class: big, middle

# Engineering 1020: Introduction to Programming

.title[
  .lecture[Lecture 19:]
  .title[Sets]
  
  
]

.footer[[/lecture/19/](/lecture/19/)]

---

# Previously:

### Collections

* lists (flexible, mutable)
* tuples (simple, immutable)
* arrays (fixed-size, homogeneous, high-performance)

---

# Collections

### What do these all have in common?

```python
snowfall = [8, 0, 80, 0, 2, 1, 1]
names = ('Aaron', 'Abdul', 'Abdullah', 'Abigail', 'Adam', 'Adam', 'Adam', 'Agatha')
temperatures = numpy.array([7.8, 6.4, -2.1, 6.4, 8.0, 12.8, 6.4])
```

???

All of these values are **ordered** collections:
they keep track of which value was first, which was second, etc.
This can be important for many use cases.

Also, all of these have **duplicate entries**!

---

# Something different

### How about these values?

```python
topics_covered = ['values', 'expressions', 'functions', 'expressions']
rooms_visited = [2007, 2040, 2043, 2040, 2007, 2040, 2043, 2007, 2040]
```

### How to ask "has Dr Anderson been to room X"?

???

```python
rooms_visited = [2007, 2040, 2043, 2040, 2007, 2040, 2043, 2007, 2040]

def is_room_visited(room):
    for r in rooms_visited:
        if r == room:
            return True

# or:
    return room in rooms_visited
```

---

# Sets

### Allow us to store _unique_ values

* e.g., "students who are not promotable to Term 3"
--

* called _existential_ storage

???

Existential storage tells us whether or not a value exists in a collection.
It's not to be confused with
[existentialism](https://en.wikipedia.org/wiki/Existentialism),
the philosophical system!

### Allow us to perform set _operations_

* union, intersection

---

# Creating sets

.floatleft[
### Mathematics:

$$\textrm{let}~S = \\{ 1, 2, 3 \\}$$
]

.floatleft[
### Python:

```python
s = set([1, 2, 3])
```
]

---

# Updating sets

.floatleft[
### Adding:

```python
>>> s
{1, 2, 3}
>>> s.add(4)
>>> s
{1, 2, 3, 4}
>>> s.add(4)
>>> s
{1, 2, 3, 4}
```
]

???

Note that adding a value to a set for a second time **changes nothing**!

.floatleft[
### Removing:

```python
>>> s
{1, 2, 3, 4}
>>> s.remove(4)
>>> s
{1, 2, 3}
```
]

## OK, that's nice, but...

## So?

---

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/4/49/Venn-stainedglass-gonville-caius.jpg" height="600"/>
]

# Set operations

### Union

### Intersection

### Difference

### Symmetric difference

---

# Union

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/320px-Venn0111.svg.png"/>
]

### Mathematics: $A \cup B$

### Python:

```python
passed_courses = set([202101234, 202101235, 202112346])
sufficient_average = set([202101235, 202112346, 202112347])

promotable = passed_courses.union(sufficient_average)
```

---

# Intersection

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/384px-Venn0001.svg.png"/>
]

### Mathematics: $A \cap B$

### Python:

```python
high_gpa = set([202101234, 202101235, 202112346])
leaders = set([202101235, 202112346, 202112347])

awardable = high_gpa.intersection(leaders)
```

---

# Difference

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/384px-Venn0010.svg.png"/>
]

### Mathematics: $A - B$

```python
admitted = set([202101234, 202101235, 202112346])
enrolled = set([202101235, 202112346, 202112347])

missing = admitted - enrolled

```

---

# Symmetric difference

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/384px-Venn0110.svg.png"/>
]

### Mathematics: $A \triangle B$

```python
good_average = set([202101234, 202101235, 202112346])
passed_all = set([202101235, 202112346, 202112347])

not_promotable = good_average.symmetric_difference(passed_all)
```

---

# Career advice

.centered[
<img src="venn-career.svg" width="450"/>
]

???

Or, if you want to make the diagram more complicated, you can add a fourth
circle for "what the world needs" — this is called
[_ikigai_](https://www.thestar.com/life/relationships/why-north-americans-should-consider-dumping-age-old-retirement-pasricha/article_12f4d041-b492-57e4-a892-fb042ff20073.html)
in Japanese.

---

# Exercise

.floatright[
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Venn_diagram_gr_la_ru.svg/622px-Venn_diagram_gr_la_ru.svg.png" height="400"/>
]

### DO try this at home:

1. Create three sets: `greek`, `latin` and
   [`cyrillic`](https://en.wikipedia.org/wiki/Cyrillic_script#Letters)
2. Find intersections, unions and differences by hand
3. Check your work using Python

---

# Summary:

### Sets

* _existential_ data storage
* set operations

---
class: big, middle

(here endeth the lesson)