\subsection{Solution}
Finding this solution takes less then $35$ seconds and is shown in
-Figure~\ref{fig:s2}.
+Table~\ref{tab:s2}.
-Light gray blocks represent regular components and the darker gray
-blocks represent power components.
-
-\begin{figure}[H]
+\begin{table}[H]
\centering
- \includegraphics[scale=0.70]{s2.png}
-\label{fig:s2}
+ \input{a2.tex}
+\label{tab:s2}
\caption{Solution visualization for problem 2}
-\end{figure}
+\end{table}
\subsection{Solution}
The bash script finds and shows the minimal solution in which all jobs are
finished in $37$ time units. Finding this solution takes less then $0.85$
-seconds and is shown in Figure~\ref{fig:s3}.
+seconds and is shown in Figure~\ref{tab:s3}.
-Light gray blocks represent normal tasks and the darker gray blocks represent
-tasks from $J'$.
-
-\begin{figure}[H]
+\begin{table}[H]
\centering
- \includegraphics[width=\linewidth]{s3.png}
-\label{fig:s3}
+ \input{a3.tex}
+\label{tab:s3}
\caption{Solution visualization for problem 3}
-\end{figure}
+\end{table}
the step chosen in transition between iterations.
\begin{table}[H]
\centering
- $\begin{array}{cc|ccccc}
- \toprule
- n & i & a_2 & a_3 & a_4 & a_5 & a_6\\
- \midrule
- 0 & - & 2 & 3 & 4 & 5 & 6\\
- 1 & 4 & 2 & 3 & \mathbf{8} & 5 & 6\\
- 2 & 5 & 2 & 3 & 8 & \mathbf{14} & 6\\
- 3 & 2 & \mathbf{4} & 3 & 8 & 14 & 6\\
- 4 & 4 & 4 & 3 & \mathbf{17} & 14 & 6\\
- 5 & 5 & 4 & 3 & 17 & \mathbf{23} & 6\\
- 6 & 6 & 4 & 3 & 17 & 23 & \mathbf{30}\\
- 7 & 5 & 4 & 3 & 17 & \mathbf{47} & 30\\
- 8 & 4 & 4 & 3 & \mathbf{50} & 47 & 30\\
- 9 & 3 & 4 & \mathbf{54} & 50 & 47 & 30\\
- 10 & 6 & 4 & 54 & 50 & 47 & \mathbf{54}\\
- \bottomrule
- \end{array}$
+\input{a4.tex}
\caption{Solution table for problem 4}
\label{tab:s4}
\end{table}
%.fmt: pre.tex
$(LATEX) -ini -jobname="$(basename $@)" "&$(LATEX) $<\dump"
-a%.tex: src/a%.bash
+a%.tex: src/a%.bash src src/a%.py
bash $< $@ >/dev/null
clean:
\maketitle
\tableofcontents
+\setcounter{section}{-1}
\section{Introduction}
Implementing all the problems by hand in SMT-Lib format would be too much work
and therefore all problems have an accompanying bash script that does the
#!/usr/bin/env python3
import sys
+import re
trucks = {}
pallets = {'p': 'Prittles', 'n': 'Nuzzles', 'c': 'Crottles',
's': 'Skipples', 'd': 'Dupples'}
for line in sys.stdin:
- if line.startswith('(='):
- truck = line[4]
- pallet = line[5]
-
- number = int(line[7:-2])
- trucks[truck] = trucks.get(truck, {})
- trucks[truck][pallets[pallet]] = number
+ match = re.match('\(= t(?P<t>\d+)(?P<p>.) (?P<v>\d+)\)', line)
+ if match:
