add option to set minimum pace in sat solver

sat.py

@@ -29,6 +29,14 @@ class Literals():
                     }
                 }
 
+        self.pace = {
+            -1: Int(instance.initial_pace)
+            , **{
+                m: Symbol('m{}pace'.format(m), INT)
+                for m in range(instance.max_winning_moves)
+            }
+        }
+
         # strikes[m][i] == "after move m we have at least i strikes"
         self.strikes = {
                     -1: {i: Bool(i == 0) for i in range(0, instance.num_strikes + 1)}    # no strikes when we start
@@ -117,7 +125,7 @@ class Literals():
         self.incr_clues = {m: Symbol('m{}c+'.format(m)) for m in range(instance.max_winning_moves)}
 
 
-def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optional[GameState]]:
+def solve_sat(starting_state: GameState | HanabiInstance, min_pace: Optional[int] = 0) -> Tuple[bool, Optional[GameState]]:
     if isinstance(starting_state, HanabiInstance):
         instance = starting_state
         game_state = GameState(instance)
@@ -143,6 +151,9 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
         for i in range(0, 10):
             ls.clues[first_turn - 1] = Int(game_state.clues)
 
+        # set initial pace
+        ls.pace[first_turn - 1] = Int(game_state.pace)
+
         # set initial strikes
         for i in range(0, instance.num_strikes + 1):
             ls.strikes[first_turn - 1][i] = Bool(i <= game_state.strikes)
@@ -198,8 +209,12 @@ def solve_sat(starting_state: GameState | HanabiInstance) -> Tuple[bool, Optiona
         Implies(ls.incr_clues[m], Equals(ls.clues[m], ls.clues[m-1] + 1)),
         Implies(And(Or(ls.discard_any[m], ls.dummyturn[m]), Not(ls.incr_clues[m])), Equals(ls.clues[m], ls.clues[m-1])),
 
-        Iff(ls.half_clue[m], Or(And(ls.half_clue[m-1], Not(ls.incr_clues[m])), And(Not(ls.half_clue[m-1])), ls.incr_clues[m]))
+        # change of pace
-        if instance.clue_starved else Bool(True),
+        Implies(And(ls.discard_any[m], Or(ls.strike[m], Not(ls.play[m]))), Equals(ls.pace[m], ls.pace[m-1] - 1)),
+        Implies(Or(Not(ls.discard_any[m]), And(Not(ls.strike[m]), ls.play[m])), Equals(ls.pace[m], ls.pace[m-1])),
+
+        # pace is nonnegative
+        GE(ls.pace[m], Int(min_pace)),
 
         ## more than 8 clues not allowed, ls.discarding produces a strike
         # Note that this means that we will never strike while not at 8 clues.
@@ -312,6 +327,7 @@ def log_model(model, cur_game_state, ls: Literals):
         logger.debug('strikes: ' + ''.join(str(i) for i in range(1, 3) if model.get_py_value(ls.strikes[m][i])))
         logger.debug('draw: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(cur_game_state.progress, cur_game_state.instance.deck_size) if model.get_py_value(ls.draw[m][i])))
         logger.debug('discard: ' + ', '.join('{}: {}'.format(i, deck[i]) for i in range(cur_game_state.instance.deck_size) if model.get_py_value(ls.discard[m][i])))
+        logger.debug('pace: {}'.format(model.get_py_value(ls.pace[m])))
         for s in range(0, cur_game_state.instance.num_suits):
             logger.debug('progress {}: '.format(COLOR_INITIALS[s]) + ''.join(str(r) for r in range(1, 6) if model.get_py_value(ls.progress[m][s, r])))
         flags = ['discard_any', 'draw_any', 'play', 'play5', 'incr_clues', 'strike', 'extraround', 'dummyturn']
@@ -362,7 +378,7 @@ def run_deck():
         for _ in range(17):
             strat.make_move()
 
-    solvable, sol = solve_sat(gs)
+    solvable, sol = solve_sat(gs, 0)
     if solvable:
         print(sol)
         print(link(sol))