Advanced Bash−Scripting Guide

Advanced Bash−Scripting Guide
# Q(1) = Q(2) = 1
# Q(n) = Q(n − Q(n−1)) + Q(n − Q(n−2)), for n>2
# This is a "chaotic" integer series with strange and unpredictable behavior.
# The first 20 terms of the series are:
# 1 1 2 3 3 4 5 5 6 6 6 8 8 8 10 9 10 11 11 12
# See Hofstadter's book, "Goedel, Escher, Bach: An Eternal Golden Braid",
# p. 137, ff.
LIMIT=100 # Number of terms to calculate
LINEWIDTH=20 # Number of terms printed per line
Q[1]=1 # First two terms of series are 1.
Q[2]=1
echo
echo "Q−series [$LIMIT terms]:"
echo −n "${Q[1]} "
# Output first two terms.
echo −n "${Q[2]} "
for ((n=3; n 2
# Need to break the expression into intermediate terms,
# since Bash doesn't handle complex array arithmetic very well.
let "n1 = $n − 1"
let "n2 = $n − 2"
# n−1
# n−2
t0=`expr $n − ${Q[n1]}` # n − Q[n−1]
t1=`expr $n − ${Q[n2]}` # n − Q[n−2]
T0=${Q[t0]}
T1=${Q[t1]}
Q[n]=`expr $T0 + $T1`
echo −n "${Q[n]} "
# Q[n − Q[n−1]]
# Q[n − Q[n−2]]
# Q[n − Q[n−1]] + Q[n − ![n−2]]
if [ `expr $n % $LINEWIDTH` −eq 0 ] # Format output.
then # mod
echo # Break lines into neat chunks.
fi
done
echo
exit 0
# This is an iterative implementation of the Q−series.
# The more intuitive recursive implementation is left as an exercise.
# Warning: calculating this series recursively takes a *very* long time.
−−
Bash supports only one−dimensional arrays, however a little trickery permits simulating multi−dimensional
ones.
Chapter 26. Arrays 306