DAPHNE — Python Tutor v2

01 Numbers & Variables

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Key Concepts

Two number types: int (whole numbers) and float (decimals).

// — integer division (rounds down)
/ — true division (always returns float)
% — modulo (remainder)
** — power (exponentiation)

Rule: int op int → int (except / which always → float).
Any operation with a float → float.
= is assignment. == is comparison.

Predict the Output

1. 7 // 2 3

2. 7 / 2 3.5

3. 7 % 3 1

4. 2 ** 10 1024

5. type(3) <class 'int'>

6. type(3.0) <class 'float'>

7. type(3 / 1) <class 'float'>

8. 10 + 3 * 2 16

9. 17 % 5 2

10. 2 ** 0 1

Exercises

Calculate the area and volume of a rectangular prism with width=7.3, length=15.1, height=6.

exercise 1.1

# Rectangular prism: width=7.3, length=15.1, height=6
width = 7.3
length = 15.1
height = 6

area = 2 * (width*length + width*height + length*height)
volume = width * length * height

print('Area:', area)
print('Volume:', volume)

You have 1342 eggs. How many gross (144), dozens (12), and singles?

exercise 1.2

eggs = 1342

gross = eggs // 144
remaining = eggs % 144
dozens = remaining // 12
units = remaining % 12

print('Total eggs:', eggs)
print('Gross (144s):', gross)
print('Dozens:', dozens)
print('Units:', units)

Experiment freely with operators:

sandbox

# Try your own expressions
print(15 // 4)
print(15 % 4)
print(2 ** 8)
print(type(10 / 5))

02 Using Functions

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Key Concepts

Importing modules:

import math — access via math.sqrt()
from math import * — imports everything, call sqrt() directly
import math as m — alias, call m.sqrt()
from math import sin, cos — import specific functions

Useful functions: math.sqrt(), math.sin(), math.cos(), math.radians(), math.pi, round(), abs()
Random: random.randint(a, b), random.uniform(a, b)

Rule: print() displays a value but returns None.
Functions can be nested: math.sin(math.radians(45))

Predict the Output

1. print(print(3)) 3\nNone print(3) displays 3, returns None. Outer print displays None.

2. import math; math.floor(3.9) 3

3. round(3.14159, 2) 3.14

4. abs(-7) 7

Exercises

Calculate 2 × cos(π/6) rounded to 4 decimal places.

exercise 2.1

import math

result = 2 * math.cos(math.pi / 6)
print(round(result, 4))

Simulate rolling 2 dice and print the total.

exercise 2.2

import random

die1 = random.randint(1, 6)
die2 = random.randint(1, 6)

print('Die 1:', die1)
print('Die 2:', die2)
print('Total:', die1 + die2)

Risk dice: attacker rolls 3 dice, keeps the top 2. Print all 3 rolls and the kept total.

exercise 2.3

import random

d1 = random.randint(1, 6)
d2 = random.randint(1, 6)
d3 = random.randint(1, 6)

print('Rolls:', d1, d2, d3)

# Remove the smallest die
smallest = min(d1, d2, d3)
kept = d1 + d2 + d3 - smallest
print('Kept (top 2 total):', kept)

03 Strings — Basics

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Key Concepts

Strings use '...' or "...". Escape characters:

\n — new line
\t — tab
\\ — literal backslash
\' — apostrophe inside single quotes
\" — quote inside double quotes

+ concatenates strings (no space).
print(a, b) adds a space between a and b.
'abc' * 3 → 'abcabcabc'
\n counts as 1 character in len().

Predict the Output (Textbook 5.5)

1. number = 2; print('The number is', number) The number is 2

2. print('What\'s', 'the display?') What's the display?

3.

print('Some things are', 'double'*2 + ',')
print('others are', 'triple'*3 + '.')

Some things are doubledouble,\nothers are tripletripletriple.

4. print('How do you obtain\na new line?') How do you obtain\na new line? \n creates an actual line break in the output.

5. print('one\n\ttwotwo\none\ttwotwo') one\n twotwo\none twotwo

6. print('Is one the same as \"one\"?') Is one the same as "one"?

