This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/tree_decomposition_width_2
#include "../../template/template.hpp"
#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"
#include "../../structure/union-find/union-find.hpp"
#include "../../graph/others/tree-decomposition-width-2.hpp"
int main() {
string x;
int N, M;
Scanner pin(stdin);
Printer pout(stdout);
pin.read(x, x, N, M);
vector< int > A(M), B(M);
UnionFind uf(N);
for(int i = 0; i < M; i++) {
pin.read(A[i], B[i]);
--A[i], --B[i];
uf.unite(A[i], B[i]);
}
int root = -1;
for(int i = 0; i < N; i++) {
if(uf.find(i) == i) {
if(root == -1) {
root = i;
} else {
A.emplace_back(root);
B.emplace_back(i);
}
}
}
TreeDecompositionWidth2 td(N);
for(size_t i = 0; i < A.size(); i++) {
td.add_edge(A[i], B[i]);
}
auto tap = td.build();
if(tap.empty()) {
pout.writeln("-1");
return 0;
}
pout.writeln("s", "td", tap.size(), 2, N);
for(size_t i = 0; i < tap.size(); i++) {
for(auto &t : tap[i].bag) ++t;
pout.writeln("b", i + 1, tap[i].bag);
}
for(size_t i = 0; i < tap.size(); i++) {
for(auto &t : tap[i].child) pout.writeln(i + 1, t + 1);
}
}
#line 1 "test/verify/yosupo-tree-decomposition-width-2.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/tree_decomposition_width_2
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-tree-decomposition-width-2.test.cpp"
#line 1 "other/scanner.hpp"
/**
* @brief Scanner(高速入力)
*/
struct Scanner {
public:
explicit Scanner(FILE *fp) : fp(fp) {}
template <typename T, typename... E>
void read(T &t, E &...e) {
read_single(t);
read(e...);
}
private:
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
FILE *fp = nullptr;
char *st = line;
char *ed = line;
void read() {}
static inline bool is_space(char c) { return c <= ' '; }
void reread() {
ptrdiff_t len = ed - st;
memmove(line, st, len);
char *tmp = line + len;
ed = tmp + fread(tmp, 1, line_size - len, fp);
*ed = 0;
st = line;
}
void skip_space() {
while (true) {
if (st == ed) reread();
while (*st && is_space(*st)) ++st;
if (st != ed) return;
}
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
void read_single(T &s) {
skip_space();
if (st + int_digits >= ed) reread();
bool neg = false;
if (is_signed<T>::value && *st == '-') {
neg = true;
++st;
}
typename make_unsigned<T>::type y = *st++ - '0';
while (*st >= '0') {
y = 10 * y + *st++ - '0';
}
s = (neg ? -y : y);
}
template <typename T, enable_if_t<is_same<T, string>::value, int> = 0>
void read_single(T &s) {
s = "";
skip_space();
while (true) {
char *base = st;
while (*st && !is_space(*st)) ++st;
s += string(base, st);
if (st != ed) return;
reread();
}
}
template <typename T>
void read_single(vector<T> &s) {
for (auto &d : s) read(d);
}
};
#line 1 "other/printer.hpp"
/**
* @brief Printer(高速出力)
*/
struct Printer {
public:
explicit Printer(FILE *fp) : fp(fp) {}
~Printer() { flush(); }
template <bool f = false, typename T, typename... E>
void write(const T &t, const E &...e) {
if (f) write_single(' ');
write_single(t);
write<true>(e...);
}
template <typename... T>
void writeln(const T &...t) {
write(t...);
write_single('\n');
}
void flush() {
fwrite(line, 1, st - line, fp);
st = line;
}
private:
FILE *fp = nullptr;
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
char *st = line;
template <bool f = false>
void write() {}
void write_single(const char &t) {
if (st + 1 >= line + line_size) flush();
*st++ = t;
}
template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
void write_single(T s) {
if (st + int_digits >= line + line_size) flush();
st += to_chars(st, st + int_digits, s).ptr - st;
}
void write_single(const string &s) {
for (auto &c : s) write_single(c);
}
void write_single(const char *s) {
