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test/3_yukicoder/1745.test.cpp
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- Last update: 2024-12-13 13:55:16+09:00
- Problem: https://yukicoder.me/problems/no/1745
- Link: View error logs on GitHub Actions
Depends on
ds/unionfind/unionfind.hpp
- flow/bipartite.hpp
- graph/base.hpp
- graph/bipartite_vertex_coloring.hpp
- graph/strongly_connected_component.hpp
- my_template.hpp
- other/io.hpp
Code
#define PROBLEM "https://yukicoder.me/problems/no/1745"
#include "my_template.hpp"
#include "other/io.hpp"
#include "flow/bipartite.hpp"
void solve() {
LL(L, R, M);
Graph<int, 0> G(L + R);
VEC(pi, XY, M);
for (auto&& [x, y]: XY) {
--x, --y;
y += L;
}
for (auto&& [x, y]: XY) G.add(x, y);
G.build();
BipartiteMatching<decltype(G)> X(G);
auto [K, W] = X.DM_decomposition();
for (auto&& [x, y]: XY) Yes(W[x] == W[y]);
}
signed main() {
cout << fixed << setprecision(15);
ll T = 1;
// LL(T);
FOR(T) solve();
return 0;
}#line 1 "test/3_yukicoder/1745.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1745"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "graph/bipartite_vertex_coloring.hpp"
#line 2 "ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
x = (*this)[x];
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
vc<int> get_all() {
vc<int> A(n);
FOR(i, n) A[i] = (*this)[i];
return A;
}
};
#line 5 "graph/bipartite_vertex_coloring.hpp"
// 二部グラフでなかった場合には empty
template <typename GT>
vc<int> bipartite_vertex_coloring(GT& G) {
assert(!GT::is_directed);
assert(G.is_prepared());
int n = G.N;
UnionFind uf(2 * n);
for (auto&& e: G.edges) {
int u = e.frm, v = e.to;
uf.merge(u + n, v), uf.merge(u, v + n);
}
vc<int> color(2 * n, -1);
FOR(v, n) if (uf[v] == v && color[uf[v]] < 0) {
color[uf[v]] = 0;
color[uf[v + n]] = 1;
}
FOR(v, n) color[v] = color[uf[v]];
color.resize(n);
FOR(v, n) if (uf[v] == uf[v + n]) return {};
return color;
}
#line 3 "graph/strongly_connected_component.hpp"
template <typename GT>
pair<int, vc<int>> strongly_connected_component(GT& G) {
static_assert(GT::is_directed);
assert(G.is_prepared());
int N = G.N;
int C = 0;
vc<int> comp(N), low(N), ord(N, -1), path;
int now = 0;
auto dfs = [&](auto& dfs, int v) -> void {
low[v] = ord[v] = now++;
path.eb(v);
for (auto&& [frm, to, cost, id]: G[v]) {
if (ord[to] == -1) {
dfs(dfs, to), chmin(low[v], low[to]);
} else {
chmin(low[v], ord[to]);
}
}
if (low[v] == ord[v]) {
while (1) {
int u = POP(path);
ord[u] = N, comp[u] = C;
if (u == v) break;
}
++C;
}
};
FOR(v, N) {
if (ord[v] == -1) dfs(dfs, v);
}
FOR(v, N) comp[v] = C - 1 - comp[v];
return {C, comp};
}
template <typename GT>
Graph<int, 1> scc_dag(GT& G, int C, vc<int>& comp) {
Graph<int, 1> DAG(C);
vvc<int> edges(C);
for (auto&& e: G.edges) {
int x = comp[e.frm], y = comp[e.to];
if (x == y) continue;
edges[x].eb(y);
}
FOR(c, C) {
UNIQUE(edges[c]);
for (auto&& to: edges[c]) DAG.add(c, to);
}
DAG.build();
return DAG;
}
#line 4 "flow/bipartite.hpp"
template <typename GT>
struct BipartiteMatching {
int N;
GT& G;
vc<int> color;
vc<int> dist, match;
vc<int> vis;
BipartiteMatching(GT& G) : N(G.N), G(G), dist(G.N, -1), match(G.N, -1) {
color = bipartite_vertex_coloring(G);
if (N > 0) assert(!color.empty());
while (1) {
bfs();
vis.assign(N, false);
int flow = 0;
FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
if (!flow) break;
}
}
BipartiteMatching(GT& G, vc<int> color)
: N(G.N), G(G), color(color), dist(G.N, -1), match(G.N, -1) {
