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algorithms.sty - biu din thut ton
Nguyn Hu inKhoa Ton - C - Tin hc
HKHTN H Ni, HQGHN
1 Gii thiu gi lnh
Gi lnh th hin cc thut ton, c ti a ch
http://tug.ctan.org/tex-archive/macros/latex/contrib/algorithms/
Tc gi ca gi lnh l Rogrio Brito.
2 Cch s dng
2.1 Mi trng algorithmic
1. y l mi trng chnh cha cc lnh iu khin ca thut ton.
V d:
\begin{algorithmic}
\STATE $S \leftarrow 0$
\end{algorithmic}
Kt qu:
S 0
2. nh s cc dng lnh
\begin{algorithmic}[1]
\FORALL{$i$ such that $0\leq i\leq 10$}
\STATE carry out some processing
\ENDFOR
\end{algorithmic}
Kt qu:
1: for all i such that 0 i 10 do2: carry out some processing3:
end for
2.2 Cc loi lnh trong mi trng
1. Lnh n gin \STATE v d:
\begin{algorithmic}
\STATE $S \leftarrow 0$
\end{algorithmic}
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Kt qu
S 0
2. Lnh if-then-else
\IF{} \ENDIF
\IF{} \ELSE \ENDIF
\IF{} \ELSIF{} \ELSE \ENDIF
V d:
\begin{algorithmic}
\IF{C1}
\STATE B1
\ELSIF {C2}
\STATE B2
\ENDIF
\end{algorithmic}
Kt qu:
if C1 thenB1
else if C2 thenB2
end if
3. Lnh for
\FOR{} \ENDFOR
\FORALL{} \ENDFOR
V d:
\begin{algorithmic}[1]
\FORALL{$i$ such that $0\leq i\leq 10$}
\STATE carry out some processing
\ENDFOR
\end{algorithmic}
Kt qu:
1: for all i such that 0 i 10 do2: carry out some processing3:
end for
C thm TO
\begin{algorithmic}
\FOR{$i=0$ \TO $10$}
\STATE carry out some processing
\ENDFOR
\end{algorithmic}
for i = 0 to 10 docarry out some processing
end for
4. Vng lp while
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\WHILE{} \ENDWHILE
V d
\begin{algorithmic}
\WHILE{some condition holds}
\STATE carry out some processing
\ENDWHILE
\end{algorithmic}
Kt qu:
while some condition holds docarry out some processing
end while
5.Vng lp repeat-until
\REPEAT \UNTIL{}
V d
\begin{algorithmic}
\REPEAT
\STATE carry out some processing
\UNTIL{some condition is met}
\end{algorithmic}
Kt qu:
repeat
carry out some processinguntil some condition is met
6. Lp v hn
\LOOP \ENDLOOP
V d:
\begin{algorithmic}
\LOOP
\STATE this processing will be repeated forever
\ENDLOOP
\end{algorithmic}
loop
this processing will be repeated foreverend loop
7. Lnh logic
\AND
\OR
\XOR
\NOT
V d:
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\begin{algorithmic}
\IF{\NOT ($year \bmod 400$ \XOR $year \bmod 100$ \XOR $year
\bmod 4$)}
\STATE $year$ does not represent a leap year.
\ENDIF
\end{algorithmic}
if not (year mod 400 xor year mod 100 xor year mod 4) thenyear
does not represent a leap year.
end if
8. Lnh tr v gi tr v gi tr ng sai
\RETURN
V d:
\begin{algorithmic}
\IF{$n$ is odd}
\RETURN \TRUE
\ELSE
\RETURN \FALSE
\ENDIF
\end{algorithmic}
if n is odd thenreturn true
else
return false
end if
9. Cc lnh khc
\PRINT
\begin{algorithmic}
\PRINT \texttt{Hello, World!}
\end{algorithmic}
print Hello, World!
