#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) {
bool fst = 1; str res = "{";
F0R(i,sz(v)) {
if (!fst) res += ", ";
fst = 0; res += ts(v[i]);
}
res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class T> str ts(T v) {
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
/**
* Description: Disjoint Set Union with path compression.
* Add edges and test connectivity. Use for Kruskal's
* minimum spanning tree.
* Time: O(\alpha(N))
* Source: CSAcademy, KACTL
* Verification: USACO superbull
*/
struct DSU {
vi e; void init(int n) { e = vi(n,-1); }
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
bool sameSet(int a, int b) { return get(a) == get(b); }
int size(int x) { return -e[get(x)]; }
bool unite(int x, int y) { // union-by-rank
x = get(x), y = get(y); if (x == y) return 0;
if (e[x] > e[y]) swap(x,y);
e[x] += e[y]; e[y] = x; return 1;
}
};
/**template<class T> T kruskal(int n, vector<pair<T,pi>> ed) {
sort(all(ed));
T ans = 0; DSU D; D.init(n+1); // edges that unite are in MST
trav(a,ed) if (D.unite(a.s.f,a.s.s)) ans += a.f;
return ans;
}*/
/**
* Description: Calculates least common ancestor in tree
* with root $R$ using binary jumping.
* Time: O(N\log N) build, O(\log N) query
* Source: USACO Camp
* Verification: Debug the Bugs
*/
template<int SZ> struct LCA {
static const int BITS = 32-__builtin_clz(SZ);
int N = 1, par[BITS][SZ], depth[SZ], mind[SZ][2];
int ind[SZ]; //index of edge from i to par[i]
vpi adj[SZ];
/// INITIALIZE
void ae(int u, int v, int i) { adj[u].pb(mp(v, i)), adj[v].pb(mp(u, i)); }
void dfs(int u, int prev, int index = 0){
ind[u] = index;
par[0][u] = prev; depth[u] = depth[prev]+1;
trav(v,adj[u]) if (v.f != prev) dfs(v.f, u, v.s);
}
void propmind(int node, int prv){
for(auto u: adj[node]){
if(u.f == prv) continue;
propmind(u.f, node);
for(int j = 0; j < 2; j++){
ckmin(mind[node][j], mind[u.f][j]);
}
}
}
void init(int _N) {
N = _N;
for(int i = 1; i <= N; i++){
//dbg(i);
mind[i][0] = mind[i][1] = MOD;
if(depth[i] == 0) dfs(i, 0);
}
FOR(k,1,BITS) FOR(i,1,N+1)
par[k][i] = par[k-1][par[k-1][i]];
}
/// QUERY
int getPar(int a, int b) {
R0F(k,BITS) if (b&(1<<k)) a = par[k][a];
return a; }
int lca(int u, int v){
if (depth[u] < depth[v]) swap(u,v);
u = getPar(u,depth[u]-depth[v]);
R0F(k,BITS) if (par[k][u] != par[k][v])
u = par[k][u], v = par[k][v];
return u == v ? u : par[0][u];
}
int dist(int u, int v) {
return depth[u]+depth[v]-2*depth[lca(u,v)]; }
};
const int mx = 100005;
int n, m, p;
pi elist[mx];
int dir[mx]; //0 = both, 1 = right, 2 = left
vpi adj[mx];
pi cond[mx];
bool visited[mx];
bool processed[mx];
int dist[mx];
int mindepth[mx];
int par[mx];
vi child[mx];
DSU dsu;
LCA<100105> lca;
void genDFS(int node, int d = 0){
//dbg(node, d);
visited[node] = 1;
dist[node] = d;
for(auto u: adj[node]){
if(processed[u.s] == 1) continue;
processed[u.s] = 1;
if(visited[u.f] == 1){
//backedge
//dbg(node, u.f);
ckmin(mindepth[node], dist[u.f]);
continue;
}
child[node].pb(u.f);
par[u.f] = node;
genDFS(u.f, d+1);
}
}
void propMinDepth(int node){
for(auto u: child[node]){
propMinDepth(u);
ckmin(mindepth[node], mindepth[u]);
}
}
int main() {
setIO();
//#warning self & double edges?
//Input
cin >> n >> m;
for(int i = 1; i <= m; i++){
int a, b;
cin >> a >> b;
elist[i] = mp(a, b);
if(a == b) continue; //take care of self edges
adj[a].pb(mp(b, i));
adj[b].pb(mp(a, i));
}
int p;
cin >> p;
for(int i = 1; i <= p; i++){
int x, y;
cin >> x >> y;
cond[i] = mp(x, y);
}
//Generate dfs forest with depths & parent. When backedge occurs, put mindepth on that node.
for(int i = 1; i <= n; i++) mindepth[i] = MOD;
for(int i = 1; i <= n; i++){
if(visited[i] == 1) continue;
genDFS(i);
}
//mindepth of every node becomes min of mindepth of all its children
for(int i = 1; i <= n; i++){
if(dist[i] == 0) propMinDepth(i);
}
//for(int i = 1; i <= n; i++) dbg(i, mindepth[i]);
//If mindepth < depth, merge and its parent in the DSU.
dsu.init(n+5);
for(int i = 1; i <= n; i++){
//dbg(i, par[i]);
if(mindepth[i] < dist[i]){
//dbg(i, par[i]);
dsu.unite(i, par[i]);
}
}
//create LCA forest with new edges with dsu.get(), init. Probably change init
for(int i = 1; i <= m; i++){
elist[i].f = dsu.get(elist[i].f);
elist[i].s = dsu.get(elist[i].s);
int a = elist[i].f;
int b = elist[i].s;
if(a != b){
lca.ae(a, b, i);
//dbg(a, b, i);
}
}
lca.init(n);
//Upedges from a to lca, downedges from lca to b.
