Created
October 3, 2011 05:42
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Linear 2-SAT solver.
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#include <list> | |
#include <vector> | |
#include <queue> | |
#include <iostream> | |
using namespace std; | |
typedef unsigned int uint; | |
typedef vector<list<uint>> adj_list; | |
typedef vector<int> vint; | |
typedef vector<bool> vbool; | |
#define NOT(n) (n & 1 ? ((n)-1) : ((n)+1)) | |
#define ABS(n) ((n) & 1 ? ((n)-1) : (n)) | |
#define VAR(n) (ABS(n)/2) | |
#define SGN(n) ((n) & 1 ? 0 : 1) | |
bool exists_contradiction_bfs(uint s, const adj_list& G) { | |
queue<uint> Q; | |
Q.push(s); | |
vbool seen(Q.size()); | |
seen[s] = true; | |
while(!Q.empty()) { | |
uint v = Q.front(); | |
Q.pop(); | |
for(uint w : G[v]) { | |
if(seen[w]) continue; | |
if(VAR(w) == VAR(s)) return true; | |
Q.push(w); | |
seen[w] = true; | |
} | |
} | |
return false; | |
} | |
void marking_bfs(uint s, const adj_list& G, vint& assignment) { | |
queue<uint> Q; | |
Q.push(s); | |
assignment[VAR(s)] = SGN(s); | |
while(!Q.empty()) { | |
uint v = Q.front(); | |
Q.pop(); | |
for(uint x : G[v]) { | |
if(assignment[VAR(x)] != -1) continue; | |
assignment[VAR(x)] = SGN(x); | |
Q.push(x); | |
} | |
} | |
} | |
int main() { | |
int n; | |
cin >> n; | |
while(n--) { | |
int m, terms; | |
cin >> m >> terms; | |
vint assignment(m, -1); | |
vbool contradictions(2*m); | |
adj_list G(2*m); | |
char sgn, letter, sgn2, letter2; | |
bool sat = true; | |
while(terms--) { | |
cin >> sgn >> letter >> sgn2 >> letter2; | |
letter -= 'A'; | |
letter2 -= 'A'; | |
uint p, q; | |
p = static_cast<uint>(letter*2); | |
q = static_cast<uint>(letter2*2); | |
if(sgn == '-') p++; | |
if(sgn2 == '-') q++; | |
G[NOT(p)].push_back(q); | |
G[NOT(q)].push_back(p); | |
} | |
for(int i = 0; i < 2*m; i++) { | |
contradictions[i] = exists_contradiction_bfs(i, G); | |
if(contradictions[i] && contradictions[NOT(i)]) { | |
sat = false; | |
break; | |
} | |
} | |
if(sat) { | |
for(int i = 0; i < 2*m; i++) { | |
if(!contradictions[i] && assignment[VAR(i)] == -1) marking_bfs(i, G, assignment); | |
} | |
cout << "Instance: "; | |
for(int i = 0; i < m; i++) { | |
if(assignment[i] == 0) cout << "-"; | |
cout << static_cast<char>('A' + i) << " "; | |
} | |
cout << endl; | |
} else cout << "Instance is not satisfiable." << endl; | |
} | |
} |
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