7. x = 1; y = 2; print('the sum of', x, 'and', y, 'is equal to', x+y) the sum of 1 and 2 is equal to 3

8.

x = 'one'; y = 'two'
print('Does \"' + x, y + '\" = \"' + x + y + '\"?')

Does "one two" = "onetwo"? + concatenates (no space), comma in print adds a space.

Exercises

Build a box around "The answer is 42" using +, *, and \n.

exercise 3.1

message = 'The answer is 42'
border = '+' + '-' * (len(message) + 2) + '+'
middle = '| ' + message + ' |'

print(border)
print(middle)
print(border)

Experiment with string operations:

sandbox

# Try concatenation, repetition, len()
word = 'Hello'
print(word + ' ' + 'World')
print(word * 3)
print('Length:', len(word))
print('a\tb\nc')

04 Booleans & Decisions

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Key Concepts

Comparison operators: ==, !=, <, >, <=, >=
Logical operators: and, or, not

Precedence: not binds tightest, then and, then or.
Think of and like multiplication and or like addition.
Common mistake: = (assignment) vs == (comparison).
Truthiness: 0, 0.0, '', [] are False. Everything else is True.

Predict the Boolean (Textbook 6.7)

1. True or False True

2. 1 < 2 or 1 > 2 True

3. 1 < 2 and 1 > 2 False

4. (1 != 2 and 'a' == 'a') or 2 == 3 True

5. 1 != 2 and 'a' == 'a' or 2 == 3 True and binds first: (True and True) or False → True

6. (1 != 2 or 'a' == 'a') and 2 == 3 False

7. 1 != 2 or 'a' == 'a' and 2 == 3 True and binds first: True or (True and False) → True or False → True

8. (1 < 2 or 3 == 3) and (1 == 0 or 1 != 1) False

9. 1 < 2 or 3 == 3 and 1 == 0 or 1 != 1 True True or (True and False) or False → True or False or False → True

10. (1 < 2 and 3 == 3) or (1 == 0 and 1 != 1) True

11. 1 < 2 and 3 == 3 or 1 == 0 and 1 != 1 True (True and True) or (False and False) → True or False → True

12. True or False and True or False and True or False True True or (F and T) or (F and T) or F → True or F or F or F → True

Predict If/Else Output

1.

x = 5
if x > 3:
  print('big')
else:
  print('small')

big

2.

x = 5
if x > 10:
  print('A')
elif x > 3:
  print('B')
else:
  print('C')

B

3.

x = 7
if x > 5:
  print('A')
if x > 3:
  print('B')

A\nB Two separate if statements — both can trigger.

4.

x = 0
if x:
  print('truthy')
else:
  print('falsy')

falsy 0 is falsy in Python.

5.

s = ''
if s:
  print('has content')
else:
  print('empty')

empty

Exercises

Letter grade program: convert a mark (0-100) to A/B/C/D/E/F.

exercise 4.1

mark = 73  # Change this to test different grades

if mark >= 90:
    grade = 'A'
elif mark >= 80:
    grade = 'B'
elif mark >= 70:
    grade = 'C'
elif mark >= 60:
    grade = 'D'
elif mark >= 50:
    grade = 'E'
else:
    grade = 'F'

print('Mark:', mark, '-> Grade:', grade)

Discount calculator: 10% off over $100, additional 5% off over $200.

exercise 4.2

price = 250  # Change this to test

if price > 200:
    discount = 0.15  # 10% + 5%
elif price > 100:
    discount = 0.10
else:
    discount = 0

savings = price * discount
final = price - savings

print('Original:', price)
print('Discount:', str(int(discount * 100)) + '%')
print('You save:', savings)
print('Final price:', final)

05 While Loops

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Key Concepts

While loop repeats as long as the condition is True.

Three essentials:
1. Variable in test must be defined before the loop.
2. The loop body must update the test variable (or it runs forever!).
3. Loop body is indented.

