/*
* powered by ANDRIY POPYK
* in honor of MYSELF and SEGMENT DECOMPOSITION and N^(log(N)) and (Harry Potter and the Methods of Rationality) and Monkie D. Luffy
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
//#pragma GCC optimize("O3")
//#pragma GCC target("avx,avx2,fma")
//#pragma GCC optimization ("unroll-loops")
//#pragma GCC target("avx,avx2,sse,sse2,sse3,sse4,popcnt")
using namespace std;
using namespace __gnu_pbds;
#define int long long
#define float long double
#define elif else if
#define endl "\n"
#define mod 1000000007
#define pi acos(-1)
#define eps 0.000000001
#define inf 1000'000'000'000'000'000LL
#define FIXED(a) cout << fixed << setprecision(a)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define time_init auto start = std::chrono::high_resolution_clock::now()
#define time_report \
auto end = std::chrono::high_resolution_clock::now(); \
std::cout << std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() << " ms" << endl
#define debug(x) \
{ cerr << #x << " = " << x << endl; }
#define len(x) (int) x.size()
#define sqr(x) ((x) * (x))
#define cube(x) ((x) * (x) * (x))
#define bit(x, i) (((x) >> (i)) & 1)
#define set_bit(x, i) ((x) | (1LL << (i)))
#define clear_bit(x, i) ((x) & (~(1LL << (i))))
#define toggle_bit(x, i) ((x) ^ (1LL << (i)))
#define low_bit(x) ((x) & (-(x)))
#define count_bit(x) __builtin_popcountll(x)
#define srt(x) sort(all(x))
#define rsrt(x) sort(rall(x))
#define mp make_pair
#define maxel(x) (*max_element(all(x)))
#define minel(x) (*min_element(all(x)))
#define maxelpos(x) (max_element(all(x)) - x.begin())
#define minelpos(x) (min_element(all(x)) - x.begin())
#define sum(x) (accumulate(all(x), 0LL))
#define product(x) (accumulate(all(x), 1LL, multiplies<int>()))
#define gcd __gcd
#define lcm(a, b) ((a) / gcd(a, b) * (b))
#define rev(x) (reverse(all(x)))
#define shift_left(x, k) (rotate(x.begin(), x.begin() + k, x.end()))
#define shift_right(x, k) (rotate(x.rbegin(), x.rbegin() + k, x.rend()))
#define is_sorted(x) (is_sorted_until(all(x)) == x.end())
#define is_even(x) (((x) &1) == 0)
#define is_odd(x) (((x) &1) == 1)
#define pow2(x) (1LL << (x))
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
template<typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T>
using matrix = vector<vector<T>>;
template<typename T>
using graph = vector<vector<T>>;
using hashmap = gp_hash_table<int, int, custom_hash>;
template<typename T>
vector<T> vect(int n, T val) {
return vector<T>(n, val);
}
template<typename T>
vector<vector<T>> vect(int n, int m, T val) {
return vector<vector<T>>(n, vector<T>(m, val));
}
template<typename T>
vector<vector<vector<T>>> vect(int n, int m, int k, T val) {
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, val)));
}
template<typename T>
vector<vector<vector<vector<T>>>> vect(int n, int m, int k, int l, T val) {
return vector<vector<vector<vector<T>>>>(n, vector<vector<vector<T>>>(m, vector<vector<T>>(k, vector<T>(l, val))));
}
template<typename T>
matrix<T> new_matrix(int n, int m, T val) {
return matrix<T>(n, vector<T>(m, val));
}
template<typename T>
graph<T> new_graph(int n) {
return graph<T>(n);
}
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);
}
using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
template<typename T>
using vec = vector<T>;
using pII = pair<int, int>;
template<typename T>
using enumerated = pair<T, int>;
struct Bridges {
private:
graph<pair<int, int>> g;
vector<int> tin, fup;
vector<bool> used;
int timer;
void build_dfs(int v, int p = -1, int edge_idx = -1) {
used[v] = true;
tin[v] = fup[v] = timer++;
for (auto [u, id]: g[v]) {
if (u == p) {
continue;
}
if (used[u]) {
fup[v] = min(fup[v], tin[u]);
} else {
build_dfs(u, v, id);
fup[v] = min(fup[v], fup[u]);
}
}
if (p != -1 and fup[v] > tin[p]) {
is_bridge[edge_idx] = true;
bridges.insert(edge_idx);
}
}
void build_components_dfs(int v, int comp) {
components[v] = comp;
for (auto [u, id]: g[v]) {
if (components[u] == -1 and !is_bridge[id]) {
build_components_dfs(u, comp);
}
}
}
public:
set<int> bridges;
vec<bool> is_bridge;
vec<int> components;
int components_count;
