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--- computer_science:programming:algorithm [2021/09/25 05:25] – [Loop] mana
+++ computer_science:programming:algorithm [2021/10/14 03:35] (current) – [Gauss Sum] mana
@@ Line 3: / Line 3: @@
 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>
++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"
@@ Line 22: / Line 81: @@
 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
+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
++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 $\Theta(n^2)$