+ trucks[match.group('t')] = trucks.get(match.group('t'), {})
+ trucks[match.group('t')][pallets[match.group('p')]] = \
+ int(match.group('v'))
print('$\\begin{array}{|l|lllll|}')
print('\t\\toprule')
-print('\tTruck & {}\\\\'.format(' & '.join(sorted(pallets.values()))))
+print('\t\\text{{Truck}} & {}\\\\'.format(
+ ' & '.join('\\text{{{}}}'.format(p) for p in sorted(pallets.values()))))
print('\t\\midrule')
for truck in sorted(trucks):
print('\t{} & {}\\\\'.format(truck, ' & '.join(
str(p[1]) for p in sorted(trucks[truck].items()))))
print('\t\\midrule')
-print('\tTotal & {}\\\\'.format(' & '.join(
+print('\t\\text{{Total}} & {}\\\\'.format(' & '.join(
str(sum(t[p] for t in trucks.values())) for p in
sorted(pallets.values()))))
print('\t\\bottomrule')
-python3 a2.py | yices-smt -m
+#!/bin/bash
+MAXX=29
+MAXY=22
+PD=17
+PC="1 2 3"
+RC="4 5 6 7 8 9 10 11"
+
+function wp {
+ case $1 in
+ 1) echo 3;;
+ 2) echo 3;;
+ 3) echo 3;;
+ 4) echo 8;;
+ 5) echo 11;;
+ 6) echo 9;;
+ 7) echo 17;;
+ 8) echo 19;;
+ 9) echo 9;;
+ 10) echo 7;;
+ 11) echo 9;;
+ *);;
+ esac
+}
+
+function hp {
+ case $1 in
+ 1) echo 1;;
+ 2) echo 1;;
+ 3) echo 1;;
+ 4) echo 6;;
+ 5) echo 5;;
+ 6) echo 6;;
+ 7) echo 4;;
+ 8) echo 3;;
+ 9) echo 5;;
+ 10) echo 5;;
+ 11) echo 7;;
+ *);;
+ esac
+}
+
+function generate {
+ local i j
+ echo "(benchmark a4.smt"
+ echo ":logic QF_UFLIA"
+ echo ":extrafuns ("
+ for i in $PC $RC; do
+ echo "(c${i}x Int) (c${i}y Int) (c${i}w Int) (c${i}h Int)"
+ done
+ echo ")"
+ echo ":formula"
+ echo "(and"
+ for i in $PC $RC; do
+ echo "(or"
+ echo "(and (= c${i}w $(wp $i)) (= c${i}h $(hp $i)))"
+ echo "(and (= c${i}w $(hp $i)) (= c${i}h $(wp $i)))"
+ echo ")"
+
+ echo "(> c${i}x 0) (> c${i}y 0)"
+ echo "(<= (+ c${i}x c${i}w) $MAXX) (<= (+ c${i}y c${i}h) $MAXY)"
+
+ for j in $PC $RC; do
+ if [ $i != $j ]; then
+ echo "(or"
+ echo "(> c${i}x (+ c${j}x c${j}w)) (< (+ c${i}x c${i}w) c${j}x)"
+ echo "(> c${i}y (+ c${j}y c${j}h)) (< (+ c${i}y c${i}h) c${j}y)"
+ echo ")"
+ fi
+ done
+ done
+
+ for i in $PC; do
+ for j in $PC; do
+ if [ $i != $j ]; then
+ echo "(or"
+ echo "(> (- (+ c${i}x (/ c${i}w 2)) (+ c${j}x (/ c${j}w 2))) $PD)"
+ echo "(> (- (+ c${j}x (/ c${j}w 2)) (+ c${i}x (/ c${i}w 2))) $PD)"
+ echo "(> (- (+ c${i}y (/ c${i}h 2)) (+ c${j}y (/ c${j}h 2))) $PD)"
+ echo "(> (- (+ c${j}y (/ c${j}h 2)) (+ c${i}y (/ c${i}h 2))) $PD)"
+ echo ")"
+ fi
+ done
+ done
+
+ for i in $RC; do
+ echo "(or"
+ for j in $PC; do
+ if [ $i != $j ]; then
+ echo "(not (or "
+ echo "(> c${i}x (+ c${j}x 1 c${j}w)) (< (+ c${i}x c${i}w) (- c${j}x 1))"