\COMMENT{}
\begin{algorithmic}
\STATE do something \COMMENT{this is a comment}
\end{algorithmic}
do something {this is a comment}
10. V d tng hp
\begin{algorithmic}
\REQUIRE $n \geq 0$
\ENSURE $y = x^n$
\STATE $y \leftarrow 1$
\STATE $X \leftarrow x$
\STATE $N \leftarrow n$
\WHILE{$N \neq 0$}
\IF{$N$ is even}
\STATE $X \leftarrow X \times X$
\STATE $N \leftarrow N / 2$
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\ELSE[$N$ is odd]
\STATE $y \leftarrow y \times X$
\STATE $N \leftarrow N - 1$
\ENDIF
\ENDWHILE
\end{algorithmic}
Require: n 0Ensure: y = xn
y 1X xN nwhile N 6= 0 do
if N is even thenX X XN N/2
else {N is odd}y y XN N 1
end if
end while
2.3 Ty chn v t li cu hnh
1. Lnh \algsetup{indent=lenght} t tht hng lnh
\algsetup{indent=2em}
\begin{algorithmic}[1]
\STATE $a \leftarrow 1$
\IF{$a$ is even}
\PRINT $a$ is even
\ELSE
\PRINT $a$ is odd
\ENDIF
\end{algorithmic}
Kt qu:
a 1if a is even then
print a is evenelse
print a is oddend if
2. t li nh s v du chm
\algsetup{
linenosize=\small,
linenodelimiter=.
}
\begin{algorithmic}[1]
\STATE $i \leftarrow 10$
\RETURN $i$
\end{algorithmic}
1. i 10
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2. return i
3. C th t li ccc lnh trn
\newcommand{\algorithmicrequire}{\textbf{Require:}}
\newcommand{\algorithmicensure}{\textbf{Ensure:}}
\newcommand{\algorithmicend}{\textbf{end}}
\newcommand{\algorithmicif}{\textbf{if}}
\newcommand{\algorithmicthen}{\textbf{then}}
\newcommand{\algorithmicelse}{\textbf{else}}
\newcommand{\algorithmicelsif}{\algorithmicelse\
\algorithmicif}
\newcommand{\algorithmicendif}{\algorithmicend\
\algorithmicif}
\newcommand{\algorithmicfor}{\textbf{for}}
\newcommand{\algorithmicforall}{\textbf{for all}}
\newcommand{\algorithmicdo}{\textbf{do}}
\newcommand{\algorithmicendfor}{\algorithmicend\
\algorithmicfor}
\newcommand{\algorithmicwhile}{\textbf{while}}
\newcommand{\algorithmicendwhile}{\algorithmicend\
\algorithmicwhile}
\newcommand{\algorithmicloop}{\textbf{loop}}
\newcommand{\algorithmicendloop}{\algorithmicend\
\algorithmicloop}
\newcommand{\algorithmicrepeat}{\textbf{repeat}}
\newcommand{\algorithmicuntil}{\textbf{until}}
\newcommand{\algorithmicprint}{\textbf{print}}
\newcommand{\algorithmicreturn}{\textbf{return}}
\newcommand{\algorithmictrue}{\textbf{true}}
\newcommand{\algorithmicfalse}{\textbf{false}}
3 Mi trng algorithms
Mi trng ny dng nh s v nhn cho thut ton
\begin{algorithm}
\caption{Calculate $y = x^n$}
\label{alg1}
\begin{algorithmic}
\REQUIRE $n \geq 0 \vee x \neq 0$
\ENSURE $y = x^n$
\STATE $y \leftarrow 1$
\IF{$n < 0$}
\STATE $X \leftarrow 1 / x$
\STATE $N \leftarrow -n$
\ELSE
\STATE $X \leftarrow x$
\STATE $N \leftarrow n$
\ENDIF
\WHILE{$N \neq 0$}
\IF{$N$ is even}
\STATE $X \leftarrow X \times X$
\STATE $N \leftarrow N / 2$
\ELSE[$N$ is odd]
\STATE $y \leftarrow y \times X$
\STATE $N \leftarrow N - 1$
\ENDIF
\ENDWHILE
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\end{algorithmic}
\end{algorithm}
Algorithm 3.1 Calculate y = xn
Require: n 0 x 6= 0Ensure: y = xn
y 1if n < 0 then
X 1/xN n
else
X xN n
end if
while N 6= 0 doif N is even then
X X XN N/2
else {N is odd}y y XN N 1
end if
end while
Lit k danh sch thut ton
\listofalgorithms
t tn li bng danh sch
\newcommand{\listalgorithmname}{List of Algorithms}
Thay tn
\floatname{algorithm}{Procedure}