while (*s != 0) write_single(*s++);
}
template <typename T>
void write_single(const vector<T> &s) {
for (size_t i = 0; i < s.size(); i++) {
if (i) write_single(' ');
write_single(s[i]);
}
}
};
#line 7 "test/verify/yosupo-tree-decomposition-width-2.test.cpp"
#line 2 "structure/union-find/union-find.hpp"
struct UnionFind {
vector<int> data;
UnionFind() = default;
explicit UnionFind(size_t sz) : data(sz, -1) {}
bool unite(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y];
data[y] = x;
return true;
}
int find(int k) {
if (data[k] < 0) return (k);
return data[k] = find(data[k]);
}
int size(int k) { return -data[find(k)]; }
bool same(int x, int y) { return find(x) == find(y); }
vector<vector<int> > groups() {
int n = (int)data.size();
vector<vector<int> > ret(n);
for (int i = 0; i < n; i++) {
ret[find(i)].emplace_back(i);
}
ret.erase(remove_if(begin(ret), end(ret),
[&](const vector<int> &v) { return v.empty(); }),
end(ret));
return ret;
}
};
#line 9 "test/verify/yosupo-tree-decomposition-width-2.test.cpp"
#line 2 "graph/others/tree-decomposition-width-2.hpp"
/**
* @brief Tree Decomposition Width 2(木幅2の木分解)
* @see https://ei1333.hateblo.jp/entry/2020/02/12/150319
*
*/
struct DecompNode {
vector<int> bag, child;
DecompNode() = default;
};
struct TreeDecompositionWidth2 {
vector<vector<int> > g;
explicit TreeDecompositionWidth2(int V) : g(V) {}
void add_edge(int a, int b) {
g[a].emplace_back(b);
g[b].emplace_back(a);
}
vector<DecompNode> build() {
const int N = (int)g.size();
vector<int> used(N, -1), deg(N);
queue<int> que;
for (int i = 0; i < N; i++) {
deg[i] = (int)g[i].size();
if (deg[i] <= 2) que.emplace(i);
}
vector<set<int> > exists(N);
for (int i = 0; i < N; i++) {
for (auto &j : g[i]) {
if (i < j) exists[i].emplace(j);
}
}
vector<DecompNode> ret;
ret.emplace_back();
while (!que.empty()) {
int idx = que.front();
que.pop();
if (deg[idx] > 2 || used[idx] != -1) continue;
DecompNode r;
r.bag.emplace_back(idx);
int u = -1, v = -1;
for (auto &to : g[idx]) {
if (used[to] == -1) {
(u == -1 ? u : v) = to;
r.bag.emplace_back(to);
} else if (used[to] >= 0) {
r.child.emplace_back(used[to]);
used[to] = -2;
}
}
if (u == -1) {
} else if (v == -1) {
--deg[u];
} else {
if (u > v) swap(u, v);
if (!exists[u].count(v)) {
g[u].emplace_back(v);
g[v].emplace_back(u);
exists[u].emplace(v);
} else {
--deg[u];
--deg[v];
}
}
for (auto &to : g[idx]) {
if (deg[to] <= 2) que.emplace(to);
}
used[idx] = (int)ret.size();
deg[idx] = 0;
ret.emplace_back(r);
}
for (int i = 0; i < N; i++) {
if (deg[i] > 0) return {};
}
ret.front() = ret.back();
ret.pop_back();
return ret;
}
};
void to_nice(vector<DecompNode> &g, int root = 0) {
for (auto &p : g) {
sort(p.bag.begin(), p.bag.end());
}
stack<int> st;
st.emplace(root);
while (!st.empty()) {
int idx = st.top();
st.pop();
// join
while (g[idx].child.size() > 2) {
DecompNode r;
r.child.resize(2);
r.child[0] = g[idx].child.back();
g[idx].child.pop_back();
r.child[1] = g[idx].child.back();
g[idx].child.pop_back();
r.bag = g[idx].bag;
g[idx].child.emplace_back((int)g.size());
g.emplace_back(r);
}
if (g[idx].child.size() == 2) {
for (auto &ch : g[idx].child) {
if (g[ch].bag != g[idx].bag) {
DecompNode r;
r.child = {ch};
r.bag = g[idx].bag;
ch = (int)g.size();
g.emplace_back(r);
}
}
}
// introduce / forget
if (g[idx].child.size() == 1) {
int &ch = g[idx].child[0];
vector<int> latte, malta;
set_difference(g[idx].bag.begin(), g[idx].bag.end(), g[ch].bag.begin(),
g[ch].bag.end(), back_inserter(latte));
set_difference(g[ch].bag.begin(), g[ch].bag.end(), g[idx].bag.begin(),
g[idx].bag.end(), back_inserter(malta));
if (latte.size() + malta.size() > 1) {
DecompNode r;
r.child = {ch};