+ echo "(> c${i}y (+ c${j}y 1 c${j}h)) (< (+ c${i}y c${i}h) (- c${j}y 1))"
+ echo "))"
+ fi
+ done
+ echo ")"
+ done
+ echo "))"
+}
+generate | yices-smt -m | python3 src/a2.py > $1
#!/usr/bin/env python3
-pc = [(4, 2), (4, 2), (4, 2)]
-rc = [(9, 7), (12, 6), (10, 7), (18, 5), (20, 4), (10, 6), (8, 6), (10, 8)]
-mx = 29
-my = 22
-pd = 17
+import sys
+import re
-# Print variables and preamble
-print('(benchmark a4.smt')
-print(':logic QF_UFLIA')
-print(':extrafuns (')
-for i, (w, h) in enumerate(pc+rc, 1):
- print('(c{}x Int)'.format(i), end=' ')
- print('(c{}y Int)'.format(i), end=' ')
- print('(c{}w Int)'.format(i), end=' ')
- print('(c{}h Int)'.format(i))
-print(')')
+comps = {}
-print(':formula')
-print('(and')
+for line in sys.stdin:
+ match = re.match('\(= c(?P<c>\d+)(?P<t>.) (?P<v>\d+)\)', line)
+ if match:
+ comps[match.group('c')] = comps.get(match.group('c'), {})
+ comps[match.group('c')][match.group('t')] = int(match.group('v'))
-# Print the PC and RC subformulas
-for i, (w, h) in enumerate(pc+rc, 1):
- # Print the width and height
- print(('(or '
- '(and (= c{0}w {1}) (= c{0}h {2})) '
- '(and (= c{0}w {2}) (= c{0}h {1})))').format(i, w-1, h-1))
- # Print the bounds of the coordinates
- print(('(> c{0}x 0) (> c{0}y 0)'
- '(<= (+ c{0}x c{0}w) {1}) (<= (+ c{0}y c{0}h) {2})'
- ).format(i, mx, my))
+maxx = max(c['x']+c['w'] for c in comps.values())
+maxy = max(c['y']+c['h'] for c in comps.values())
+print('$\\begin{{array}}{{|l|{}|}}'.format('@{}c@{}'*maxx))
+print('\t\\toprule')
+print('\t & {}\\\\'.format(
+ ' & '.join(map(str, range(1, maxx+1)))))
+print('\t\\midrule')
+for y in range(1, maxy+1):
+ print('\t{} & '.format(y), end='')
+ for x in range(1, maxx+1):
+ cs = [c for c in comps if
+ comps[c]['y'] + comps[c]['h'] >= y and comps[c]['y'] <= y and
+ comps[c]['x'] + comps[c]['w'] >= x and comps[c]['x'] <= x]
+ if cs:
+ print('\\hspace{{.5mm}}{}\\hspace{{.5mm}}'.format(cs[0]), end='')
+ if x != maxx:
+ print(' & ', end='')
+ print('\\\\')
- # Print the non overlap with others
- for j in range(1, 1+len(pc+rc)):
- if i != j:
- print((
- '(or '
- '(> c{0}x (+ c{1}x c{1}w)) (< (+ c{0}x c{0}w) c{1}x) '
- '(> c{0}y (+ c{1}y c{1}h)) (< (+ c{0}y c{0}h) c{1}y)'
- ')').format(i, j))
-
-# Print the PC distance to eachother
-for i, _ in enumerate(pc, 1):
- for j, _ in enumerate(pc, 1):
- if i != j:
- print(('(or '
- '(> (- (+ c{0}x (/ c{0}w 2)) (+ c{1}x (/ c{1}w 2))) {2}) '
- '(> (- (+ c{1}x (/ c{1}w 2)) (+ c{0}x (/ c{0}w 2))) {2}) '
- '(> (- (+ c{0}y (/ c{0}h 2)) (+ c{1}y (/ c{1}h 2))) {2}) '
- '(> (- (+ c{1}y (/ c{1}h 2)) (+ c{0}y (/ c{0}h 2))) {2})'