graph<pair<int, int>> condensation;
vec<pair<int, int>> edges;
Bridges(graph<pII> >, int m) {
g = gt;
int idx = m;
tin = fup = vector<int>(len(g));
used = vector<bool>(len(g));
timer = 0;
is_bridge = vec<bool>(idx);
for (int i = 0; i < len(g); ++i) {
if (!used[i]) {
build_dfs(i);
}
}
}
void build_components() {
components = vec<int>(len(g), -1);
components_count = 0;
for (int i = 0; i < len(g); ++i) {
if (components[i] == -1) {
build_components_dfs(i, components_count++);
}
}
}
void build_condensation() {
condensation = graph<pII>(components_count);
vec<set<pair<int, int>>> edges_(components_count);
for (int i = 0; i < len(g); ++i) {
for (auto &to: g[i]) {
if (components[i] != components[to.first]) {
edges_[components[i]].insert({components[to.first], to.second});
}
}
}
for (int i = 0; i < components_count; ++i) {
for (auto &to: edges_[i]) {
condensation[i].push_back(to);
}
}
}
void print_condensation() {
// print edges of condensation
for (int i = 0; i < components_count; ++i) {
for (auto [u, id]: condensation[i]) {
cout << i << " " << u << " " << id << endl;
}
}
}
};
struct state {
public:
int left_f, right_f;
int left_s, right_s;
state &operator=(state _val) {
this->left_f = _val.left_f;
this->right_f = _val.right_f;
this->left_s = _val.left_s;
this->right_s = _val.right_s;
return *this;
}
};
template<typename T>
struct option {
T val;
bool is_empty;
option() : is_empty(true) {}
option(T val) : val(val), is_empty(false) {}
option<T> &operator=(T _val) {
this->val = _val;
this->is_empty = false;
return *this;
}
option<T> &operator=(option<T> _val) {
this->val = _val;
this->is_empty = false;
return *this;
}
T operator*() {
if (is_empty) {
throw runtime_error("option is none");
}
return val;
}
bool operator==(option<T> _val) {
if (is_empty and _val.is_empty) {
return true;
}
if (is_empty or _val.is_empty) {
return false;
}
return val == _val.val;
}
bool operator!=(option<T> _val) {
return !(*this == _val);
}
bool is_some() {
return !is_empty;
}
bool is_none() {
return is_empty;
}
};
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int n, m;
cin >> n >> m;
graph<pII> g(n);
vec<pII> edges(m);
for (int i = 0; i < m; ++i) {
int v, u;
cin >> v >> u;
--v, --u;
g[v].emplace_back(u, i);
g[u].emplace_back(v, i);
edges[i] = {v, u};
}
Bridges b(g, m);
b.build_components();
b.build_condensation();
vec<char> ans(m,'B');
for (int i = 0; i < m; i++) {
if (!b.is_bridge[i]) {
ans[i] = 'B';
}
}
int p;
cin >> p;
vec<pair<int, int>> queries;
while (p--) {
int v, u;
cin >> v >> u;
--v, --u;
v = b.components[v];
u = b.components[u];
queries.emplace_back(v, u);
}
int dn = b.components_count;
// b.print_condensation();
vec<int> alias(dn, -1);
vec<pII> sub_tree(dn);
int cnt = 0;
function<void(int)> build_alias = [&](int v) {
alias[v] = cnt++;
sub_tree[v] = {alias[v], alias[v]};
for (auto [u, id]: b.condensation[v]) {
if (alias[u] == -1) {
build_alias(u);
}
}
sub_tree[v].second = cnt - 1;
};
vec<option<state>> dp(dn);
vec<int> to_finish_left(dn);
vec<int> to_finish_right(dn);
vec<int> to_start_left(dn);
vec<int> to_start_right(dn);
for (int i = 0; i < dn; ++i) {
if (alias[i] == -1) {
build_alias(i);
}
}
for (int i = 0; i < dn; i++) {
to_finish_left[i] = to_finish_right[i] = to_start_left[i] = to_start_right[i] = alias[i];
}
for (auto [v, u]: queries) {
chmin(to_finish_left[v], alias[u]);
chmax(to_finish_right[v], alias[u]);
chmin(to_start_left[u], alias[v]);
chmax(to_start_right[u], alias[v]);
}
function<void(int, int, int)> dfs = [&](int v, int p, int id = -1) {
if (dp[v].is_some())
return;
state cur = {to_finish_left[v], to_finish_right[v], to_start_left[v], to_start_right[v],};
for (auto [u, uid]: b.condensation[v]) {
if (u == p)
continue;
dfs(u, v, uid);
if (dp[u].is_some()) {
state s = *dp[u];
chmin(cur.left_f, s.left_f);
chmin(cur.left_s, s.left_s);
chmax(cur.right_f, s.right_f);
chmax(cur.right_s, s.right_s);
}
}
dp[v] = cur;
if (id != -1) {
ans[id] = 'B';
if (sub_tree[v].first > cur.left_f or sub_tree[v].second < cur.right_f) {
if (b.components[edges[id].first] != p)
ans[id] = 'R';
else
ans[id] = 'L';
}
if (sub_tree[v].first > cur.left_s or sub_tree[v].second < cur.right_s) {