r.bag = g[idx].bag;
if (!latte.empty()) {
r.bag.erase(find(r.bag.begin(), r.bag.end(), latte.back()));
} else {
r.bag.emplace_back(malta.back());
}
ch = (int)g.size();
g.emplace_back(r);
}
}
// leaf
if (g[idx].child.empty()) {
if (g[idx].bag.size() > 1) {
DecompNode r;
r.bag = g[idx].bag;
r.bag.pop_back();
g[idx].child.emplace_back((int)g.size());
g.emplace_back(r);
}
}
for (auto &ch : g[idx].child) {
st.emplace(ch);
}
}
}
#line 11 "test/verify/yosupo-tree-decomposition-width-2.test.cpp"
int main() {
string x;
int N, M;
Scanner pin(stdin);
Printer pout(stdout);
pin.read(x, x, N, M);
vector< int > A(M), B(M);
UnionFind uf(N);
for(int i = 0; i < M; i++) {
pin.read(A[i], B[i]);
--A[i], --B[i];
uf.unite(A[i], B[i]);
}
int root = -1;
for(int i = 0; i < N; i++) {
if(uf.find(i) == i) {
if(root == -1) {
root = i;
} else {
A.emplace_back(root);
B.emplace_back(i);
}
}
}
TreeDecompositionWidth2 td(N);
for(size_t i = 0; i < A.size(); i++) {
td.add_edge(A[i], B[i]);
}
auto tap = td.build();
if(tap.empty()) {
pout.writeln("-1");
return 0;
}
pout.writeln("s", "td", tap.size(), 2, N);
for(size_t i = 0; i < tap.size(); i++) {
for(auto &t : tap[i].bag) ++t;
pout.writeln("b", i + 1, tap[i].bag);
}
for(size_t i = 0; i < tap.size(); i++) {
for(auto &t : tap[i].child) pout.writeln(i + 1, t + 1);
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | cactus_00 | AC | 634 ms | 135 MB |
g++ | cactus_01 | AC | 923 ms | 159 MB |
g++ | example_00 | AC | 7 ms | 4 MB |
g++ | example_01 | AC | 6 ms | 4 MB |
g++ | many_series_parallel_00 | AC | 566 ms | 119 MB |
g++ | many_series_parallel_01 | AC | 560 ms | 119 MB |
g++ | max_cycle_00 | AC | 898 ms | 172 MB |
g++ | max_parallel_00 | AC | 324 ms | 84 MB |
g++ | max_sparse_random_00 | AC | 590 ms | 142 MB |
g++ | max_sparse_random_01 | AC | 509 ms | 142 MB |
g++ | max_sparse_random_02 | AC | 521 ms | 142 MB |
g++ | outer_planer_00 | AC | 341 ms | 111 MB |
g++ | outer_planer_01 | AC | 423 ms | 132 MB |
g++ | outer_planer_fix_00 | AC | 596 ms | 120 MB |
g++ | outer_planer_fix_01 | AC | 645 ms | 140 MB |
g++ | series_parallel_00 | AC | 351 ms | 84 MB |
g++ | series_parallel_01 | AC | 375 ms | 84 MB |
g++ | small_random_00 | AC | 7 ms | 4 MB |
g++ | small_random_01 | AC | 6 ms | 4 MB |
g++ | small_random_02 | AC | 7 ms | 4 MB |
g++ | small_random_03 | AC | 6 ms | 4 MB |
g++ | small_random_04 | AC | 7 ms | 4 MB |
g++ | tree_00 | AC | 477 ms | 140 MB |
g++ | tree_01 | AC | 501 ms | 140 MB |
clang++ | cactus_00 | AC | 630 ms | 133 MB |
clang++ | cactus_01 | AC | 821 ms | 158 MB |
clang++ | example_00 | AC | 7 ms | 4 MB |
clang++ | example_01 | AC | 6 ms | 4 MB |
clang++ | many_series_parallel_00 | AC | 558 ms | 119 MB |
clang++ | many_series_parallel_01 | AC | 557 ms | 119 MB |
clang++ | max_cycle_00 | AC | 922 ms | 172 MB |
clang++ | max_parallel_00 | AC | 341 ms | 84 MB |
clang++ | max_sparse_random_00 | AC | 551 ms | 142 MB |
clang++ | max_sparse_random_01 | AC | 541 ms | 142 MB |
clang++ | max_sparse_random_02 | AC | 554 ms | 142 MB |
clang++ | outer_planer_00 | AC | 361 ms | 111 MB |
clang++ | outer_planer_01 | AC | 416 ms | 132 MB |
clang++ | outer_planer_fix_00 | AC | 564 ms | 122 MB |
clang++ | outer_planer_fix_01 | AC | 642 ms | 140 MB |
clang++ | series_parallel_00 | AC | 339 ms | 84 MB |
clang++ | series_parallel_01 | AC | 360 ms | 84 MB |
clang++ | small_random_00 | AC | 7 ms | 4 MB |
clang++ | small_random_01 | AC | 6 ms | 4 MB |
clang++ | small_random_02 | AC | 6 ms | 4 MB |
clang++ | small_random_03 | AC | 6 ms | 4 MB |
clang++ | small_random_04 | AC | 6 ms | 4 MB |
clang++ | tree_00 | AC | 453 ms | 140 MB |
clang++ | tree_01 | AC | 485 ms | 140 MB |