This documentation is automatically generated by online-judge-tools/verification-helper
#include "random/random_graph.hpp"
#include "graph/base.hpp"
#include "random/base.hpp"
#include "random/shuffle.hpp"
#include "ds/unionfind/unionfind.hpp"
void random_relabel(int N, vc<pair<int, int>>& G) {
shuffle(G);
vc<int> A(N);
FOR(i, N) A[i] = i;
shuffle(A);
for (auto& [a, b]: G) a = A[a], b = A[b];
}
template <int DIRECTED>
vc<pair<int, int>> random_graph(int n, bool simple) {
vc<pair<int, int>> G, cand;
FOR(a, n) FOR(b, n) {
if (simple && a == b) continue;
if (!DIRECTED && a > b) continue;
cand.eb(a, b);
}
int m = RNG(0, len(cand) + 1);
set<int> ss;
FOR(m) {
while (1) {
int i = RNG(0, len(cand));
if (simple && ss.count(i)) continue;
ss.insert(i);
auto [a, b] = cand[i];
G.eb(a, b);
break;
}
}
random_relabel(n, G);
return G;
}
vc<pair<int, int>> random_tree(int n) {
vc<pair<int, int>> G;
FOR(i, 1, n) { G.eb(RNG(0, i), i); }
random_relabel(n, G);
return G;
}
// EDGE = true: 各辺が唯一のサイクル(関節点でサイクルまたは辺)
// EDGE = false: 各頂点が唯一のサイクル(橋でサイクルまたは辺)
vc<pair<int, int>> random_cactus(int N, bool EDGE) {
if (!EDGE) {
// n 頂点を 1 または 3 以上に分割
vvc<int> A;
int n = RNG(1, N + 1);
vc<int> S(n, 1);
int rest = N - n;
while (rest > 0) {
int k = RNG(0, n);
if (S[k] == 1) {
if (rest == 1) {
S.eb(1), rest = 0;
} else {
S[k] += 2, rest -= 2;
}
} else {
S[k]++, rest--;
}
}
n = len(S);
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
int m = len(A);
auto H = random_tree(m);
vc<pair<int, int>> G;
FOR(i, m) {
vc<int>& V = A[i];
if (len(V) == 1) continue;
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
G.eb(a, b);
}
random_relabel(N, G);
return G;
}
assert(EDGE);
if (N == 1) return {};
int n = RNG(1, N);
vc<int> S(n, 2);
int rest = N - 1 - n;
while (rest > 0) {
int k = RNG(0, n);
S[k]++, --rest;
}
vvc<int> A;
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
assert(p == N + n - 1);
UnionFind uf(p);
auto H = random_tree(n);
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
uf.merge(a, b);
}
vc<int> new_idx(p);
int x = 0;
FOR(i, p) if (uf[i] == i) new_idx[i] = x++;
assert(x == N);
FOR(i, p) new_idx[i] = new_idx[uf[i]];
vc<pair<int, int>> G;
FOR(i, n) {
vc<int>& V = A[i];
for (auto& v: V) v = new_idx[v];
if (len(V) == 2) {
G.eb(V[0], V[1]);
} else {
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
}
random_relabel(N, G);
return G;
}
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#line 3 "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;
}
HashMap<int> MP_FOR_EID;
int get_eid(u64 a, u64 b) {
if (len(MP_FOR_EID) == 0) {
MP_FOR_EID.build(N - 1);
for (auto& e: edges) {
u64 a = e.frm, b = e.to;
u64 k = to_eid_key(a, b);
MP_FOR_EID[k] = e.id;
}
}
return MP_FOR_EID.get(to_eid_key(a, b), -1);
}
u64 to_eid_key(u64 a, u64 b) {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
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 "random/base.hpp"
u64 RNG_64() {
static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "random/shuffle.hpp"
template <typename T>
void shuffle(vc<T>& A) {
FOR(i, len(A)) {
int j = RNG(0, i + 1);
if (i != j) swap(A[i], A[j]);
}
}
#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 "random/random_graph.hpp"
void random_relabel(int N, vc<pair<int, int>>& G) {
shuffle(G);
vc<int> A(N);
FOR(i, N) A[i] = i;
shuffle(A);
for (auto& [a, b]: G) a = A[a], b = A[b];
}
template <int DIRECTED>
vc<pair<int, int>> random_graph(int n, bool simple) {
vc<pair<int, int>> G, cand;
FOR(a, n) FOR(b, n) {
if (simple && a == b) continue;
if (!DIRECTED && a > b) continue;
cand.eb(a, b);
}
int m = RNG(0, len(cand) + 1);
set<int> ss;
FOR(m) {
while (1) {
int i = RNG(0, len(cand));
if (simple && ss.count(i)) continue;
ss.insert(i);
auto [a, b] = cand[i];
G.eb(a, b);
break;
}
}
random_relabel(n, G);
return G;
}
vc<pair<int, int>> random_tree(int n) {
vc<pair<int, int>> G;
FOR(i, 1, n) { G.eb(RNG(0, i), i); }
random_relabel(n, G);
return G;
}
// EDGE = true: 各辺が唯一のサイクル(関節点でサイクルまたは辺)
// EDGE = false: 各頂点が唯一のサイクル(橋でサイクルまたは辺)
vc<pair<int, int>> random_cactus(int N, bool EDGE) {
if (!EDGE) {
// n 頂点を 1 または 3 以上に分割
vvc<int> A;
int n = RNG(1, N + 1);
vc<int> S(n, 1);
int rest = N - n;
while (rest > 0) {
int k = RNG(0, n);
if (S[k] == 1) {
if (rest == 1) {
S.eb(1), rest = 0;
} else {
S[k] += 2, rest -= 2;
}
} else {
S[k]++, rest--;
}
}
n = len(S);
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
int m = len(A);
auto H = random_tree(m);
vc<pair<int, int>> G;
FOR(i, m) {
vc<int>& V = A[i];
if (len(V) == 1) continue;
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
G.eb(a, b);
}
random_relabel(N, G);
return G;
}
assert(EDGE);
if (N == 1) return {};
int n = RNG(1, N);
vc<int> S(n, 2);
int rest = N - 1 - n;
while (rest > 0) {
int k = RNG(0, n);
S[k]++, --rest;
}
vvc<int> A;
int p = 0;
FOR(i, n) {
vc<int> C;
FOR(v, p, p + S[i]) C.eb(v);
A.eb(C);
p += S[i];
}
assert(p == N + n - 1);
UnionFind uf(p);
auto H = random_tree(n);
for (auto& [c1, c2]: H) {
int a = A[c1][RNG(0, len(A[c1]))];
int b = A[c2][RNG(0, len(A[c2]))];
uf.merge(a, b);
}
vc<int> new_idx(p);
int x = 0;
FOR(i, p) if (uf[i] == i) new_idx[i] = x++;
assert(x == N);
FOR(i, p) new_idx[i] = new_idx[uf[i]];
vc<pair<int, int>> G;
FOR(i, n) {
vc<int>& V = A[i];
for (auto& v: V) v = new_idx[v];
if (len(V) == 2) {
G.eb(V[0], V[1]);
} else {
FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
}
}
random_relabel(N, G);
return G;
}