Lecture 2

16 August 2021

Admin Matters
Unit 3: Functions
Unit 4: Types

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RemindersKeep 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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RemindersMy office hour: Tues 4-5pm, F2F and Online
Questions? Issues?  Please use Piazza
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AccountsBy 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?AY2122 S1              5

Why vim?AY2122 S1              6

via reddit reddit

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Stackoverflow 2021 Developer Survey

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Tutorials and LabsStarts 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 1Problem Set from Unit 2
Lab 1Setup, Unix, vim, Exercise 0
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flowchart
https://xkcd.com/518

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Flowchart

flowchart

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FunctionsAY2122 S1              13

flowchart

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flowchart

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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)AY2122 S1              17

Refer to a previous solution to a sub-problem, which we assume we already know how to solve.AY2122 S1              18

Wishful ThinkingAY2122 S1              19

Wishful ThinkingA 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!AY2122 S1              21

A C program is just a collection of functionswritten by you
provided by the standard C library
provided by other libraries
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Find the MeanGive an algorithm to find the mean value given a list L of k integers.
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\frac{sum(L,k)}{k}AY2122 S1              24

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-problemsAY2122 S1              27

$\sqrt{\frac{\sum_{i=0}^{k-1}(l_i - \mu)^2}{k}}$

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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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flowchart

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Wishful Thinkingsquare(L)
subtract(L, \mu)
sqrt(x)
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flowchart

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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.AY2122 S1              36

Find the maximum among these numbers

5  9  8
1  3  2

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Find the maximum among these numbers12  20  11  20  14  2   24  36  43  16  27  6   11  7 
15  38  10  22  7   16  26  32  30  11  9   30  6 
6   27  19  26  10  27  6   19  34  5   9   3   22
4   13  1   10  22  43  36  39  29  41  12  13  25
8   30  31  29  38  2   42  7   45  24  33  9   40
29  37  2   26  17  19  34  6   7   34  22  21  41
5   15  13  9   1   42  39  5   29  38  4   22  29
10  26  32  30  26  16  16  18  22  32  34  14  10
 17  25  16  19  6   31  16  3   13  8   42  41  0 
30  44  1   41  14  5   39  40  38  6   37  38  9 
.
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Compare 12 to the maximum among    20  11  20  14  2   24  36  43  16  27  6   11  7 
15  38  10  22  7   16  26  32  30  11  9   30  6 
6   27  19  26  10  27  6   19  34  5   9   3   22
4   13  1   10  22  43  36  39  29  41  12  13  25
8   30  31  29  38  2   42  7   45  24  33  9   40
29  37  2   26  17  19  34  6   7   34  22  21  41
5   15  13  9   1   42  39  5   29  38  4   22  29
10  26  32  30  26  16  16  18  22  32  34  14  10
 17  25  16  19  6   31  16  3   13  8   42  41  0 
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_jSo max(L, k) is just max'(L, 0, k-1)AY2122 S1              41

if i \not = j, then max'(L, i, j) is the larger betweenl_i and
max'(L, i+1, j) 
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if i equals j, max'(L, i, j) is just l_iAY2122 S1              43

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flowchart

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Find the maximum among12  20  11  20  14  2   24  36  43  16  27  6   11  7 
15  38  10  22  7   16  26  32  30  11  9   30  6 
6   27  19  26  10  27  6   19  34  5   9   3   22
4   13  1   10  22  43  36  39  29  41  12  13  25
8   30  31  29  38  2   42  7   45  24  33  9   40
29  37  2   26  17  19  34  6   7   34  22  21  41
5   15  13  9   1   42  39  5   29  38  4   22  29
10  26  32  30  26  16  16  18  22  32  34  14  10
 17  25  16  19  6   31  16  3   13  8   42  41  0 
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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Compare the maximum among these numbers12  20  11  20  14  2   24                            
15  38  10  22  7   16                            
6   27  19  26  10  27                            
4   13  1   10  22  43                            
8   30  31  29  38  2                             
29  37  2   26  17  19                            
5   15  13  9   1   42                            
10  26  32  30  26  16                            
 17  25  16  19  6   31                            
30  44  1   41  14  5                             
.
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With the maximum among these numbers                            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.AY2122 S1              51

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flowchart

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Divide and ConquerAY2122 S1              55

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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flowchart

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RecursionA function calling itselfAY2122 S1              58

TypesAY2122 S1              59

1010010101010101001111010.. can mean1933091
34.95108
hello
an image
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A variable needs a type to be interpreted correctly.AY2122 S1              61

A type is represented by a fixed, finite, number of bits.Different types can be represented by a different number of bits.AY2122 S1              62

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 valuesAY2122 S1              65

more bits \rightarrow more memory, but can represent bigger rangefewer bits \rightarrow less memory, but represent smaller rangeAY2122 S1              66

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.AY2122 S1              67

IntegersAY2122 S1              68

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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CharactersAY2122 S1              71

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.AY2122 S1              75

Not every real number can be presented precisely

E.g., 0.1 + 0.2 is 0.30000000000000004

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foodpanda

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Rule: Use integer type unless you absolutely need to use a real number type.AY2122 S1              78

We normally use 32, 64, or 128 bits to represent real numbers.AY2122 S1              79

A variable needs a type to be interpreted correctly.AY2122 S1              80

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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HomeworkProblem 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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Lecture 2

16 August 2021

Reminders

Reminders

Accounts

Why Unix CLI?

Why vim?

Stackoverflow 2021 Developer Survey

Tutorials and Labs

Tutorial 1

Lab 1

Flowchart

Functions

Find The Range

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

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

Wishful Thinking

Wishful Thinking

A C program is just a collection of functions!

A C program is just a collection of functions

Find the Mean

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

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

Find the Std Dev

Let's break it down into sub-problems

Wishful Thinking

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.

Find the maximum among these numbers

Find the maximum among these numbers

Compare 12 to the maximum among

Wishful Thinking

Let max'(L, i, j)max'(L, i, j) returns the maximum among l_i, l_{i+1} \ldots l_jl_i, l_{i+1} \ldots l_j

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

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

if ii equals jj, max'(L, i, j)max'(L, i, j) is just l_il_i

Find the maximum among

Wishful Thinking

Compare the maximum among these numbers

With the maximum among these numbers

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

if jj equals ii, max(L,i,j)max(L,i,j) is just l_il_i.

Divide and Conquer

Find the factorial of nn

Recursion

A function calling itself

Types

1010010101010101001111010.. can mean

A variable needs a type to be interpreted correctly.

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

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

1 bit: 1 or 0

2 bits: 11, 10, 01, or 00

In general, kk bits can represent 2^k2^k values

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

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

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.

Integers

8 bits: 256 different integers

64 bits signed

Characters

8 bits: 127 different symbols using ASCII standards

up to 32 bits: Unicode (UTF-8)

Real numbers

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

Not all of real numbers can be represented.

Not every real number can be presented precisely

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

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

A variable needs a type to be interpreted correctly.

Homework

Reminders

Help

Why `vim`?

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

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

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

Compare `12` to the maximum among

Let $max'(L, i, j)$ returns the maximum among $l_i, l_{i+1} \ldots l_j$

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

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

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

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

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

Find the factorial of $n$

`1010010101010101001111010..` can mean

1 bit: `1` or `0`

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

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

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

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