Accumulator pattern: total = 0 before loop, total += value inside.
Shorthand: x += 1 is the same as x = x + 1

Predict the Output

1.

k = 1
while k <= 3:
  print(k)
  k += 1

1\n2\n3

2.

total = 0; k = 1
while k <= 4:
  total += k
  k += 1
print(total)

10 1 + 2 + 3 + 4 = 10

3.

n = 8
while n > 1:
  n = n // 2
  print(n)

4\n2\n1

Exercises

Print the squares of 1 through 10.

exercise 5.1

k = 1
while k <= 10:
    print(k, '->', k ** 2)
    k += 1

Calculate the sum of squares from 1 to N (try N=10).

exercise 5.2

N = 10
total = 0
k = 1

while k <= N:
    total += k ** 2
    k += 1

print('Sum of squares from 1 to', N, '=', total)

Integer division using repeated subtraction (compute a // b without using //).

exercise 5.3

a = 17
b = 5

# Count how many times b fits into a
quotient = 0
remainder = a

while remainder >= b:
    remainder -= b
    quotient += 1

print(a, '//', b, '=', quotient)
print(a, '%', b, '=', remainder)
print('Check:', quotient, '* ', b, '+', remainder, '=', quotient * b + remainder)

GCD using the Euclidean algorithm.

exercise 5.4

a = 48
b = 18

# Save originals for display
orig_a, orig_b = a, b

while b != 0:
    remainder = a % b
    a = b
    b = remainder

print('GCD of', orig_a, 'and', orig_b, 'is', a)

06 Lists

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Key Concepts

Lists are ordered, mutable collections: [1, 2, 3]

list[i] — access element at index i (0-based)
list[-1] — last element
list[a:b] — slice from index a to b-1
append(), insert(), remove(), pop(), sort()
len(), sum(), min(), max()

Lists are mutable — you can change elements in place.
Tuples (1, 2, 3) are immutable — once created, cannot be changed.
list.index(x) returns the position of x in the list.

Predict the Output

1. a = [10, 20, 30, 40, 50]; print(a[0]) 10

2. a = [10, 20, 30, 40, 50]; print(a[-1]) 50

3. a = [10, 20, 30, 40, 50]; print(a[1:3]) [20, 30]

4. a = [10, 20, 30, 40, 50]; print(a[:2]) [10, 20]

5. a = [10, 20, 30, 40, 50]; print(a[3:]) [40, 50]

6. a = [3, 1, 4, 1, 5]; a.sort(); print(a) [1, 1, 3, 4, 5]

7. a = [1, 2, 3]; a.append(4); print(len(a)) 4

8. a = [1, 2, 3]; b = a.pop(); print(b, a) 3 [1, 2]

Exercises

Generate 10 random numbers (1-100), find min, max, and average.

exercise 6.1

import random

numbers = []
k = 0
while k < 10:
    numbers.append(random.randint(1, 100))
    k += 1

print('Numbers:', numbers)
print('Min:', min(numbers))
print('Max:', max(numbers))
print('Sum:', sum(numbers))
print('Average:', sum(numbers) / len(numbers))

Build a list of squares from 1 to 20.

exercise 6.2

squares = []
k = 1
while k <= 20:
    squares.append(k ** 2)
    k += 1

print(squares)

07 For Loops

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Key Concepts

For loop iterates over a sequence (list, range, string).

range(n) → 0, 1, 2, ..., n-1
range(a, b) → a, a+1, ..., b-1
range(a, b, step) → a, a+step, a+2*step, ... (while < b)
enumerate(list) → gives both index and value

List comprehension: [expr for x in sequence]
Compact way to build a list in one line.
Example: [x**2 for x in range(5)] → [0, 1, 4, 9, 16]

Predict the Output

1. [x**2 for x in range(5)] [0, 1, 4, 9, 16]

2. list(range(3, 8)) [3, 4, 5, 6, 7]

3. list(range(0, 10, 3)) [0, 3, 6, 9]

4. list(range(5, 0, -1)) [5, 4, 3, 2, 1]

5. [c.upper() for c in 'hello'] ['H', 'E', 'L', 'L', 'O']

