CS1010 AY21/22 S1 Lecture 2

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# Lecture 2

### 16 August 2021

Admin Matters 
**Unit 3**: Functions 
**Unit 4**: Types

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### Reminders

- Keep your mic muted unless you need my attention
- Use Zoom Chat to discuss/chat among yourselves (I won't pay attention to it)
- Use Pizza Live Q&A to ask me question during class

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### Reminders

- My office hour: Tues 4-5pm, F2F and Online
- Questions? Issues?  Please use Piazza

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### Accounts

- By now you should have your Piazza, GitHub, and SoC accounts setup and ready to go.
- Target this week: 
    - able to `ssh` into on PE environments
    - go through Unix CLI and `vim` tutorials

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## Why Unix CLI?

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## Why `vim`?

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.tiny[[via reddit](https://www.reddit.com/r/nus/comments/nwpc54/nus_cs_fun/h1b2ikz/?context=3)]
.fit[![reddit](figures/reddit-vim-is-helpful.png)]

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### [Stackoverflow 2021 Developer Survey](https://insights.stackoverflow.com/survey/2021#section-most-loved-dreaded-and-wanted-collaboration-tools)

.fit[![reddit](figures/stackoverflow-vim-most-loved.png)]

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### Tutorials and Labs

- Starts next week
- Appeal via ModReg if you still haven't gotten a slot.
- We might appeal to you to switch rooms to balanced out the groups (please say yes)

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### Tutorial 1

- Problem Set from Unit 2

### Lab 1

- Setup, Unix, `vim`, Exercise 0

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.smaller[.fit[![flowchart](../figures/xkcd/flow_charts.png)] https://xkcd.com/518]
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## Flowchart

.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.001.png)]

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## Functions

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.002.png)]

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.003.png)]

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### Find The Range

- The _range_ of a given list of $k$ integers is the difference between the max and the min values in the list.

- Give an algorithm to find the range given a list $L$ of $k$ integers.

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## $max(L, k) - min(L, k)$

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### Refer to a previous solution to a sub-problem, which we assume we already know how to solve.

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## Wishful Thinking

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### Wishful Thinking

- A powerful tool to help us think at a higher level.
- We can focus on _what_ a function does, not _how_ it does it.

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### A C program is just a collection of functions!

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### A C program is just a collection of functions

- written by you
- provided by the standard C library
- provided by other libraries

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### Find the Mean

- Give an algorithm to find the mean value given a list $L$ of $k$ integers.

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## $\frac{sum(L,k)}{k}$

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Assume $len(L)$ returns the size of the list.

## $\frac{sum(L)}{len(L)}$

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### Find the Std Dev

- Give an algorithm to find the standard deviation of a list $L$ of $k$ integers.

$$\sqrt{\frac{\sum\_{i=0}^{k-1}(l\_i - \mu)^2}{k}}$$

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## Let's break it down into sub-problems

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$$\sqrt{\frac{\sum\_{i=0}^{k-1}(l\_i - \mu)^2}{k}}$$

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$$\sum\_{i=0}^{k-1}(l\_i - \mu)^2$$

set $\mu$ to $mean(L)$

set $L'$ to $subtract(L, \mu)$

set $L''$ to $square(L')$

set $total$ to $sum(L'')$

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$$\sum\_{i=0}^{k-1}(l\_i - \mu)^2$$

$sum(square(subtract(L, mean(L))))$

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$$\frac{\sum\_{i=0}^{k-1}(l\_i - \mu)^2}{k}$$

$mean(square(subtract(L, mean(L))))$

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$$\sqrt\frac{\sum\_{i=0}^{k-1}(l\_i - \mu)^2}{k}$$

$sqrt(mean(square(subtract(L,mean(L)))))$

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.008.png)]

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### Wishful Thinking

- $square(L)$
- $subtract(L, \mu)$
- $sqrt(x)$

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.006.png)]

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### **IMPORTANT**: Break down a problem into sub-problems and solve them one-by-one with functions.  Then compose the functions to solve the original given task.

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### Find the maximum among these numbers

```
5  9  8
1  3  2
```

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### Find the maximum among these numbers

.tiny[
```
12  20  11  20  14  2   24  36  43  16  27  6   11  7 
10  15  38  10  22  7   16  26  32  30  11  9   30  6 
20  6   27  19  26  10  27  6   19  34  5   9   3   22
10  4   13  1   10  22  43  36  39  29  41  12  13  25
17  8   30  31  29  38  2   42  7   45  24  33  9   40
34  29  37  2   26  17  19  34  6   7   34  22  21  41
38  5   15  13  9   1   42  39  5   29  38  4   22  29
41  10  26  32  30  26  16  16  18  22  32  34  14  10
5   17  25  16  19  6   31  16  3   13  8   42  41  0 
13  30  44  1   41  14  5   39  40  38  6   37  38  9 
.