while (1) {
bfs();
vis.assign(N, false);
int flow = 0;
FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
if (!flow) break;
}
}
void bfs() {
dist.assign(N, -1);
queue<int> que;
FOR(v, N) if (!color[v] && match[v] == -1) que.emplace(v), dist[v] = 0;
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto&& e: G[v]) {
dist[e.to] = 0;
int w = match[e.to];
if (w != -1 && dist[w] == -1) dist[w] = dist[v] + 1, que.emplace(w);
}
}
}
bool dfs(int v) {
vis[v] = 1;
for (auto&& e: G[v]) {
int w = match[e.to];
if (w == -1 || (!vis[w] && dist[w] == dist[v] + 1 && dfs(w))) {
match[e.to] = v, match[v] = e.to;
return true;
}
}
return false;
}
vc<pair<int, int>> matching() {
vc<pair<int, int>> res;
FOR(v, N) if (v < match[v]) res.eb(v, match[v]);
return res;
}
vc<int> vertex_cover() {
vc<int> res;
FOR(v, N) if (color[v] ^ (dist[v] == -1)) { res.eb(v); }
return res;
}
vc<int> independent_set() {
vc<int> res;
FOR(v, N) if (!(color[v] ^ (dist[v] == -1))) { res.eb(v); }
return res;
}
vc<int> edge_cover() {
vc<bool> done(N);
vc<int> res;
for (auto&& e: G.edges) {
if (done[e.frm] || done[e.to]) continue;
if (match[e.frm] == e.to) {
res.eb(e.id);
done[e.frm] = done[e.to] = 1;
}
}
for (auto&& e: G.edges) {
if (!done[e.frm]) {
res.eb(e.id);
done[e.frm] = 1;
}
if (!done[e.to]) {
res.eb(e.id);
done[e.to] = 1;
}
}
sort(all(res));
return res;
}
/* Dulmage–Mendelsohn decomposition
https://en.wikipedia.org/wiki/Dulmage%E2%80%93Mendelsohn_decomposition
http://www.misojiro.t.u-tokyo.ac.jp/~murota/lect-ouyousurigaku/dm050410.pdf
https://hitonanode.github.io/cplib-cpp/graph/dulmage_mendelsohn_decomposition.hpp.html
- 最大マッチングとしてありうる iff 同じ W を持つ
- 辺 uv が必ず使われる：同じ W を持つ辺が唯一
- color=0 から 1 への辺：W[l] <= W[r]
- color=0 の点が必ず使われる：W=1,2,...,K
- color=1 の点が必ず使われる：W=0,1,...,K-1
*/
pair<int, vc<int>> DM_decomposition() {
// 非飽和点からの探索
vc<int> W(N, -1);
vc<int> que;
auto add = [&](int v, int x) -> void {
if (W[v] == -1) {
W[v] = x;
que.eb(v);
}
};
FOR(v, N) if (match[v] == -1 && color[v] == 0) add(v, 0);
FOR(v, N) if (match[v] == -1 && color[v] == 1) add(v, infty<int>);
while (len(que)) {
auto v = POP(que);
if (match[v] != -1) add(match[v], W[v]);
if (color[v] == 0 && W[v] == 0) {
for (auto&& e: G[v]) { add(e.to, W[v]); }
}
if (color[v] == 1 && W[v] == infty<int>) {
for (auto&& e: G[v]) { add(e.to, W[v]); }
}
}
// 残った点からなるグラフを作って強連結成分分解
vc<int> V;
FOR(v, N) if (W[v] == -1) V.eb(v);
int n = len(V);
Graph<bool, 1> DG(n);
FOR(i, n) {
int v = V[i];
if (match[v] != -1) {
int j = LB(V, match[v]);
DG.add(i, j);
}
if (color[v] == 0) {
for (auto&& e: G[v]) {
if (W[e.to] != -1 || e.to == match[v]) continue;
int j = LB(V, e.to);
DG.add(i, j);
}
}
}
DG.build();
auto [K, comp] = strongly_connected_component(DG);
K += 1;
// 答
FOR(i, n) { W[V[i]] = 1 + comp[i]; }
FOR(v, N) if (W[v] == infty<int>) W[v] = K;
return {K, W};
}
#ifdef FASTIO
void debug() {
print("match", match);
print("min vertex covor", vertex_cover());
print("max indep set", independent_set());
print("min edge cover", edge_cover());
}
#endif
};
#line 5 "test/3_yukicoder/1745.test.cpp"
void solve() {
LL(L, R, M);
Graph<int, 0> G(L + R);
VEC(pi, XY, M);
for (auto&& [x, y]: XY) {
--x, --y;
y += L;
}
for (auto&& [x, y]: XY) G.add(x, y);
G.build();
BipartiteMatching<decltype(G)> X(G);
auto [K, W] = X.DM_decomposition();
for (auto&& [x, y]: XY) Yes(W[x] == W[y]);
}
signed main() {
cout << fixed << setprecision(15);
ll T = 1;
// LL(T);
FOR(T) solve();
return 0;
}