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| #include<bits/stdc++.h>
#include<cassert>
using namespace std;
namespace atcoder {
namespace internal {
template <class E> struct csr {
std::vector<int> start;
std::vector<E> elist;
explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
: start(n + 1), elist(edges.size()) {
for (auto e : edges) {
start[e.first + 1]++;
}
for (int i = 1; i <= n; i++) {
start[i] += start[i - 1];
}
auto counter = start;
for (auto e : edges) {
elist[counter[e.first]++] = e.second;
}
}
};
struct scc_graph {
public:
explicit scc_graph(int n) : _n(n) {}
int num_vertices() {
return _n;
}
void add_edge(int from, int to) {
edges.push_back({from, {to}});
}
std::pair<int, std::vector<int>> scc_ids() {
auto g = csr<edge>(_n, edges);
int now_ord = 0, group_num = 0;
std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
visited.reserve(_n);
auto dfs = [&](auto self, int v) -> void {
low[v] = ord[v] = now_ord++;
visited.push_back(v);
for (int i = g.start[v]; i < g.start[v + 1]; i++) {
auto to = g.elist[i].to;
if (ord[to] == -1) {
self(self, to);
low[v] = std::min(low[v], low[to]);
} else {
low[v] = std::min(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (true) {
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};
}
std::vector<std::vector<int>> scc() {
auto ids = scc_ids();
int group_num = ids.first;
std::vector<int> counts(group_num);
for (auto x : ids.second) counts[x]++;
std::vector<std::vector<int>> groups(ids.first);
for (int i = 0; i < group_num; i++) {
groups[i].reserve(counts[i]);
}
for (int i = 0; i < _n; i++) {
groups[ids.second[i]].push_back(i);
}
return groups;
}
private:
int _n;
struct edge {
int to;
};
std::vector<std::pair<int, edge>> edges;
};
}
struct two_sat {
public:
two_sat() : _n(0), scc(0) {}
explicit two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
void add_clause(int i, bool f, int j, bool g) {
assert(0 <= i && i < _n);
assert(0 <= j && j < _n);
scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
}
bool satisfiable() {
auto id = scc.scc_ids().second;
for (int i = 0; i < _n; i++) {
if (id[2 * i] == id[2 * i + 1]) return false;
_answer[i] = id[2 * i] < id[2 * i + 1];
}
return true;
}
std::vector<bool> answer() {
return _answer;
}
private:
int _n;
std::vector<bool> _answer;
internal::scc_graph scc;
};
}
using namespace atcoder;
#ifdef LOCAL
#define debug(...) fprintf(stdout, ##__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
inline int read(){int x=0,f=1;char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')f=-1;
ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<1)+
(x<<3)+(ch^48);ch=getchar();}return x*f;}
#define Z(x) (x)*(x)
#define pb push_back
#define fi first
#define se second
struct node {
int i, j, y, z;
};
int n, m, i, j, k, T;
int y, z, n1, n2;
signed main()
{
#ifdef LOCAL
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#endif
T = read();
while(T--) {
n1 = read(); n2 = read(); m = read();
vector<int>flg(n1 + n2 + 10);
vector<node>v;
two_sat ts(n1 + n2 + 5);
for(k = 1; k <= m; ++k) {
i = read(); j = read(); y = read(); z = read();
if(y == 1 && z == 0) flg[j] = 1;
v.pb({i, j, y, z});
}
auto No = [&] (int i, int x, int j, int y) -> void {
debug("%d == %d || %d == %d\n", i, 1 - x, j + n1, 1 - y);
ts.add_clause(i, (bool)(1 - x), j + n1, (bool)(1 - y));
};
for(auto t : v) {
i = t.i; j = t.j; y = t.y; z = t.z;
if(flg[j]) {
for(k = 0; k <= 1; ++k) {
if((k ^ y) != z) No(i, k, j, 0);
if((k & y) != z) No(i, k, j, 1);
}
}
else {
for(k = 0; k <= 1; ++k) {
if((k | y) != z) No(i, k, j, 0);
if((k & y) != z) No(i, k, j, 1);
}
}
debug("---(%d)--\n", flg[j]);
}
if(ts.satisfiable()) {
printf("YES\n");
vector<bool>ans = ts.answer();
for(i = 1; i <= n1; ++i) {
auto t = ans[i];
printf(t ? "1" : "0");
}
printf("\n");
for(i = 1; i <= n2; ++i) {
auto t = ans[i + n1];
if(flg[i]) printf(t ? "&" : "^");
else printf(t ? "&" : "|");
}
printf("\n");
}
else printf("NO\n");
}
return 0;
}
|