Exercises

Sum of the first 100 positive integers using a for loop.

exercise 7.1

total = 0
for i in range(1, 101):
    total += i

print('Sum of 1 to 100 =', total)
print('Check (Gauss formula):', 100 * 101 // 2)

Print a multiplication table (1-5).

exercise 7.2

for i in range(1, 6):
    row = ''
    for j in range(1, 6):
        row += str(i * j).rjust(4)
    print(row)

Use a list comprehension to get squares of even numbers from 0 to 20.

exercise 7.3

squares = [x**2 for x in range(0, 21) if x % 2 == 0]
print(squares)

Enumerate: print each fruit with its index.

exercise 7.4

fruits = ['apple', 'banana', 'cherry', 'date']
for i, fruit in enumerate(fruits):
    print(i, '->', fruit)

08 Strings — Advanced

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Key Concepts

f-strings (formatted string literals): f"Hello {name}"
String methods:

.split() — split into list by whitespace (or given delimiter)
' '.join(list) — join list items with a separator
.upper(), .lower() — case conversion
.replace(old, new) — replace substrings
.find(sub) — find position of substring (-1 if not found)
.strip() — remove leading/trailing whitespace

String slicing: s[a:b] works just like list slicing.
s[::-1] reverses the string.
Strings are immutable — methods return new strings.

Predict the Output

1. name = 'Alice'; f"Hello, {name}!" 'Hello, Alice!'

2. x = 3; f"{x} squared is {x**2}" '3 squared is 9'

3. 'hello world'.split() ['hello', 'world']

4. '-'.join(['a', 'b', 'c']) 'a-b-c'

5. 'Python'[::-1] 'nohtyP'

6. 'hello'.replace('l', 'L') 'heLLo'

7. 'banana'.find('nan') 2

Exercises

Reverse a string using slicing.

exercise 8.1

text = 'Programming in Science'
reversed_text = text[::-1]
print('Original:', text)
print('Reversed:', reversed_text)

Count the vowels in a string.

exercise 8.2

text = 'Programming in Science'
vowels = 'aeiouAEIOU'
count = 0

for char in text:
    if char in vowels:
        count += 1

print(f'"{text}" has {count} vowels')

Experiment with f-strings and string methods.

sandbox

name = 'Sebastien'
age = 25

# f-string formatting
print(f'{name} is {age} years old')
print(f'Pi is approximately {3.14159:.2f}')
print(f'{"hello":>20}')  # Right-align in 20 chars
print(f'{42:08b}')  # Binary with zero-padding

09 Functions

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Key Concepts

Defining a function: def function_name(parameters):
Returning a value: return value

print vs return:
print() displays a value on screen. return sends a value back to the caller.
A function without return returns None.

Scope: Variables inside a function are local — they don't exist outside.
Order: A function must be defined before it is called.
Default arguments: def greet(name='World')

Predict the Output

1.

def add(a, b):
  return a + b
print(add(3, 4))

7

2.

def add(a, b):
  print(a + b)
result = add(3, 4)
print(result)

7\nNone print() inside the function displays 7, but the function returns None.

3.

x = 10
def change():
  x = 20
change()
print(x)

10 x inside the function is local — it doesn't affect the global x.

4.

def greet(name='World'):
  return f'Hello, {name}!'
print(greet())
print(greet('Alice'))

Hello, World!\nHello, Alice!

Exercises

Write an is_even(n) function that returns True if n is even.

exercise 9.1

def is_even(n):
    return n % 2 == 0

# Test it
print(is_even(4))   # True
print(is_even(7))   # False
print(is_even(0))   # True
print(is_even(-3))  # False

Write factorial(n) using recursion.

exercise 9.2

def factorial(n):
    if n <= 1:
        return 1
    return n * factorial(n - 1)

# Test it
print('5! =', factorial(5))    # 120
print('0! =', factorial(0))    # 1
print('10! =', factorial(10))  # 3628800

Write distance(x1, y1, x2, y2) that computes the Euclidean distance.

