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sat.cpp
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sat.cpp
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#include<bits/stdc++.h>
#include "parser.cpp"
using namespace std;
bool compare(int a, int b)
{
if (abs(a) == abs(b))return a < b;
return abs(a) < abs(b);
}
struct Assigned
{
int value;//0 or 1
int depth;//in which layer
int order;
};
//literal have sign, variable does not.
class sat_solver
{
public:
sat_solver(vector<vector<int>> Clauses, int Maxindex, double Decay_constant, int Max_clause_size)
{
clauses = Clauses;
maxindex = Maxindex;
find_clauses.clear();
positive_watch = vector<vector<int>>(maxindex + 5);
negative_watch = vector<vector<int>>(maxindex + 5);
two_literal_watching = vector<vector<int>>(clauses.size());
antecedent = vector<vector<int>>(maxindex + 5);
assignment = vector<Assigned>(maxindex + 5, { -1,-1,-1 });
single_literal.clear();
vsids_value = vector<double>(maxindex * 2 + 5, 0);
assigned_number = 0;
decay_constant = Decay_constant;
max_clause_size = Max_clause_size;
conflict_counter = 0;
}
int valued(int);
void vsids_value_decay();
int vsids_pick();
vector<int> tidy_up_clause(vector<int>);
vector<int> resolve_clauses(vector<int>, vector<int>, int);
bool prepare();
int FirstUIP(vector<int>, int);
int add_new_clause(vector<int>);
void backtrack(int);
int four_case(int, int);
int BCP(int, int);
int DPLL(int, int);
bool check_solve();
map<vector<int>, int> find_clauses;
vector<vector<int>> clauses;
vector<vector<int>> positive_watch;
vector<vector<int>> negative_watch;
vector<vector<int>> two_literal_watching; //store the index of watching literal
vector<vector<int>> antecedent;//what clause imply the variable
vector<Assigned> assignment;
vector<int> single_literal;
vector<double> vsids_value;
int maxindex;
int assigned_number;
double decay_constant;
int max_clause_size;
int conflict_counter;
};
int sat_solver::valued(int literal)
{
if (assignment[abs(literal)].value == -1)return -1;
if (assignment[abs(literal)].value == 0 && literal < 0)return 1;
if (assignment[abs(literal)].value == 1 && literal > 0)return 1;
return 0;
}
void sat_solver::vsids_value_decay()
{
for (int i = 1; i <= maxindex * 2; i++)
vsids_value[i] /= decay_constant;
}
int sat_solver::vsids_pick()
{
int candidate_variable = 0;
for (int i = 1; i <= maxindex * 2; i++)
{
if (assignment[(i + 1) / 2].value == -1) //unassigned
{
if (vsids_value[i] >= vsids_value[candidate_variable])
candidate_variable = i;
}
}
if (candidate_variable % 2) return (candidate_variable + 1) / 2;
return -(candidate_variable + 1) / 2;
}
vector<int> sat_solver::tidy_up_clause(vector<int> clause)
{
vector<int> simply_clause;
sort(clause.begin(), clause.end(), compare);
simply_clause.push_back(clause[0]);
for (int num : clause)
{
if (num == simply_clause.back())continue;// repeated
if (num == -simply_clause.back()) return vector<int>();// always true
simply_clause.push_back(num);
}
sort(simply_clause.begin(), simply_clause.end(), compare);
return simply_clause;
}
vector<int> sat_solver::resolve_clauses(vector<int> clause_1, vector<int> clause_2, int resolve_variable)
{
vector<int> new_clause;
for (int num : clause_1)
if (abs(num) != resolve_variable)
new_clause.push_back(num);
for (int num : clause_2)
if (abs(num) != resolve_variable)
new_clause.push_back(num);
return tidy_up_clause(new_clause);
}
bool sat_solver::prepare()
{
// tidy up each clause
for (int i = clauses.size() - 1; i >= 0; i--)
{
clauses[i] = tidy_up_clause(clauses[i]);
if (clauses[i].empty())
clauses.erase(clauses.begin() + i);
else if (clauses[i].size() == 1)
{
if (valued(clauses[i][0]) == 0)//conflict
return 0;
else //fix the value of this variable
{
single_literal.push_back(clauses[i][0]);
}
