This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"
#include "../../../src/template/template.hpp"
#include "../../../src/math/two_sat.hpp"
int main(void) {
string p, cnf;
int n, m;
cin >> p >> cnf >> n >> m;
TwoSAT ts(n);
rep(i, 0, m) {
int a, b, z;
cin >> a >> b >> z;
bool f = a > 0, g = b > 0;
a = abs(a) - 1;
b = abs(b) - 1;
ts.add_clause(a, f, b, g);
}
if(ts.satisfiable()) {
cout << "s SATISFIABLE" << '\n';
vector<bool> ans = ts.answer();
cout << "v ";
rep(i, 0, n) {
if(!ans[i]) cout << '-';
cout << i + 1 << ' ';
}
cout << 0 << '\n';
} else {
cout << "s UNSATISFIABLE" << '\n';
}
}
#line 1 "verify/library_checker/other/2_sat.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_sat"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
SetupIO() {
ios::sync_with_stdio(0);
cin.tie(0);
cout << fixed << setprecision(30);
}
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
int from, to;
T cost;
int idx;
Edge()
: from(-1), to(-1), cost(-1), idx(-1) {}
Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const {
return to;
}
};
template <typename T>
struct Graph {
Graph(const int N)
: n(N), es(0), g(N) {}
int size() const {
return n;
}
int edge_size() const {
return es;
}
void add_edge(const int from, const int to, const T& cost = 1) {
assert(0 <= from and from < n);
assert(0 <= to and to < n);
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void add_directed_edge(const int from, const int to, const T& cost = 1) {
assert(0 <= from and from < n);
assert(0 <= to and to < n);
g[from].emplace_back(from, to, cost, es++);
}
inline vector<Edge<T>>& operator[](const int& k) {
assert(0 <= k and k < n);
return g[k];
}
inline const vector<Edge<T>>& operator[](const int& k) const {
assert(0 <= k and k < n);
return g[k];
}
private:
int n, es;
vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/graph/compressed_sparse_row.hpp"
template <typename T>
struct CompressedSparseRow {
vector<int> start, elist;
CompressedSparseRow(const Graph<T>& g)
: start(g.size() + 1), elist(g.edge_size()) {
const int n = g.size();
for(int i = 0; i < n; ++i) {
start[i + 1] = start[i] + g[i].size();
int counter = start[i];
for(const Edge<T>& e : g[i]) {
elist[counter++] = e.to;
}
}
}
};
#line 5 "src/graph/strongly_connected_components.hpp"
template <typename T>
pair<int, vector<int>> scc_ids(const Graph<T>& g) {
const int n = g.size();
const CompressedSparseRow<T> g_csr(g);
int now_ord = 0, group_num = 0;
vector<int> visited, low(n), ord(n, -1), ids(n);
visited.reserve(n);
auto dfs = [&](const auto& dfs, const int v) -> void {
low[v] = ord[v] = now_ord++;
visited.emplace_back(v);
for(int i = g_csr.start[v]; i < g_csr.start[v + 1]; ++i) {
const int to = g_csr.elist[i];
if(ord[to] == -1) {
dfs(dfs, to);
low[v] = min(low[v], low[to]);
} else {
low[v] = min(low[v], ord[to]);
}
}
if(low[v] == ord[v]) {
while(true) {
const int u = visited.back();
visited.pop_back();
ord[u] = n;
ids[u] = group_num;
if(u == v) break;
}
++group_num;
}
};
for(int i = 0; i < n; ++i) {
if(ord[i] == -1) {
dfs(dfs, i);
}
}
for(auto& x : ids) x = group_num - 1 - x;
return {group_num, ids};
}
template <typename T>
vector<vector<int>> strongly_connected_components(const Graph<T>& g) {
const auto [group_num, ids] = scc_ids(g);
const int n = g.size();
vector<int> counts(group_num);
for(const int x : ids) ++counts[x];
vector<vector<int>> groups(group_num);
for(int i = 0; i < group_num; ++i) groups[i].reserve(counts[i]);
for(int i = 0; i < n; ++i) groups[ids[i]].emplace_back(i);
return groups;
}
#line 5 "src/math/two_sat.hpp"
struct TwoSAT {
TwoSAT(int N)
: n(N), ans(N), graph(2 * N) {}
void add_clause(const int i, const bool f, const int j, const bool g) {
graph.add_directed_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
graph.add_directed_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
}
bool satisfiable() {
const vector<int> id = scc_ids(graph).second;
for(int i = 0; i < n; ++i) {
if(id[2 * i] == id[2 * i + 1]) return false;
ans[i] = id[2 * i] < id[2 * i + 1];
}
return true;
}
vector<bool> answer() const {
return ans;
}
private:
int n;
vector<bool> ans;
Graph<int> graph;
};
#line 4 "verify/library_checker/other/2_sat.test.cpp"
int main(void) {
string p, cnf;
int n, m;
cin >> p >> cnf >> n >> m;
TwoSAT ts(n);
rep(i, 0, m) {
int a, b, z;
cin >> a >> b >> z;
bool f = a > 0, g = b > 0;
a = abs(a) - 1;
b = abs(b) - 1;
ts.add_clause(a, f, b, g);
}
if(ts.satisfiable()) {
cout << "s SATISFIABLE" << '\n';
vector<bool> ans = ts.answer();
cout << "v ";
rep(i, 0, n) {
if(!ans[i]) cout << '-';
cout << i + 1 << ' ';
}
cout << 0 << '\n';
} else {
cout << "s UNSATISFIABLE" << '\n';
}
}