exercise 9.3

import math

def distance(x1, y1, x2, y2):
    return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)

# Test it
print(distance(0, 0, 3, 4))    # 5.0
print(distance(1, 1, 4, 5))    # 5.0
print(round(distance(0, 0, 1, 1), 4))  # 1.4142

Challenge: write a function that checks if a number is prime.

exercise 9.4

def is_prime(n):
    if n < 2:
        return False
    k = 2
    while k * k <= n:
        if n % k == 0:
            return False
        k += 1
    return True

# Test it
for num in [2, 3, 4, 17, 18, 97, 100]:
    print(f'{num}: {is_prime(num)}')

10 Exam Prep Workbook

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Quick Reference Card

f-strings:     f"text {variable} more {expression:.2f}"
sum/max/min:   sum(list), max(list), min(list), list.index(max(list))
while pattern: total=0; i=0; while i<n: total+=item; i+=1
bool precedence: not > and > or (like: NOT > * > +)
slicing:       s[start:stop:step], s[::-1] reverses

Topic 1: String Formatting & f-strings

f-string syntax: Prefix a string with f and put expressions inside {}.
Format specifiers go after a colon inside the braces:

:.2f — 2 decimal places (float)
:>10 — right-align in 10 characters
:<10 — left-align in 10 characters
:^10 — center in 10 characters
:08d — zero-pad to 8 digits

f"Pi is {3.14159:.2f}" → "Pi is 3.14"
f"{'hello':>20}" → right-aligned in 20 chars
You can put any expression inside the braces: f"{2 + 3}" → "5"

Exercise 1: Given price = 19.99, produce the string "The price is $19.99" using an f-string.

Use :.2f inside the curly braces to format to 2 decimal places.

f"The price is ${price:.2f}"

Exercise 2: Format a table row: name left-aligned in 15 characters, grade right-aligned in 5 characters. Test with name="Alice", grade="A+".

Use :<15 for left-align and :>5 for right-align.

The f-string looks like: f"{name:<15}{grade:>5}"

Add a separator: f"| {name:<15} | {grade:>5} |"

Exercise 3: Build a receipt with aligned columns: item name (left, 20 chars), quantity (right, 5), unit price (right, 8, 2 decimals), total (right, 10, 2 decimals).

Create a list of tuples: [("Widget", 3, 9.99), ("Gadget", 1, 24.50)]

f"{item:<20}{qty:>5}{price:>8.2f}{qty*price:>10.2f}"

Topic 2: List Operations

Key list operations:

list[i] — access by index, list[-1] — last element
list[a:b] — slice, list[::-1] — reverse
append(), insert(i, x), remove(x), pop()
sum(), max(), min(), len(), sorted()
list.index(x) — find position of value x

Find max and its position:
highest = max(scores)
position = scores.index(highest)

Exercise 1: Given scores = [88, 92, 75, 98, 84], find the highest score and its position (index).

Use max() to find the highest value.

Use .index() to find where that value is in the list.

best = max(scores) then pos = scores.index(best)

Exercise 2: Remove duplicates from [3, 1, 4, 1, 5, 9, 2, 6, 5, 3] while preserving order.

Use if item not in seen to check for duplicates.

Keep a seen list and a unique list. Append to both when new.

Exercise 3: Compute the running average of [10, 20, 30, 40, 50]. After each element, print the average of all elements seen so far.

Keep a running total and divide by the count at each step.

Use enumerate() to get both index and value. Index + 1 = count.

total += val then avg = total / (i + 1)

Topic 3: While Loop Patterns

Common while-loop patterns:

Counter: i = 0; while i < n: ...; i += 1
Accumulator: total = 0; while ...: total += value
Sentinel: Loop until a special value is encountered
Validation: Keep asking until input is valid

Always ensure:
1. Loop variable initialized before the loop
2. Loop variable updated inside the loop
3. Condition will eventually become False

Exercise 1: Sum the integers from 1 to 100 using a while loop.

Start with total = 0 and i = 1.

Loop while i <= 100, adding i to total each time.