clauses.erase(clauses.begin() + i);
}
}
//set watching, each clause has at least two literal
for (int i = 0; i < clauses.size(); i++)
{
vector<int> clause = clauses[i];
find_clauses[clause] = 1;
for (int j = 0; j < 2; j++)
{
two_literal_watching[i].push_back(j);
if (clause[j] < 0) negative_watch[abs(clause[j])].push_back(i);
if (clause[j] > 0) positive_watch[abs(clause[j])].push_back(i);
}
}
//update VSIDS value
for (vector<int> clause : clauses)
for (int literal : clause)
(literal > 0) ? vsids_value[abs(literal) * 2 - 1] += 1 : vsids_value[abs(literal) * 2] += 1;
return 1;
}
int sat_solver::FirstUIP(vector<int> conflict_clause, int current_depth)
{
while (1)
{
int current_depth_assigned = 0;
for (int literal : conflict_clause)
if (assignment[abs(literal)].value != -1 && assignment[abs(literal)].depth == current_depth)
current_depth_assigned++;
if (current_depth_assigned <= 1)
break;
int last_assigned = abs(conflict_clause[0]);
for (int i = 0; i < conflict_clause.size(); i++)
{
if (assignment[abs(conflict_clause[i])].order > assignment[last_assigned].order)
last_assigned = abs(conflict_clause[i]);
}
conflict_clause = resolve_clauses(conflict_clause, antecedent[last_assigned], last_assigned);
}
if (conflict_clause.empty())return -1;
return add_new_clause(conflict_clause);
}
int sat_solver::add_new_clause(vector<int> new_clause)
{
if (new_clause.size() == 1)//imply a fixed variable
{
backtrack(0);
single_literal.push_back(new_clause[0]);
return 0;//backtrack to initial
}
/*if(new_clause.size()>max_clause_size)
{
//this clause is too large.
}*/
//find second deepest and backtrack
int deepest = 0;
int second_deepest = 0;
for (int num : new_clause)
deepest = max(deepest, assignment[abs(num)].depth);
for (int num : new_clause)
if (assignment[abs(num)].depth != deepest && assignment[abs(num)].depth > second_deepest)
second_deepest = assignment[abs(num)].depth;
backtrack(second_deepest);
//add new clause
sort(new_clause.begin(), new_clause.end(), compare);
//update VSIDS value
for(int literal:new_clause)
(literal > 0) ? vsids_value[abs(literal) * 2 - 1] += 1 : vsids_value[abs(literal) * 2] += 1;
if (!find_clauses[new_clause])
{
find_clauses[new_clause] = 1;
clauses.push_back(new_clause);
two_literal_watching.push_back(vector<int>());
for (int i = 0, watching_count = 0; i < new_clause.size(), watching_count < 2; i++)
{
if (valued(new_clause[i]) != 0)
{
two_literal_watching[clauses.size() - 1].push_back(i);
if (new_clause[i] < 0)
negative_watch[abs(new_clause[i])].push_back(clauses.size() - 1);
else
positive_watch[abs(new_clause[i])].push_back(clauses.size() - 1);
watching_count++;
}
}
}
return second_deepest - 1;
}
void sat_solver::backtrack(int goal_layer)
{
for (int num = 1; num <= maxindex; num++)
{
if (assignment[num].depth >= goal_layer)//
{
assigned_number--;
assignment[num] = { -1,-1,-1 };
antecedent[num] = vector<int>();
}
}
}
int sat_solver::four_case(int clause_index, int assigned_literal)
{
vector<int> current_clause = clauses[clause_index];
int watching_index;// 0 or 1 in 2-literal watching
for (int i = 0; i < 2; i++)
{
if (current_clause[two_literal_watching[clause_index][i]] == assigned_literal)
watching_index = i;
}
int another_watching_index = 1 - watching_index;
for (int i = 0; i < current_clause.size(); i++)
{
if (i == two_literal_watching[clause_index][0] || i == two_literal_watching[clause_index][1])continue;
if (valued(current_clause[i]) == 0)continue;
//find case 1 literal
two_literal_watching[clause_index][watching_index] = i;//update watching
if (current_clause[i] < 0)
negative_watch[abs(current_clause[i])].push_back(clause_index);
else
positive_watch[abs(current_clause[i])].push_back(clause_index);
return 1;// case 1 return
}
if (valued(current_clause[two_literal_watching[clause_index][another_watching_index]]) == -1) //case 2