if (b.components[edges[id].first] != p)
ans[id] = 'L';
else
ans[id] = 'R';
}
}
};
for (int i = 0; i < dn; ++i) {
if (dp[i].is_none()) {
dfs(i, -1, -1);
}
}
for (int i = 0; i < m; ++i) {
cout << ans[i];
}
}
Compilation message
oneway.cpp: In member function 'void Bridges::build_dfs(long long int, long long int, long long int)':
oneway.cpp:158:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
158 | for (auto [u, id]: g[v]) {
| ^
oneway.cpp: In member function 'void Bridges::build_components_dfs(long long int, long long int)':
oneway.cpp:177:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
177 | for (auto [u, id]: g[v]) {
| ^
oneway.cpp: In member function 'void Bridges::print_condensation()':
oneway.cpp:236:23: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
236 | for (auto [u, id]: condensation[i]) {
| ^
oneway.cpp: In lambda function:
oneway.cpp:352:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
352 | for (auto [u, id]: b.condensation[v]) {
| ^
oneway.cpp: In function 'int main()':
oneway.cpp:377:15: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
377 | for (auto [v, u]: queries) {
| ^
oneway.cpp: In lambda function:
oneway.cpp:388:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17'
388 | for (auto [u, uid]: b.condensation[v]) {
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
604 KB |
Output is correct |
| 4 |
Correct |
1 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
1 ms |
604 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
1 ms |
464 KB |
Output is correct |
| 10 |
Correct |
1 ms |
604 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
604 KB |
Output is correct |
| 4 |
Correct |
1 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
1 ms |
604 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
1 ms |
464 KB |
Output is correct |
| 10 |
Correct |
1 ms |
604 KB |
Output is correct |
| 11 |
Correct |
32 ms |
13612 KB |
Output is correct |
| 12 |
Correct |
39 ms |
15500 KB |
Output is correct |
| 13 |
Correct |
47 ms |
18832 KB |
Output is correct |
| 14 |
Correct |
66 ms |
26880 KB |
Output is correct |
| 15 |
Correct |
82 ms |
29820 KB |
Output is correct |
| 16 |
Correct |
125 ms |
49236 KB |
Output is correct |
| 17 |
Correct |
136 ms |
50816 KB |
Output is correct |
| 18 |
Correct |
126 ms |
49232 KB |
Output is correct |
| 19 |
Correct |
121 ms |
52052 KB |
Output is correct |
| 20 |
Correct |
42 ms |
16628 KB |
Output is correct |
| 21 |
Correct |
48 ms |
16708 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
604 KB |
Output is correct |
| 4 |
Correct |
1 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
1 ms |
604 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
1 ms |
860 KB |
Output is correct |
| 9 |
Correct |
1 ms |
464 KB |
Output is correct |
| 10 |
Correct |
1 ms |
604 KB |
Output is correct |
| 11 |
Correct |
32 ms |
13612 KB |
Output is correct |
| 12 |
Correct |
39 ms |
15500 KB |
Output is correct |
| 13 |
Correct |
47 ms |
18832 KB |
Output is correct |
| 14 |
Correct |
66 ms |
26880 KB |
Output is correct |
| 15 |
Correct |
82 ms |
29820 KB |
Output is correct |
| 16 |
Correct |
125 ms |
49236 KB |
Output is correct |
| 17 |
Correct |
136 ms |
50816 KB |
Output is correct |
| 18 |
Correct |
126 ms |
49232 KB |
Output is correct |
| 19 |
Correct |
121 ms |
52052 KB |
Output is correct |
| 20 |
Correct |
42 ms |
16628 KB |
Output is correct |
| 21 |
Correct |
48 ms |
16708 KB |
Output is correct |
| 22 |
Correct |
144 ms |
51032 KB |
Output is correct |
| 23 |
Correct |
154 ms |
49412 KB |
Output is correct |
| 24 |
Correct |
174 ms |
49604 KB |
Output is correct |
| 25 |
Correct |
154 ms |
55308 KB |
Output is correct |
| 26 |
Correct |
156 ms |
50632 KB |
Output is correct |
| 27 |
Correct |
141 ms |
49496 KB |
Output is correct |
| 28 |
Correct |
25 ms |
12240 KB |
Output is correct |
| 29 |
Correct |
56 ms |
19400 KB |
Output is correct |
| 30 |
Correct |
51 ms |
19440 KB |
Output is correct |
| 31 |
Correct |
58 ms |
19740 KB |
Output is correct |
| 32 |
Correct |
106 ms |
32200 KB |
Output is correct |