- ')').format(i, j, pd))
-
- # Print the constraint that they have to be connected to a ps
-for i, _ in enumerate(rc, 1+len(pc)):
- print('(or')
- for j, _ in enumerate(pc, 1):
- print(('(not (or '
- '(> c{0}x (+ c{1}x 1 c{1}w)) (< (+ c{0}x c{0}w) (- c{1}x 1)) '
- '(> c{0}y (+ c{1}y 1 c{1}h)) (< (+ c{0}y c{0}h) (- c{1}y 1))'
- '))').format(i, j))
- print(')')
-
-# Close the and,benchmark parenthesis
-print('))')
+print('\t\\bottomrule')
+print('\\end{array}$')
echo "T=$((i++)) is still unsat"
done
echo "T=$i is sat thus the minimum T=$i"
+generate $i | yices-smt -m | python3 src/a3.py > $1
--- /dev/null
+#!/usr/bin/env python3
+import sys
+import re
+
+schedule = {}
+jobs = set()
+levels = {}
+for line in sys.stdin:
+ match = re.match('\(= j(?P<j>\d+) (?P<x>\d+)\)', line)
+ if match:
+ j = int(match.group('j'))
+ x = int(match.group('x'))
+ jobs.add(j)
+ for t in range(x, x+j):
+ schedule[t] = schedule.get(t, [])
+ schedule[t].append(j)
+
+tmax = max(schedule)+1
+levels = {j:max(schedule[t].index(j) if j in schedule[t] else 0
+ for t in range(1, tmax)) for j in jobs}
+schedule = {k:sorted(v) for k,v in schedule.items()}
+depth = max(map(len, schedule.values()))
+print('$\\begin{{array}}{{|{}}}'.format('@{}c@{}|'*tmax))
+print('\t\\toprule')
+print('\t{}\\\\'.format(' & '.join(map(str, range(1, tmax)))))
+print('\t\\midrule')
+for d in range(depth):
+ print('\t', end='')
+ for t in range(1, tmax):
+ cj = [j for j in jobs if levels[j] == d and j in schedule[t]]
+ if cj:
+ print('\\hspace{{.5mm}}{}\\hspace{{.5mm}}'.format(cj[0]), end='')
+ if t != tmax-1:
+ print(' & ', end='')
+ print('\\\\')
+print('\t\\bottomrule')
+print('\\end{array}$')
i=$((i+1))
done
echo "N=$i is sat thus minimum N=$i"
+generate $i | yices-smt -m | python src/a4.py > $1
--- /dev/null
+#!/usr/bin/env python3
+import sys
+import re
+
+iterations = {}
+
+for line in sys.stdin:
+ match = re.match('\(= i(?P<i>\d+)a(?P<a>\d+) (?P<v>\d+)\)', line)
+ if match:
+ iterations[match.group('i')] = iterations.get(match.group('i'), {})
+ iterations[match.group('i')][match.group('a')] = match.group('v')
+
+print('$\\begin{array}{|l|lllllll|}')
+print('\t\\toprule')
+print('\t\\text{{n}} & a_1 & {} & a_7\\\\'.format(
+ ' & '.join('a_{}'.format(a) for a in sorted(iterations['0']))))
+print('\t\\midrule')
+for i in sorted(iterations, key=int):
+ print('\t{} & 1 & {} & 7\\\\'.format(i, ' & '.join(
+ iterations[i][a] for a in sorted(iterations[i], key=int)
+ )))
+print('\t\\bottomrule')
+print('\\end{array}$')
repositories / ar1516.git / commitdiff