What this session is for

• Control the shape of your output with escape characters
• Get fluent with ord() / chr() and bin() / oct() / hex()
• Measure for yourself which digit floats start lying at, rather than just hearing that “floats are inexact”
• Internalize the type rules for /, //, % and **

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Part A — required

2-1 Draw a bear with escape characters

Use print() to produce the bear below. It contains backslashes and quotes, and every one of them has to be escaped correctly:

        (()__(()
        /       \
       ( /    \  \
        \ o o    /
        (_()_)__/ \
       / _,==.____ \
      (   |--|      )
      /\_.|__|'-.__/\_
     / (        /     \
     \  \      (      /
      )  '._____)    /
   (((____.--(((____/

Escape it right and you get a friendly bear. Escape it wrong and you get a deformed one.

2-2 Change of case (marked by the platform)

Convert an uppercase letter to lowercase. Use only ord() and chr() — .lower() is not allowed. Anything that is not an uppercase letter comes back unchanged.

to_lower('H')  →  'h'
to_lower('a')  →  'a'
to_lower('7')  →  '7'

2-3 The life of one character

Pick an English letter from your own name (say Z) and work through this in sequence — no functions, no loops:

1. Get its code with ord()
2. Print that code in binary, octal and hex with bin() / oct() / hex()
3. Turn the code back into a character with chr() and confirm you get what you started with
4. Add 32 to the code and chr() it again. What comes out?

2-4 Area of a triangle

Given sides a, b and c, Heron’s formula is:

s = (a + b + c) / 2
area = √(s(s−a)(s−b)(s−c))

Take the square root with ** 0.5 (math.sqrt needs an import, which is L3).

Compute both of these and print the results exactly as they come, without rounding:

The second triangle’s sides are exactly a tenth of the first, so its area should be exactly a hundredth.

Is it? One of the answer-sheet questions asks exactly this. Part B explains what you see.

2-5 Comparing floats safely (marked by the platform)

Implement almost_equal(a, b, eps=1e-9): two floats count as equal when the absolute value of their difference is below eps.

One line is enough. abs() is built in.

almost_equal(0.1 + 0.2, 0.3)   →  True
almost_equal(1.0, 1.5)         →  False

Part B uses this function.

2-6 Predict the type

Without running anything, write down the value and the type of each expression. Then run them and check. The answer sheet picks one of them to ask about, and asks which ones you got wrong:

8 / 4
8 // 4
8.0 // 4
8 % 3
-8 % 3
-8 // 3
2 ** 10
2 ** -2
2 ** 0.5
True + True

2-7 Roots of a quadratic (marked by the platform)

Implement roots(a, b, c) for a·x² + b·x + c = 0, larger root first.

You may assume a > 0 and that the discriminant b² − 4ac is positive — exactly two distinct real roots. (The other cases need if, which is L4.)

roots(1, -3, 2)   →  (2.0, 1.0)
roots(2, 5, -3)   →  (0.5, -3.0)

Square root by ** 0.5, as before.

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Part B — going deeper: which digit does floating point lie at?

“Floats are inexact” is an empty phrase until you know at which digit, and under what circumstances. Four questions here, each a few lines of straight-line code.

B-1 Look at the actual values

print(0.1 + 0.2 == 0.3)
print(0.1 + 0.3 == 0.4)

One is False and the other is True. Two decimals added in both cases — why the different answers?

Print all four of these to twenty decimal places with f"{x:.20f}" and compare:

print(f"{0.1:.20f}")
print(f"{0.3:.20f}")
print(f"{0.1 + 0.3:.20f}")
print(f"{0.4:.20f}")

On the answer sheet: is the stored 0.1 above or below the real 0.1? Work out which way 0.3 leans too — the next question needs it.

B-2 Find three examples of your own

0.1 + 0.2 == 0.3 is False. Find three more pairs that are equal in arithmetic but compare False, printing both sides of each at .20f.

Do not reuse the one you were given.

B-3 Large numbers swallow small ones

Try these two lines:

print(1e15 + 1 == 1e15)
print(1e16 + 1 == 1e16)

One is False, the other True. Past a certain magnitude, adding 1 has no effect whatsoever.

Answer:

1. From which power of ten does + 1 stop working?
2. At that magnitude, does + 2 still work? What about + 4? Try it and record what you find.
3. Explain why, in one sentence. (Hint: a float has a fixed number of significant bits.)

B-4 Back to the question from Lab 1

In Lab 1’s B-3 you replaced

x = 3.9 * x * (1 - x)

with the algebraically identical

x = 3.9 * x - 3.9 * x * x

Same starting value, same formula, different results. You were asked to guess then. Now you can answer.

1. At which round do the two versions first differ? (Run it and compare both values at twenty decimals.)
2. Why do they differ? Explain using B-1 to B-3.
3. So which version is “right”?

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Part C — fundamentals: files and directories

Last week’s pwd, ls and cd let you look and move. This week: create, copy, rename, delete.

Seeing the files you normally cannot

ls hides anything whose name starts with . — that is the convention for “hidden” files, and configuration files almost all look like that (.gitignore, .bashrc, macOS’s .DS_Store).

ls -a       # show everything, dotfiles included
ls -l       # one per line, with size, time and permissions
ls -al      # both at once

ls -a turns up two extra entries, . and ... They are not ordinary files but two entries every directory carries:

That is what last week’s cd .. was using, and the trailing . in cp ../hello.py . too.

Absolute and relative paths

• An absolute path is written out from the root: /home/yourname/cs1602/hello.py (on Windows, C:\cs1602\hello.py)
• A relative path starts from where you are: hello.py, ../hello.py, code/hello.py

. is the current directory, .. is the parent, ~ is your home directory.

C-1 Walk through it

Do these in order and copy the commands and their output onto the answer sheet:

1. cd into your cs1602 folder
2. mkdir week2, then ls to confirm it appeared
3. cd week2, then touch note.txt for an empty file
4. cp ../hello.py . — copy last week’s hello.py here (mind that trailing .)
5. mv note.txt readme.txt — rename it, and ls to confirm
6. cat hello.py — look at the contents
7. ls -a — did . and .. show up? Any other hidden files?
8. cd .., then pwd to confirm you are back up a level

C-2 Think it through

No typing required:

1. After cp a.txt b.txt, is a.txt still there? And after mv a.txt b.txt?
2. You are in ~/cs1602/week2 and want to reach ~/cs1602/hello.py. What is the relative path?

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Submitting

Submit on the grading platform, inside Homework 1. 2-2, 2-5 and 2-7 are code problems, marked the moment you submit. Everything else — Part A’s observations and all of Parts B and C — goes on the three answer sheets, where the multiple choice is marked immediately and your written answers go into the grading report for a TA.