BookML test: algorithm2e.sty — package for algorithms release 5.2


Data: this text


Result: how to write algorithm with LaTeXLaTeX2e

initialization;


while not at end of this document do

     
read current section;

     
if understand then

          
go to next section;

          
current section becomes this one;

else

          
go back to the beginning of current section;

end if

end while

Algorithm 1 How to write algorithms

input : A bitmap $Im$ of size $w\times l$


output : A partition of the bitmap


special treatment of the first line;


for  $i\leftarrow 2$  to  $l$  do

     
special treatment of the first element of line  $i$ ;

     
for  $j\leftarrow 2$  to  $w$  do

          
left  $\leftarrow$  FindCompress( $Im[i,j-1]$ );

          
up  $\leftarrow$  FindCompress( $Im[i-1,]$ );

          
this  $\leftarrow$  FindCompress( $Im[i,j]$ );

          
if left compatible with this then // O(left,this)==1

               
if left  $<$  this then Union(left,this);

               
else Union(this,left);

13 end if

14 if up compatible with this then // O(up,this)==1

               
if up  $<$  this then Union(up,this);

               
// this is put under up to keep tree as flat as possible

               
else Union(this,up);

               // this linked to up

19 end if

21 end for

22 foreach element $e$ of the line $i$ do FindCompress(p);

24 end for

Algorithm 2 disjoint decomposition

Data: $G=(X,U)$ such that $G^{tc}$ is an order.


Result:  $G^{\prime}=(X,V)$  with  $V\subseteq U$  such that  $G^{\prime tc}$  is an
interval order.


begin

     
 $V\longleftarrow U$

     
 $S\longleftarrow\emptyset$

     
for  $x\in X$  do

          
 $NbSuccInS(x)\longleftarrow 0$

          
 $NbPredInMin(x)\longleftarrow 0$

          
 $NbPredNotInMin(x)\longleftarrow|ImPred(x)|$

for $x\in X$ do

          
if  $NbPredInMin(x)=0$  and  $NbPredNotInMin(x)=0$  then

               
 $AppendToMin(x)$

1 while $S\neq\emptyset$ do

REM

          
 remove  $x$  from the list of  $T$  of maximal index

          
while  $|S\cap ImSucc(x)|\neq|S|$  do

               
for  $y\in S-ImSucc(x)$  do

                    
{ remove from  $V$  all the arcs  $zy$  : }

                    
for  $z\in ImPred(y)\cap Min$  do

                         
remove the arc  $zy$  from  $V$

                         
 $NbSuccInS(z)\longleftarrow NbSuccInS(z)-1$

                         
move  $z$  in  $T$  to the list preceding its present list

                         
{i.e. If  $z\in T[k]$ , move  $z$  from  $T[k]$  to
 $T[k-1]$ }

$NbPredInMin(y)\longleftarrow 0$

                    
 $NbPredNotInMin(y)\longleftarrow 0$

                    
 $S\longleftarrow S-\{y\}$

                    
 $AppendToMin(y)$

$RemoveFromMin(x)$

Algorithm 3 IntervalRestriction


Function FnRecursive(some args) /* algorithm as a recursive function  */

     
Data: Some input data

     these inputs can be displayed on several lines and one
input can be wider than line’s width.

     
Result: Same for output data

     
/* this is a comment to tell you that we will now really start code  */

     
if this is true then /* a simple if but with a comment on the same line  */

          
we do that, else nothing

          
/* we will include other if so you can see this is possible  */

          
if we agree that then

               
we do that

9 else

               
else we will do a more complicated if using else if

               
if this first condition is true then

                    
we do that

               
else if this other condition is true then

                    
this is done

16 /* else if */

               
else

                    
in other case, we do this

20 /* else */

22 end if

24 end if

26 end if

27 /* now loops */

     
for  $i=0$  to  $n$  do

          
a for loop

31 end for

32 while $i<n$ do

          
a while loop including a repeat–until loop

          
repeat

               
do this things

37 until this end condition

38 end while

     They are many other possibilities and customization possible that you have to
discover by reading the documentation.

40 end

Algorithm 4 Generic example with most classical expressions derived in pseudo-code