#include <bits/stdc++.h>
using namespace std;
/*
se p dois intervalos [a,b] a cobre b, ent a e b tem que ter tipos diferentes
resposta válida tem que ter alguem que cobre outro
ignorar os cobertos
pensar no círculo
vendo os independentes posso colocar eles de cores diferentes pra aproveitar interseções
parte com eles sozinhos tem que ter intervalos contidos bons
qnt par deles fechou
*/
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long double, long double> pdd;
const int MAXN = 1e5+10;
vector<int> f[MAXN][2]; // {start, end} fios
pii cb[MAXN];
bool ty[MAXN];
bool ind[MAXN], iscy[MAXN]; // se é independente, ciclo
int pai[MAXN]; // pros ruins, quem contem ele
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
// cout << fixed << setprecision(7);
int n, m;
cin >> n >> m;
int a, b, cyd=0, cyl=1e9+1;
vector<pair<pii, int>> ord, cy;
for (int i=0;i<m;i++){
cin >> a >> b;
cb[i] = {a,b}, pai[i]=-1;
if(b<a){
if (b==a-1){
a=1,b=n;
cb[i]={a,b};
}else{
cyd = max(cyd, b), cyl = min(cyl, a), iscy[i]=1;
cy.push_back({{a,-b}, i});
f[1][0].push_back(i);
f[b][1].push_back(i);
f[a][0].push_back(i);
continue;
}
}
ord.push_back({{a,-b}, i});
f[a][0].push_back(i);
f[b][1].push_back(i);
}
if (!ord.empty()) sort(ord.begin(), ord.end());
bool ruim = 0;
for (auto &x:ord){
x.first.second = -x.first.second;
if (x.first.second <= cyd) continue;
if (x.first.first >= cyl) break;
cyd = x.first.second, ind[x.second]=1, ruim^=1;
}
if (!ord.empty() && ord[0].first.first == 1 && ord[0].first.second==n) ruim=0; // se tem um cara que cobre todo mundo ou nn tem ciclos
else{ // ver ciclos
sort(cy.begin(), cy.end());
cyd = 0;
for (auto &x:cy){
x.first.second*=-1;
if (x.first.second<=cyd) continue;
cyd=x.first.second, ind[x.second]=1, ruim^=1;
}
}
ord.clear();
cy.clear();
set<int> all, im;
vector<int> bn; // bons (ciclos aparecem só no final)
int lst=0;
map<pii, bool> valid;
for (int i=1;i<=n;i++){
for (auto &u:f[i][0]) if (ind[u]){
if (!iscy[u] || i>=cyl) bn.push_back(u);
im.insert(u);
lst = u;
}
while (!f[i][0].empty()){
int u = f[i][0].back();
f[i][0].pop_back();
if (ind[u]) continue;
all.insert(u);
pai[u] = lst; // se um ruim cobre um trecho sem importantes ent ele deveria ser importante
}
if (im.size()+all.size()<2){
cout << "impossible\n";
return 0;
}
if (im.size()==2){
pii srch = {*im.begin(), *next(im.begin())};
if (!valid.count(srch)) valid[srch] = 1;
if (all.empty()) valid[srch] = 0;
}
while (!f[i][1].empty()){
int u = f[i][1].back();
f[i][1].pop_back();
if (ind[u]) im.erase(u);
else all.erase(u);
}
}
pii want = {-1,-1};
for (auto &x:valid) if (x.second){
want = x.first;
break;
}
if (want.first==-1){ // pegar não-interseção
lst = bn.back();
for (int i=0;i<bn.size();i++){
int l = cb[bn[i]].first, r=cb[bn[i]].second;
if (l>cyd){
want = {bn[i], lst};
// cerr << bn[i] << ' ' << lst << ' ' << " for " << cyd << '\n';
break;
}
if (l<=r) cyd=cb[bn[i]].second;
else cyd=n;
}
}
if (ruim && want.first==-1){ // quantidade é ímpar e não tem uma interseção que é válida nem um cara que cobre todo mundo
cout << "impossible\n";
return 0;
}
// for (auto &x:bn) cerr << x << '\n';
int sz = bn.size();
if (!ruim){
ty[bn[0]]=1;
for (int i=1;i<sz;i++) ty[bn[i]] = !ty[bn[i-1]];
}else{
for (int i=0;i<sz;i++){
if (bn[i]==want.first) want.first = m+i;
else if (bn[i]==want.second) want.second=m+i;
}
want.first-=m, want.second-=m;
if (want.second<want.first) swap(want.first, want.second);
bool color = 1;
if (want == ((pii){0,sz-1})){
for (int i=0;i<sz;i++){
ty[bn[i]] = color, color=!color;
}
}else{
for (int i=want.second;i<sz;i++){
ty[bn[i]] = color, color=!color;
}
for (int i=0;i<=want.first;i++){
ty[bn[i]] = color, color=!color;
}
}
}
for (int i=0;i<m;i++){
if (pai[i] == -1) cout << ty[i];
else cout << !ty[pai[i]];
}
cout << '\n';
return 0;
}
Compilation message
alternating.cpp: In function 'int main()':
alternating.cpp:128:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
128 | for (int i=0;i<bn.size();i++){
| ~^~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 2 |
Correct |
2 ms |
6224 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
6224 KB |
'impossible' claimed, but there is a solution |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 2 |
Correct |
2 ms |
6224 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
6224 KB |
'impossible' claimed, but there is a solution |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 2 |
Correct |
2 ms |
6224 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
6224 KB |
'impossible' claimed, but there is a solution |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
45 ms |
13296 KB |
Output is correct |
| 2 |
Correct |
4 ms |
6224 KB |
Output is correct |
| 3 |
Correct |
13 ms |
10248 KB |
Output is correct |
| 4 |
Correct |
24 ms |
12720 KB |
Output is correct |
| 5 |
Correct |
55 ms |
13412 KB |
Output is correct |
| 6 |
Correct |
40 ms |
12284 KB |
Output is correct |
| 7 |
Correct |
50 ms |
13052 KB |
Output is correct |
| 8 |
Correct |
5 ms |
6736 KB |
Output is correct |
| 9 |
Correct |
4 ms |
6480 KB |
Output is correct |
| 10 |
Correct |
71 ms |
13772 KB |
Output is correct |
| 11 |
Correct |
47 ms |
12284 KB |
Output is correct |
| 12 |
Correct |
44 ms |
13256 KB |
Output is correct |
| 13 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 14 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 15 |
Correct |
42 ms |
11260 KB |
Output is correct |
| 16 |
Correct |
30 ms |
12808 KB |
Output is correct |
| 17 |
Correct |
85 ms |
13820 KB |
Output is correct |
| 18 |
Correct |
76 ms |
11588 KB |
Output is correct |
| 19 |
Correct |
4 ms |
6736 KB |
Output is correct |
| 20 |
Correct |
34 ms |
11388 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
3 ms |
6224 KB |
Output is correct |
| 2 |
Correct |
2 ms |
6224 KB |
Output is correct |
| 3 |
Incorrect |
2 ms |
6224 KB |
'impossible' claimed, but there is a solution |
| 4 |
Halted |
0 ms |
0 KB |
- |
