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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#426413 | #6329. Colorful Graph | EXODUS | TL | 0ms | 3616kb | C++17 | 5.6kb | 2024-05-31 10:17:35 | 2024-05-31 10:17:36 |
Judging History
answer
#include <vector>
#include <algorithm>
#include <cassert>
namespace exodus{
namespace internal{
class nothing{
public:
nothing(){}
friend nothing operator +(const nothing&,const nothing&){return nothing();}
};
}
template<class info=internal::nothing>
struct dsu{
public:
struct node{
public:
node(){anc=-1,siz=1,ifo=info();}
int anc,siz;
info ifo;
};
dsu():_n(0){}
explicit dsu(int n){
_n=n;node.resize(n);
for(int i=0;i<n;i++)
node[i].anc=i;
}
void build(int n){
_n=n;
node.clear();
node.resize(n);
for(int i=0;i<n;i++)
node[i].anc=i;
}
int find(int u){
assert(0<=u&&u<_n);
return __find(u);
}
void merge(int u,int v){
assert(0<=u&&u<_n);
assert(0<=v&&v<_n);
u=__find(u),v=__find(v);
if(node[u].siz<node[v].siz)std::swap(u,v);
node[v].anc=u;
node[u].ifo=node[u].ifo+node[v].ifo;
}
bool check(int u,int v){
assert(0<=u&&u<_n);
assert(0<=v&&v<_n);
u=__find(u),v=__find(v);
return u==v;
}
private:
int _n;
std::vector<node>node;
int __find(int u){
return u==node[u].anc?u:node[u].anc=__find(node[u].anc);
}
};
}
#include <algorithm>
#include <array>
#include <cassert>
#include <functional>
#include <numeric>
#include <queue>
#include <tuple>
#include <vector>
#include <iostream>
namespace exodus{
struct scc_graph{
public:
scc_graph(){n=0;}
explicit scc_graph(int _n){n=_n;g.resize(n);}
std::vector<std::pair<int,int>>edges(){return edge;}
std::pair<int,int>get_edge(int i){
assert(0<=i&&i<(int)edge.size());
return edge[i];
}
void add_edge(int u,int v){
assert(0<=u&&u<n);
assert(0<=v&&v<n);
g[u].emplace_back(v);
edge.emplace_back(u,v);
}
std::vector<std::vector<int>> scc(){
std::vector<int>dfn(n,0),low(n,0),stk,ins(n,0),col(n,-1);
int dfx=0,col_cnt=0;
stk.reserve(n);
std::function<void(int)>tarjan=[&](int u){
dfn[u]=low[u]=++dfx;ins[u]=true;stk.emplace_back(u);
for(auto v:g[u])
if(!dfn[v])tarjan(v),low[u]=std::min(low[u],low[v]);
else if(ins[v])low[u]=std::min(low[u],dfn[v]);
if(dfn[u]==low[u]){
while(u!=stk.back())col[stk.back()]=col_cnt,ins[stk.back()]=false,stk.pop_back();
col[stk.back()]=col_cnt,ins[stk.back()]=false,stk.pop_back();
++col_cnt;
}
};
for(int i=0;i<n;i++)
if(!dfn[i])
tarjan(i);
std::vector<std::vector<int>>res(col_cnt);
for(int i=0;i<n;i++)
res[col[i]].emplace_back(i);
return res;
}
private:
int n;
std::vector<std::vector<int>>g;
std::vector<std::pair<int,int>>edge;
};
}
#include<bits/stdc++.h>
using namespace std;
bitset<7000>bts[7000];
int main(){
cin.tie(nullptr)->sync_with_stdio(false);
int n,m;
cin>>n>>m;
vector<pair<int,int>>edge(m);
for(auto& [u,v]:edge)
cin>>u>>v,--u,--v;
exodus::scc_graph sccG(n);
for(auto [u,v]:edge)
sccG.add_edge(u,v);
auto scc=sccG.scc();
vector<int>col(n);
for(auto& vertex:scc){
static int colx=0;
for(auto& u:vertex){