```
]

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### Compare `12` to the maximum among

.tiny[
```
    20  11  20  14  2   24  36  43  16  27  6   11  7 
10  15  38  10  22  7   16  26  32  30  11  9   30  6 
20  6   27  19  26  10  27  6   19  34  5   9   3   22
10  4   13  1   10  22  43  36  39  29  41  12  13  25
17  8   30  31  29  38  2   42  7   45  24  33  9   40
34  29  37  2   26  17  19  34  6   7   34  22  21  41
38  5   15  13  9   1   42  39  5   29  38  4   22  29
41  10  26  32  30  26  16  16  18  22  32  34  14  10
5   17  25  16  19  6   31  16  3   13  8   42  41  0 
13  30  44  1   41  14  5   39  40  38  6   37  38  9 
.

```
]

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### Wishful Thinking

We know how to find $max(L,k)$ for smaller $k$

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### Let $max'(L, i, j)$ returns the maximum among $l\_i, l\_{i+1} \ldots l\_j$

### So $max(L, k)$ is just $max'(L, 0, k-1)$

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### if $i \not = j$, then $max'(L, i, j)$ is the larger between

- $l\_i$ and
- $max'(L, i+1, j)$

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### if $i$ equals $j$, $max'(L, i, j)$ is just $l_i$

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.004.png)]

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### Find the maximum among

```
]

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### Wishful Thinking

We know how to find $max(L,k)$ for smaller $k$

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### Compare the maximum among these numbers

.tiny[
```
12  20  11  20  14  2   24                            
10  15  38  10  22  7   16                            
20  6   27  19  26  10  27                            
10  4   13  1   10  22  43                            
17  8   30  31  29  38  2                             
34  29  37  2   26  17  19                            
38  5   15  13  9   1   42                            
41  10  26  32  30  26  16                            
5   17  25  16  19  6   31                            
13  30  44  1   41  14  5                             
.

```
]

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### With the maximum among these numbers

.tiny[
```
                            36  43  16  27  6   11  7 
                            26  32  30  11  9   30  6 
                            6   19  34  5   9   3   22
                            36  39  29  41  12  13  25
                            42  7   45  24  33  9   40
                            34  6   7   34  22  21  41
                            39  5   29  38  4   22  29
                            16  18  22  32  34  14  10
                            16  3   13  8   42  41  0 
                            39  40  38  6   37  38  9 
.

```
]

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### if $j \not= i$, $max(L,i,j)$ is the larger between

- $max'(L, i, n)$ and 
- $max'(L, n+1, j)$

where $n = \left\lfloor\frac{i+j}{2}\right\rfloor$

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### if $j$ equals $i$, $max(L,i,j)$ is just $l_i$.

---

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.011.png)]

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## Divide and Conquer

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## Find the factorial of $n$

- $n! = n \times n-1 \times \ldots \times 2 \times 1$
  
- $n! = n \times (n-1)!$

- Special case: $0! = 1$

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.fit[![flowchart](figures/max-flowchart-dark/max-flowchart-dark.005.png)]

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## Recursion

### A function calling itself

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# Types

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### `1010010101010101001111010..` can mean

- 1933091
- 34.95108
- `hello`
- an image

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### A variable needs a type to be interpreted correctly.

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### A type is represented by a fixed, finite, number of bits.

### Different types can be represented by a different number of bits.

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### 1 bit: `1` or `0`

black or white 
true or false 
yes or no 
S or U

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### 2 bits: `11`, `10`, `01`, or `00`

north, south, east, west 
spring, summer, fall, winter

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### In general, $k$ bits can represent $2^k$ values

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### more bits $\rightarrow$ more memory, but can represent bigger range

### fewer bits $\rightarrow$ less memory, but represent smaller range

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### When writing programs for embedded systems, IoT devices, sensors, etc, you need to be frugal with memory usage.

### In CS1010, however, we will go with more bits for better precision.

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## Integers

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### 8 bits: 256 different integers

0 to 255 (for unsigned) 
-128 to 127 (for signed)

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### 64 bits signed

-9,223,372,036,854,775,808 
to 
9,223,372,036,854,775,807

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## Characters
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### 8 bits: 127 different symbols using ASCII standards

```
0-9, A-Z, a-z
<>?:”{}!@#$%^&*
()_+-=[]\';/.,
```
return, tab, escape, etc

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### up to 32 bits: Unicode (UTF-8)

11111011000000000 😀

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## Real numbers

(also called floating point numbers)

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### There are infinitely many real numbers but only a finite sequence of bits.

### Not all of real numbers can be represented.

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### Not every real number can be presented precisely

E.g., `0.1 + 0.2` is `0.30000000000000004`

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.fit[![foodpanda](figures/foodpanda.png)]

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### Rule: Use integer type unless you absolutely need to use a real number type.

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### We normally use 32, 64, or 128 bits to represent real numbers.

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### A variable needs a type to be interpreted correctly.

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set $total$ to $sum(L, k)$ 
set $avg$ to $mean(L, k)$

$k$ is an integer 
$total$ is an integer 
$avg$ must be a real number

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## Homework

- Problem Set in Unit 3
- `ssh` into CS1010 PE hosts and follow the Unix CLI and `vim` tutorial
- Diagnostic Quiz for Lecture 2 (due this Wed)
- Diagnostic Quiz for using CS1010 PE (due next Wed)

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Version: 1.1

Last Updated: Tue Aug 18 12:24:32 +08 2020
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