Don't forget i += 1 at the end of the loop body!

Exercise 2: Input validation loop — keep asking for a number between 1 and 10. (Simulated with a pre-set list of attempts.)

while not (1 <= value <= 10)

Exercise 3: Collatz conjecture — starting from n, if even: n = n/2, if odd: n = 3n+1. Count steps to reach 1. Try n=27.

Use n % 2 == 0 to check if even.

Loop while n != 1 and increment a step counter each iteration.

Use integer division: n = n // 2 for the even case.

Topic 4: Boolean Logic & Operator Precedence

Truth tables:

True and True → True | True and False → False
True or False → True | False or False → False
not True → False | not False → True

Precedence (highest to lowest): not > and > or
Think of it like arithmetic: not = unary minus, and = multiplication, or = addition.

Short-circuit evaluation:
True or X → True (X is never evaluated)
False and X → False (X is never evaluated)

Evaluate these 15 expressions mentally, then click to reveal the answer:

1. True or False True

2. 1 < 2 or 1 > 2 True

3. 1 < 2 and 1 > 2 False

4. (1 != 2 and 'a'=='a') or 2 == 3 True

5. 1 != 2 and 'a'=='a' or 2 == 3 True

6. (1 != 2 or 'a'=='a') and 2 == 3 False

7. 1 != 2 or 'a'=='a' and 2 == 3 True TRICKY — and binds first: True or (True and False) → True

8. (1 < 2 or 3 == 3) and (1 == 0 or 1 != 1) False

9. 1 < 2 or 3 == 3 and 1 == 0 or 1 != 1 True

10. (1 < 2 and 3 == 3) or (1 == 0 and 1 != 1) True

11. 1 < 2 and 3 == 3 or 1 == 0 and 1 != 1 True

12. True or False and True or False and True or False True

13. not True and False or True True (not True) and False or True → False and False or True → True

14. not (True and False) or True True

15. not (True or False) and True False not True and True → False and True → False

Verify your answers:

verify booleans

# Run this to check all 15 answers
exprs = [
    'True or False',
    '1 < 2 or 1 > 2',
    '1 < 2 and 1 > 2',
    "(1 != 2 and 'a'=='a') or 2 == 3",
    "1 != 2 and 'a'=='a' or 2 == 3",
    "(1 != 2 or 'a'=='a') and 2 == 3",
    "1 != 2 or 'a'=='a' and 2 == 3",
    '(1 < 2 or 3 == 3) and (1 == 0 or 1 != 1)',
    '1 < 2 or 3 == 3 and 1 == 0 or 1 != 1',
    '(1 < 2 and 3 == 3) or (1 == 0 and 1 != 1)',
    '1 < 2 and 3 == 3 or 1 == 0 and 1 != 1',
    'True or False and True or False and True or False',
    'not True and False or True',
    'not (True and False) or True',
    'not (True or False) and True',
]
for i, e in enumerate(exprs, 1):
    print(f'{i:2}. {e:55} -> {eval(e)}')

Topic 5: Writing Functions

Function essentials:

def function_name(params): — define a function
return value — send a value back to the caller
print() displays but returns None
Variables inside a function are local (not visible outside)
def greet(name='World') — default argument

Common mistake: Using print() instead of return.
If you need to use the result later, the function must return it.
print() is only for displaying to the screen.

Exercise 1: Write is_palindrome(s) that checks if a string reads the same forwards and backwards.

Use s[::-1] to reverse, then compare with the original.

return s.lower() == s.lower()[::-1] (handle case insensitivity)

Exercise 2: Write letter_grade(mark) that returns A (90+), B (80+), C (70+), D (60+), E (50+), or F.

Use if/elif/else to check the ranges from highest to lowest.

Check mark >= 90 first, then >= 80, etc.

Make sure you return the grade, not print() it.

Exercise 3: Write fibonacci(n) that returns the nth Fibonacci number (0, 1, 1, 2, 3, 5, 8, ...).

Use a while loop with two variables a, b starting at 0, 1.

Loop n times: a, b = b, a + b — then a is the answer.