw_input). You need

to decrypt and print the resulting sentence. Then, read a second sentence in plain English using

(raw_input) and convert it to a cipher by encrypting it. For both sentences, you must also print

the total difference in length between the cipher and clear text versions. The difference should

always be printed as a positive number.

Here is an example run of the program (what you will see on Wing):

Enter cipher text ==> wheie stzzt saz azritzztyyys

wheie stzzt saz azritzztyyys

Deciphered as ==> why so serious

Difference in length ==> 14

Enter regular text ==> back off man I am a scientist

back off man I am a scientist

Encrypted as ==> back tzztff muq Irxrmrxr sciaz azntist

Difference in length ==> 9

The encryption rules are based on a pretty simple set of string replacements, they should be applied

in this order exactly:

‘ a’ => ‘rxr’ replace any a after a space with rxr.

‘he’ => ‘vw’ replace all occurrences of string he with vw

‘e’ => ‘az az’ replace any remaining e with az az

‘y’ => ‘eie’ replace all occurrences of string y with eie

‘u’ => ‘yyy’ replace all occurrences of string u with yyy

‘an’ => ‘uq’ replace all occurrences of string an with uq

‘th’ => ‘aige’ replace all occurrences of string th with aige

‘o’ => ‘tzzt’ replace all occurrences of string o with tzzt

For example cipher for methane is maz azaigeuqaz az. Here is how we get this:

>>> ‘methane’.replace(‘e’,’az az’)

‘maz azthanaz az’

>>> ‘maz azthanaz az’.replace(‘an’,’uq’)

‘maz azthuqaz az’

>>> ‘maz azthuqaz az’.replace(‘th’,’aige’)

‘maz azaigeuqaz az’

Of course, decrypting will involve using the rules in reverse order.

Your program must use two functions:

• Write one function encrypt(word) that takes as an argument a string in plain English, and

returns a ciphered version of it as a string.

• Write a second function decrypt(word) that does the reverse: takes a string in cipher and

returns the plain English version of it.

Both functions will be very similar in structure, but they will use the string replacement rules in

different order. You can now test whether your functions are correct by first encrypting a string,

and then decrypting. The result should be identical to the original string (assuming the replacement

rules are not ambiguous).

Use these functions to implement the above program. When you have tested your code, please

submit it as hw2_part2.py.

Part 3: A simple trick (numerical functions and one if statement)!

This is a simple parlor trick attributed to Albert Einstein, but it probably dates to an earlier date!

The trick: First, write the number 1089 on a piece of paper, fold it, and put it away. Next, ask

your friend to write down any three-digit number, emphasizing that the first and last digits must

differ by at least two. Don’t watch your friend doing the arithmetic. After your friend has written

down the three-digit number, ask him to reverse it, then subtract the smaller from the larger.

Example: 321 – 123 = 198.

Tell your friend to reverse the new number.

Example: 198 becomes 891.

Next ask your friend to add the new number and its reverse together.

Example: 198 + 891 = 1089.

If all goes as planned, your friend will be amazed. The number you wrote down at the start –1089–

will always be the same as the end result of this mathematical trick.

As we have just learnt how to do if statements, we will do a simple version of this program. Your

program must contain one function called reverse that works as follows:

>>> reverse(123)

321

>>> reverse(264)

462

Make sure you write this function first and test it with many integer inputs.

Then, write a program that produces the output given below by reading an input value from the

user and then carrying out the computation outlined above by calling the above function in two

places where you reverse the number. Show the steps of the computation. Then, add a simple if

statement at the end of your program: if the final result is 1089, you should print “You see, I told

you”, otherwise, you should print “Are you sure your input is valid?”

Your output must match the following (this is how it will look on Wing):

Enter a value ==> 294

294

Here is the computation:

492 – 294 = 198

198 + 891 = 1089

You see, I told you.

Here is another run:

Enter a value ==> 242

242

Here is the computation:

242 – 242 = 0

0 + 0 = 0

Are you sure your input is valid?

When you have tested your code, please submit it as hw2_part3.py.

Finished and still want extra challenges to sharpen your programming skills? These

are not extra credit but for you to do additional practice.

This homework has a single if statement, but you should practice with if statements for the upcoming exam. Here are some ideas.

• Write a program to take an input, encrypt first and then decrypt, then check whether the

result is the same. Print “same” if they are the same and “different” otherwise.

• Try to do part 3 in such a way that if the person enters a number that is not valid (i.e. first

and third digit do not differ by two), you immediately print a statement informing the user

and do not compute anything. Otherwise, you carry out the above computation.

Other ideas are too complex for our current level. This should be sufficient!

Note that there are many other cases in which the total after this computation seems to be 1098.

Later in semester, we can write a program to test every possible number. Not yet.

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