//for(int i = 1; i <= n; i++) dbg(i, lca.depth[i]);
for(int i = 1; i <= p; i++){
pi u = cond[i];
int a = dsu.get(u.f);
int b = dsu.get(u.s);
int c = lca.lca(a, b);
//dbg(u, a, b, c);
ckmin(lca.mind[a][0], lca.depth[c]); //up
ckmin(lca.mind[b][1], lca.depth[c]); //down
//dbg(a, c);
//dbg(b, c);
}
//mindepth (for up & down) becomes min of mindepth for all its children
for(int i = 1; i <= n; i++){
if(lca.depth[i] == 1){
lca.propmind(i, 0);
}
}
//for(int i = 1; i <= n; i++) dbg(i, lca.mind[i][0], lca.mind[i][1]);
//If mindepth < depth for up/down, direct the edge up/down.
for(int i = 1; i <= n; i++){
int z = lca.ind[i];
if(z == 0) continue;
for(int j = 0; j < 2; j++){
if(lca.mind[i][j] < lca.depth[i]){
int fac = 1;
if(elist[z].f == i) fac = 0;
//dbg(i, j, z, elist[z]);
fac^=j;
if(fac == 0){
dir[z] = 1;
}
else dir[z] = 2;
/*if(elist[z].f == i){
//if j == 0, direct it right
//if j == 1, direct it left
}
else{
//if j == 0, direct it left
//if j == 1, direct it right
}*/
}
}
}
//Go through original edgelist and print
for(int i = 1; i <= m; i++){
if(dir[i] == 0) cout << 'B';
else if(dir[i] == 1) cout << 'R';
else cout << 'L';
}
cout << "\n";
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
*/
Compilation message
oneway.cpp: In function 'void setIn(std::__cxx11::string)':
oneway.cpp:123:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
oneway.cpp: In function 'void setOut(std::__cxx11::string)':
oneway.cpp:124:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 2 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 3 |
Correct |
9 ms |
7552 KB |
Output is correct |
| 4 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 5 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 6 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 7 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 8 |
Correct |
10 ms |
7808 KB |
Output is correct |
| 9 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 10 |
Correct |
9 ms |
7680 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 2 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 3 |
Correct |
9 ms |
7552 KB |
Output is correct |
| 4 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 5 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 6 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 7 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 8 |
Correct |
10 ms |
7808 KB |
Output is correct |
| 9 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 10 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 11 |
Correct |
51 ms |
14968 KB |
Output is correct |
| 12 |
Correct |
61 ms |
17400 KB |
Output is correct |
| 13 |
Correct |
75 ms |
20688 KB |
Output is correct |
| 14 |
Correct |
92 ms |
25208 KB |
Output is correct |
| 15 |
Correct |
104 ms |
26612 KB |
Output is correct |
| 16 |
Correct |
116 ms |
27704 KB |
Output is correct |
| 17 |
Correct |
110 ms |
30200 KB |
Output is correct |
| 18 |
Correct |
118 ms |
28152 KB |
Output is correct |
| 19 |
Correct |
103 ms |
31608 KB |
Output is correct |
| 20 |
Correct |
66 ms |
19192 KB |
Output is correct |
| 21 |
Correct |
63 ms |
18936 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 2 |
Correct |
8 ms |
7552 KB |
Output is correct |
| 3 |
Correct |
9 ms |
7552 KB |
Output is correct |
| 4 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 5 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 6 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 7 |
Correct |
9 ms |
7808 KB |
Output is correct |
| 8 |
Correct |
10 ms |
7808 KB |
Output is correct |
| 9 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 10 |
Correct |
9 ms |
7680 KB |
Output is correct |
| 11 |
Correct |
51 ms |
14968 KB |
Output is correct |
| 12 |
Correct |
61 ms |
17400 KB |
Output is correct |
| 13 |
Correct |
75 ms |
20688 KB |
Output is correct |
| 14 |
Correct |
92 ms |
25208 KB |
Output is correct |
| 15 |
Correct |
104 ms |
26612 KB |
Output is correct |
| 16 |
Correct |
116 ms |
27704 KB |
Output is correct |
| 17 |
Correct |
110 ms |
30200 KB |
Output is correct |
| 18 |
Correct |
118 ms |
28152 KB |
Output is correct |
| 19 |
Correct |
103 ms |
31608 KB |
Output is correct |
| 20 |
Correct |
66 ms |
19192 KB |
Output is correct |
| 21 |
Correct |
63 ms |
18936 KB |
Output is correct |
| 22 |
Correct |
231 ms |
33184 KB |
Output is correct |
| 23 |
Correct |
210 ms |
31096 KB |
Output is correct |
| 24 |
Correct |
230 ms |
30840 KB |
Output is correct |
| 25 |
Correct |
227 ms |
36856 KB |
Output is correct |
| 26 |
Correct |
226 ms |
32504 KB |
Output is correct |
| 27 |
Correct |
216 ms |
31096 KB |
Output is correct |
| 28 |
Correct |
55 ms |
12536 KB |
Output is correct |
| 29 |
Correct |
96 ms |
21496 KB |
Output is correct |
| 30 |
Correct |
107 ms |
21880 KB |
Output is correct |
| 31 |
Correct |
107 ms |
22008 KB |
Output is correct |
| 32 |
Correct |
161 ms |
27128 KB |
Output is correct |
