Fuwakami's Archive of Knowledge

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====== Pseudocode ======
Simplified tradeoff between natural and programming language.
Pseudocode is not unique. That is to say that it does not have rigid rules. Different people may have different pseudocode syntax.

===== Design =====
  * Step 1: Do something
  * Step 2: Do something
  * Step 3: Do something
  * ...   : ...
==== Sequential steps ====
A sequential step is a single task; for example ''%%a 1 to x%%''.

==== Conditional steps ====
Ask a question that is answered with a logic answer. The answer can be ''%%true%%''/''%%false%%''.
For example:
<code>
if (x > 0) add 1 to x
else substract 1 from x
</code>

==== Loops ====
Iterative steps.
<code>
add 1/2 cup to mixture
while mixture is dry
</code>

==== Recursion ====
FIXME (This will be filled at a later point.)

==== Case study: addition ====
Example: 

<code>
 472
+593
</code>

----
FIXME
Conceptualise:
<code>
Let m => 1 be number of digits

a<sub>m-1</sub> a<sub>3</sub> a<sub>2</sub> a<sub>1</sub>

=== Algorithm ===
<code>
Step 1: get m (user provides m)
Step 2: get a<sub>m-1</sub>・・・a<sub>1</sub> a<sub>0</sub>, b<sub>m-1</sub>・・・b<sub>1</sub>b<sub>0</sub>
Step 3: set i=0, set carry=0
Step 4: while(i ≤ m-1) do Step 5 to 7
Step 5:   set c<sub>i</sub> = a<sub>i</sub> + b<sub>i</sub> + carry
Step 6:   if(c<sub>i</sub> ≥ 10) then
            set c<sub>i</sub> = c<sub>i</sub> - 10
            set carry = 1
          else
            set carry = 0
Step 7:   set i = i + 1
Step 8: set c<sub>m</sub> = carry
step 9: print c<sub>m</sub> c<sub>m-1</sub> ... c<sub>2</sub> c<sub>1</sub> c<sub>1</sub>
step 10: stop
</code>
===== Squential statements =====
  * Inputs: Get "variable"
    * Ex: get m, get radius
  * Computation: set "variable" = expression
    * Ex: set area = π*radius<sup>2</sup>
  * Output: print "variable"
    * Ex: print area

===== Conditional statements =====

===== Loop =====

<code>
do
    op1
    op2
    op3
while(condition)
</code>

* ''Do while'' loops will execute at least once, online ''while'' loops

===== Sequential Search =====
Data set of N elements: ''13'' ''4'' ''-20'' ''45'' ''112'' ・・・ ''N=10¹³ / 38944''
Therefore the list will be L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>... L<sub>N</sub>
Target: 45 〇　130 ×
This is easy for the brain because the brain is made pattern matching.

<code>
Step 1 get L1, L2, LN, N, Target
Step 2 Set Found = No
Step 3 Set i = 1
Step 4 while (Foundo = No AND i ≤ N) do Step 5 to Step 6
Step 5     if (Li = Target) then
               set Found = Yes
Step 6     else
               set i = i + 1
Step 7 if (Found = Yes) then
           print "Target found"
Step 8 else
           print "Target not found"
Step 9 stop
</code>

===== The Swap =====
x y
5 3
Swap the content of both variable so that X=3 and Y=5
<code>
Step 1 get x, y
Step 2 set temp = x
Step 3 x = y
Step 4 y = temp
Stop 5 Stop
</code>

* For swapping in other algorithm ''swap(x,y)'' can be used instead.

===== Gauss Sum =====
n ≥ 1 
1+2+3+4+...+n

Formula: $\frac{(n+1)*n}{2}$  $\Theta$
FIXME (double check this information)
When talking about efficiency we say that the efficiency of n is $\Theta(n^2)$