col[u]=colx;
}
++colx;
}
int k=scc.size();
vector<vector<int>>g(k);
set<pair<int,int>>edge_vis;
for(auto [u,v]:edge){
if(col[u]==col[v])
continue;
if(edge_vis.count(make_pair(col[u],col[v])))
continue;
edge_vis.emplace(col[u],col[v]);
g[col[u]].emplace_back(col[v]);
}
vector<int>deg(k);
auto bfs=[&](int s){
static queue<int>q;
q.emplace(s);
bts[s].reset();
bts[s].set(s);
while(!q.empty()){
int u=q.front();
q.pop();
for(auto v:g[u]){
if(!bts[s].test(v)){
bts[s].set(v);
q.emplace(v);
}
}
}
};
for(int i=0;i<k;i++){
bfs(i);
bts[i].set(i,false);
deg[i]=bts[i].count();
}
int cnt=k;
vector<int>match(k);
vector<int>nxt(k,-1);
vector<int>used(k);
auto dfs=[&](auto self,int u)-> bool {
for(int v=bts[u]._Find_first();v<7000;v=bts[u]._Find_next(v)){
if(used[v]==0){
used[v]=1;
if(nxt[v]==-1||self(self,nxt[v])){
nxt[v]=u;
return true;
}
}
}
return false;
};
vector<int>ord(k);
iota(ord.begin(),ord.end(),0);
sort(ord.begin(),ord.end(),[&](int x,int y){
return deg[x]<deg[y];
});
// mt19937 seed(chrono::steady_clock::now().time_since_epoch().count());
// shuffle(ord.begin(),ord.end(),seed);
for(int i=0;i<k;i++){
fill(used.begin(),used.end(),0);
if(dfs(dfs,ord[i]))
cnt--;
}
#ifdef EXODUS
cerr<<cnt<<'\n';
#endif
exodus::dsu dsu(k);
for(int u=0;u<k;u++){
if(nxt[u]!=-1){
dsu.merge(u,nxt[u]);
}
}
vector<int>ans(k);
for(int i=0;i<k;i++){
static int colx=0;
if(dsu.find(i)==i){
ans[i]=++colx;
}
}
for(int i=0;i<k;i++){
ans[i]=ans[dsu.find(i)];
}
for(int i=0;i<n;i++)
cout<<ans[col[i]]<<' ';
cout<<'\n';
#ifdef EXODUS
cerr<<clock()<<'\n';
vector<vector<int>>_g(n);
vector<vector<int>>reach(n,vector<int>(n));
for(auto [u,v]:edge){
_g[u].emplace_back(v);
}
auto _bfs=[&](int s){
static queue<int>q;
q.emplace(s);
reach[s][s]=true;
while(!q.empty()){
int u=q.front();
q.pop();
for(auto v:_g[u]){
if(!reach[s][v]){
reach[s][v]=true;
q.emplace(v);
}
}
}
};
for(int i=0;i<n;i++)
_bfs(i);
// for(int i=0;i<n;i++,cerr<<'\n')
// for(int j=0;j<n;j++)
// cerr<<reach[i][j]<<' ';
vector<int>_lis;
for(int i=1;i<=cnt;i++){
_lis.clear();
for(int j=0;j<n;j++)
if(ans[col[j]]==i)
_lis.emplace_back(j);
for(auto u:_lis)
for(auto v:_lis){
if(!reach[u][v]&&!reach[v][u]){
cerr<<"Wrong Answer\n";
return 1;
}
}
}
cerr<<"Accept\n";
#endif
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3616kb
input:
5 5 1 4 2 3 1 3 2 5 5 1
output:
2 1 2 1 2
result:
ok AC
Test #2:
score: 0
Accepted
time: 0ms
memory: 3576kb
input:
5 7 1 2 2 1 4 3 5 1 5 4 4 1 4 5
output:
1 1 2 1 1
result:
ok AC
Test #3:
score: 0
Accepted
time: 0ms
memory: 3616kb
input:
8 6 6 1 3 4 3 6 2 3 4 1 6 4
output:
1 1 1 1 2 1 3 4
result:
ok AC
Test #4:
score: -100
Time Limit Exceeded
input:
7000 6999 4365 4296 2980 3141 6820 4995 4781 24 2416 5844 2940 2675 3293 2163 3853 5356 262 6706 1985 1497 5241 3803 353 1624 5838 4708 5452 3019 2029 6161 3849 4219 1095 1453 4268 4567 1184 1857 2911 3977 1662 2751 6353 6496 2002 6628 1407 4623 425 1331 4445 4277 1259 3165 4994 1044 2756 5788 5496 ...