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graph/count/count_cycle.hpp
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- Last update: 2024-04-19 02:20:22+09:00
- Include:
#include "graph/count/count_cycle.hpp"
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Code
#include "enumerate/bits.hpp"
#include "graph/base.hpp"
// 頂点集合ごとにサイクルを数える. N^22^N.
// サイクルの長さは 3 以上（単純グラフを仮定）
template <typename T, typename GT>
vc<T> count_cycle(GT& G) {
const int N = G.N;
assert(N <= 32 && !GT::is_directed);
vc<u32> nbd(N);
FOR(v, N) for (auto& e: G[v]) nbd[v] |= u32(1) << (e.to);
vc<T> cyc(1 << N);
for (int v = 0; v < N; ++v) {
vc<T> dp(v << v);
for (int w = 0; w < v; ++w) {
if (nbd[v] >> w & 1) dp[(v << w) + w] = 1;
}
const u32 mask = (u32(1) << v) - 1;
for (u32 s = 0; s < (u32(1) << v); ++s) {
enumerate_bits_32(s, [&](int a) -> void {
enumerate_bits_32(nbd[a] & mask & (~s), [&](int b) -> void {
dp[v * (s | 1 << b) + b] += dp[v * s + a];
});
if (popcnt(s) >= 2 && nbd[a] >> v & 1) cyc[s | 1 << v] += dp[v * s + a];
});
}
}
for (auto& x: cyc) x /= T(2);
return cyc;
}#line 1 "enumerate/bits.hpp"
template <typename F>
void enumerate_bits_32(u32 s, F f) {
while (s) {
int i = __builtin_ctz(s);
f(i);
s ^= 1 << i;
}
}
template <typename F>
void enumerate_bits_64(u64 s, F f) {
while (s) {
int i = __builtin_ctzll(s);
f(i);
s ^= u64(1) << i;
}
}
template <typename BS, typename F>
void enumerate_bits_bitset(BS& b, int L, int R, F f) {
int p = (b[L] ? L : b._Find_next(L));
while (p < R) {
f(p);
p = b._Find_next(p);
}
}
#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}
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;
}
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 3 "graph/count/count_cycle.hpp"
// 頂点集合ごとにサイクルを数える. N^22^N.
// サイクルの長さは 3 以上（単純グラフを仮定）
template <typename T, typename GT>
vc<T> count_cycle(GT& G) {
const int N = G.N;
assert(N <= 32 && !GT::is_directed);
vc<u32> nbd(N);
FOR(v, N) for (auto& e: G[v]) nbd[v] |= u32(1) << (e.to);
vc<T> cyc(1 << N);
for (int v = 0; v < N; ++v) {
vc<T> dp(v << v);
for (int w = 0; w < v; ++w) {
if (nbd[v] >> w & 1) dp[(v << w) + w] = 1;
}
const u32 mask = (u32(1) << v) - 1;
for (u32 s = 0; s < (u32(1) << v); ++s) {
enumerate_bits_32(s, [&](int a) -> void {
enumerate_bits_32(nbd[a] & mask & (~s), [&](int b) -> void {
dp[v * (s | 1 << b) + b] += dp[v * s + a];
});
if (popcnt(s) >= 2 && nbd[a] >> v & 1) cyc[s | 1 << v] += dp[v * s + a];
});
}
}
for (auto& x: cyc) x /= T(2);
return cyc;
}