{
// imply;
return 2;
}
if (valued(current_clause[two_literal_watching[clause_index][another_watching_index]]) == 1) //case 3
{
//nothing to do
return 3;
}
return 4;//conflict
}
int sat_solver::BCP(int depth, int decide_literal)
{
queue<pair<int, vector<int>>> imply;
if (depth > 1)
{
imply.push(pair<int, vector<int>>(decide_literal, vector<int>()));
}
else if (depth == 1)
{
for (int num : single_literal)
{
imply.push(pair<int, vector<int>>(num, vector<int>()));
}
}
while (!imply.empty())
{
pair<int, vector<int>> next_imply = imply.front(); imply.pop();
int literal = next_imply.first;
int variable = abs(literal);
if (valued(literal) == 1)continue;// repeat the same imply
if (valued(literal) == 0)//conflict
{
if (depth == 1)return -1;
antecedent[variable] = next_imply.second;
return FirstUIP(antecedent[variable], depth);
}
assignment[variable].value = (literal > 0) ? 1 : 0;
assignment[variable].depth = depth;
assignment[variable].order = assigned_number;
assigned_number++;
antecedent[variable] = next_imply.second;//this clause imply this variable
if (assignment[variable].value == 1)
{
for (int i = negative_watch[variable].size() - 1; i >= 0; i--)
{
int kase = four_case(negative_watch[variable][i], -variable);
if (kase == 1)
{
negative_watch[variable].erase(negative_watch[variable].begin() + i);//remove this watching clause.
continue;
}
if (kase == 2)
{
int clause_index = negative_watch[variable][i];
int imply_literal;
for (int j = 0; j < 2; j++)
{
if (abs(clauses[clause_index][two_literal_watching[clause_index][j]]) != variable)
imply_literal = clauses[clause_index][two_literal_watching[clause_index][j]];
}
imply.push({ imply_literal,clauses[clause_index] });
}
if (kase == 3)//this clause is resolved.
{
continue;
}
if (kase == 4)//conflict
{
if (depth == 1)return -1;
return FirstUIP(clauses[negative_watch[variable][i]], depth);
}
}
}
else
{
for (int i = positive_watch[variable].size() - 1; i >= 0; i--)
{
int kase = four_case(positive_watch[variable][i], variable);
if (kase == 1)
{
positive_watch[variable].erase(positive_watch[variable].begin() + i);//remove this watching clause.
continue;
}
if (kase == 2)
{
int clause_index = positive_watch[variable][i];
int imply_literal;
for (int j = 0; j < 2; j++)
{
if (abs(clauses[clause_index][two_literal_watching[clause_index][j]]) != variable)
imply_literal = clauses[clause_index][two_literal_watching[clause_index][j]];
}
imply.push({ imply_literal,clauses[clause_index] });
}
if (kase == 3)
{
continue;
}
if (kase == 4)//conflict
{
if (depth == 1)return -1;
return FirstUIP(clauses[positive_watch[variable][i]], depth);
}
}
}
}
return depth;
}
int sat_solver::DPLL(int current_depth, int decide_literal)
{
int goal_depth = BCP(current_depth, decide_literal);
if(goal_depth < current_depth)
conflict_counter++;
if (goal_depth < 0)return 0;
if (check_solve())return 1;
if(conflict_counter && conflict_counter % 50 == 0)
vsids_value_decay();
int next_decide = vsids_pick();
if(conflict_counter && conflict_counter % 200 == 0)//random restart
{
backtrack(0);
conflict_counter = 0;
}
return DPLL(goal_depth + 1, next_decide);
}
bool sat_solver::check_solve()
{
bool ans = 1;
for (int i = 0; i < clauses.size(); i++)
ans = ans & ((valued(clauses[i][two_literal_watching[i][0]]) == 1) || (valued(clauses[i][two_literal_watching[i][1]]) == 1));
return ans;
}
int main()
{
vector<vector<int>> clauses;
int maxindex;
parse_DIMACS_CNF(clauses, maxindex, "par32-1.cnf");
sat_solver solver(clauses, maxindex, 2, 20);
if (!solver.prepare())cout << "UNSAT\n";
else
{
if (solver.DPLL(1, 0))
{
cout << "SAT\n";
for (int i = 1; i <= maxindex; i++)
{
if (solver.assignment[i].value == 0)cout << "-";
cout << i << " ";
}
}
else cout << "UNSAT\n";
}
return 0;
}