# RC2 algorithm
# basic version with some optimizations
# - process soft constraints in order of highest values first.
# - extract multiple cores, not just one
# - use built-in cardinality constraints, cheap core minimization. 
#
# See also https://github.com/pysathq/pysat and papers in CP 2014, JSAT 2015.

from z3 import *

def tt(s, f):
    return is_true(s.model().eval(f))

def add(Ws, f, w):
    Ws[f] = w + (Ws[f] if f in Ws else 0)

def sub(Ws, f, w):
    w1 = Ws[f]
    if w1 > w:
        Ws[f] = w1 - w
    else:
        del(Ws[f])

class RC2:

    def __init__(self, s):
        self.bounds = {}
        self.names = {}
        self.solver = s
        self.solver.set("sat.cardinality.solver", True)
        self.solver.set("sat.core.minimize", True)
        self.solver.set("sat.core.minimize_partial", True)
        
    def at_most(self, S, k):
        fml = simplify(AtMost(S + [k]))
        if fml in self.names:
           return self.names[fml]
        name = Bool("%s" % fml)
        self.solver.add(Implies(name, fml))
        self.bounds[name] = (S, k)
        self.names[fml] = name
        return name

    def print_cost(self):
        print("cost [", self.min_cost, ":", self.max_cost, "]")

    def update_max_cost(self):
        self.max_cost = min(self.max_cost, self.get_cost())
        self.print_cost()
    
    # sort W, and incrementally add elements of W
    # in sorted order to prefer cores with high weight.
    def check(self, Ws):
        def compare(fw):
            f, w = fw
            return -w
        ws = sorted([(k,Ws[k]) for k in Ws], key = compare)
        i = 0
        while i < len(ws):
           j = i
           # increment j until making 5% progress or exhausting equal weight entries
           while (j < len(ws) and ws[j][1] == ws[i][1]) or (i > 0 and (j - i)*20 < len(ws)):
              j += 1
           i = j
           r = self.solver.check([ws[j][0] for j in range(i)])
           if r == sat:
              self.update_max_cost()
           else:
              return r
        return sat
             
    def get_cost(self):
        return sum(self.Ws0[c] for c in self.Ws0 if not tt(self.solver, c))

    # Retrieve independent cores from Ws
    def get_cores(self, Ws):
        cores = []
        while unsat == self.check(Ws):            
            core = list(self.solver.unsat_core())
            print (self.solver.statistics())
            if not core:
               return unsat
            w = min([Ws[c] for c in core])
            for f in core:
                sub(Ws, f, w)
            cores += [(core, w)]
        self.update_max_cost()
        return cores
           
    # Add new soft constraints to replace core
    # with weight w. Allow to weaken at most
    # one element of core. Elements that are
    # cardinality constraints are weakened by
    # increasing their bounds. Non-cardinality
    # constraints are weakened to "true". They
    # correspond to the constraint Not(s) <= 0, 
    # so weakening produces Not(s) <= 1, which
    # is a tautology.
    def update_bounds(self, Ws, core, w):
        for f in core:
           if f in self.bounds:
              S, k = self.bounds[f]
              if k + 1 < len(S):
                 add(Ws, self.at_most(S, k + 1), w)                
        add(Ws, self.at_most([mk_not(f) for f in core], 1), w)

    # Ws are weighted soft constraints
    # Whenever there is an unsatisfiable core over ws
    # increase the limit of each soft constraint from a bound
    # and create a soft constraint that limits the number of
    # increased bounds to be at most one.
    def maxsat(self, Ws):
        self.min_cost = 0
        self.max_cost = sum(Ws[c] for c in Ws)
        self.Ws0 = Ws.copy()
        while True:
            cores = self.get_cores(Ws)
            if not cores:
                break
            if cores == unsat:
               return unsat
            for (core, w) in cores:
               self.min_cost += w
               self.print_cost()
               self.update_bounds(Ws, core, w)            
        return self.min_cost, { f for f in self.Ws0 if not tt(self.solver, f) }

    def from_file(self, file):
        opt = Optimize()
        opt.from_file(file)
        self.solver.add(opt.assertions())
        obj = opt.objectives()[0]
        Ws = {}        
        for f in obj.children():
            assert(f.arg(1).as_long() == 0)
            add(Ws, f.arg(0), f.arg(2).as_long())
        return self.maxsat(Ws)
    
    def from_formulas(self, hard, soft):      
        self.solver.add(hard)
        Ws = {}        
        for f, cost in soft:
            add(Ws, f, cost)
        return self.maxsat(Ws)


def main(file):
    s = SolverFor("QF_FD")
    rc2 = RC2(s)
    set_param(verbose=0)
    cost, falses = rc2.from_file(file)
    print(cost)
    print(s.statistics())

if len(sys.argv) > 1:
   main(sys.argv[1])

# main(<myfile>)
    
