added lecture examples

Lecture2/colours-solution.py

@@ -0,0 +1,28 @@
+from itertools import combinations
+from z3 import *
+
+solver = Solver()
+
+Colours = Datatype("Colours")
+Colours.declare("RED")
+Colours.declare("BLUE")
+Colours.declare("GREEN")
+Colours.declare("YELLOW")
+
+Colour = Colours.create()
+f    = Function('f', IntSort(), Colour)
+
+variables = list()
+for i in range(0,5):
+    variables.append(Int(f"x{i}"))
+    solver.add(0 <= variables[-1])
+    solver.add(variables[-1] <= 5)
+
+solver.add(Distinct(variables))
+
+for combi in combinations(variables,2):
+    solver.add(Implies(Abs(combi[0] - combi[1]) == 1, f(combi[0]) != f(combi[1])))
+
+result = solver.check()
+if result == sat:
+    print(solver.model())

Lecture2/level0.txt

@@ -0,0 +1,13 @@
+XX_________________________________XX
+_____________________________________
+________________1____________________
+_____________________________________
+_____________________________________
+_____________________________________
+_____________________________________
+_____________________________________
+_____________________________________
+_____________________________________
+_2_________________________________3_
+_____________________________________
+XX_________________________________XX

Lecture2/level1.txt

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+XXXXXXXX
+X_1__3__
+X_2__4__

Lecture2/level2.txt

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+XX___________________________XX
+_______________________________
+_2___________________________3_
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+_______________________________
+______________________1________
+_______________________________
+_______________________________
+_______________________________
+XX___________________________XX

Lecture2/maestria-in-class.py

@@ -0,0 +1,99 @@
+# coding: utf-8
+import os, sys
+from z3 import *
+import string
+# get the playground information
+directory = os.path.dirname(os.path.realpath(__file__))
+fname = directory + "/" + "test0.txt"
+
+if len(sys.argv) == 2:
+    fname = sys.argv[1]
+
+with open(fname) as f:
+    playground = f.read()
+playground = [[c for c in row] for row in playground.strip().split("\n")]
+
+# get the playground size
+size_y = len(playground)
+assert(size_y != 0)
+size_x = len(playground[0])
+assert(size_x != 0)
+for row in playground:
+    assert(len(row) == size_x)
+
+bells = {}
+for i in range(size_y):
+    for j in range(size_x):
+        c = playground[i][j]
+        if ord(c) in range(ord("1"), ord("9") + 1):
+            assert(int(c) not in bells.keys())
+            bells[int(c)] = (j, i)
+
+################################### Maestria ###################################
+
+
+print(f"Playground size : {size_x} x {size_y}")
+print("Playground:")
+print("\n".join(["".join(i) for i in playground]))
+print("Bell positions:")
+print(bells)
+print("\n")
+
+# create the solver
+solver = Solver()
+
+fudge_x, fudge_y = Ints("fudge_x fudge_y")
+
+
+# position must be in the board
+solver.add(fudge_x >= 0, fudge_x < size_x, fudge_y >= 0, fudge_y < size_y)
+
+# position must be on walkable cell
+for i in range(size_y):
+    for j in range(size_x):
+        if playground[i][j] != "_":
+            solver.add(Not(And(fudge_y == i, fudge_x == j)))
+
+# encode distances in formula
+distances = {bell: None for bell in bells.keys()}
+for bell, (x,y) in bells.items():
+    distances[bell] = (fudge_x - x) * (fudge_x - x) + (fudge_y - y) * (fudge_y - y)
+#
+# enforce ordering of distances
+distances_sorted = [distances[b] for b in sorted(bells.keys())]
+for i in range(len(distances_sorted) - 1):
+    near = distances_sorted[i]
+    far = distances_sorted[i+1]
+    solver.add(near < far)
+# call the solver and check satisfiability
+while solver.check() == sat:
+#result = solver.check()
+#if result == sat:
+    m = solver.model()
+    if fudge_x is not None and fudge_y is not None:
+        pos_x = m[fudge_x].as_long()
+        pos_y = m[fudge_y].as_long()
+        playground[pos_y][pos_x] = "F"
+        solver.add(Or(fudge_x != pos_x, fudge_y != pos_y))
+
+################################################################################
+
+from colorama import Fore, Back, Style
+
+cols = [Fore.BLUE, Fore.GREEN, Fore.RED, Fore.YELLOW, Fore.MAGENTA, Fore.CYAN]
+tones = [Style.BRIGHT, Style.DIM]
+cols = sum([[c + t for c in cols] for t in tones], [])
+
+if sys.stdout.isatty():
+    for bell in sorted(list(bells.keys())):
+        x, y = bells[bell]
+        playground[y][x] = Back.BLACK + cols[bell - 1] + playground[y][x] + Style.RESET_ALL
+    for y in range(size_y):
+        for x in range(size_x):
+            c = playground[y][x]
+            if c == "_": playground[y][x] = Fore.BLACK + Back.WHITE + c + Style.RESET_ALL
+            if c == "X": playground[y][x] = Fore.WHITE + Back.BLACK + c + Style.RESET_ALL
+            if c == "F": playground[y][x] = Fore.BLACK + Back.WHITE + c + Style.RESET_ALL
+
+text = "\n".join(["".join([c for c in row]) for row in playground])
+print(text)

Lecture2/xkcd_287.py

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+#!/usr/bin/python3
+
+from z3 import *
+
+a,b,c,d,e,f = Ints('a b c d e f')
+s = Solver()
+s.add(215*a + 275*b + 335*c + 355*d + 420*e + 580*f == 1505, a>=0, b>=0, c>=0, d>=0, e>=0, f>=0)
+
+results=[]
+while True:
+    if s.check() == sat:  #
+        m = s.model()     #
+        print(m)          #
+        results.append(m)
+        #block = [a != m[a].as_long(), b != m[b].as_long(), c != m[c].as_long(), d != m[d].as_long(), e != m[e].as_long(), f != m[f].as_long()]
+        #Different approach: Iterate over all entries in the model
+        block = []
+        for d in m.decls():
+            #print(d, type(d), d(), type(d()), m[d], type(m[d]))
+            block.append(d() != m[d].as_long())
+        s.add(Or(block))
+    else:
+        print ("All results enumerated, total =", len(results))
+        break