#include <bits/stdc++.h>
using namespace std;
#define int long long
struct cmp2
{
bool operator() (pair<int,int>x,pair<int,int>y) const
{
if (x.first != y.first)
return x.first < y.first;
return true;
}
};
struct grup
{
vector<int>noduri_alive;
int nr_oameni;
multiset<pair<int,int>,cmp2>edges;
};
int n,m,s[200005];
vector<pair<int,int>>G[200005];
int t[200005],sz[200005];
grup g[200005];
bool sol_finala[200005];
bool cmp(int x,int y)
{
if (g[x].nr_oameni != g[y].nr_oameni)
return g[x].nr_oameni < g[y].nr_oameni;
return x < y;
}
multiset<int,decltype(cmp)*>st(cmp);
int ancestor(int nod)
{
while (nod != t[nod])
nod = t[nod];
return nod;
}
void join(int x,int y)
{
if (sz[x] < sz[y])
swap(x,y);
sz[x] += sz[y];
t[y] = x;
g[x].nr_oameni += g[y].nr_oameni;
for (auto it : g[y].noduri_alive)
g[x].noduri_alive.push_back(it);
for (auto it : g[y].edges)
g[x].edges.insert(it);
g[y].nr_oameni = 0;
g[y].noduri_alive.clear();
g[y].edges.clear();
st.insert(x);
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> n >> m;
for (int i = 1; i <= n; i++)
cin >> s[i];
for (int i = 1; i <= m; i++)
{
int x,y;
cin >> x >> y;
G[x].push_back({s[y],y});
G[y].push_back({s[x],x});
}
for (int i = 1; i <= n; i++)
{
t[i] = i;
sz[i] = 1;
g[i].noduri_alive = {i};
g[i].nr_oameni = s[i];
for (auto it : G[i])
g[i].edges.insert(it);
st.insert(i);
}
while (st.size() >= 2)
{
/*for (auto it : st)
{
cout << it << ' ' << g[it].nr_oameni << endl;
for (auto itt : g[it].noduri_alive)
cout << itt << ' ';
cout << endl;
for (auto itt : g[it].edges)
cout << itt.first << ' ' << itt.second << endl;
cout << endl;
}
cout << endl;*/
int nod = *st.begin();
//cout << nod << endl;
while (true)
{
pair<int,int>aux = *(g[nod].edges.begin());
if (ancestor(aux.second) == nod)
g[nod].edges.erase(aux);
else
break;
}
pair<int,int>aux = *(g[nod].edges.begin());
//cout << aux.first << ' ' << aux.second << endl;
g[nod].edges.erase(g[nod].edges.begin());
if (aux.first > g[nod].nr_oameni)
{
//cout << "caz1 " << nod << endl;
st.erase(nod);
g[nod].noduri_alive.clear();
}
else
{
//cout << "caz2 " << nod << ' ';
int x = aux.second;
x = ancestor(x);
//cout << x << endl;
st.erase(st.find(nod));
//cout << st.size() << endl;
if (g[x].noduri_alive.size() != 0)
st.erase(x);
join(nod,x);
}
}
for (auto it : st)
{
for (auto x : g[it].noduri_alive)
sol_finala[x] = true;
}
for (int i = 1; i <= n; i++)
{
if (sol_finala[i] == false)
cout << 0;
else
cout << 1;
}
return 0;
}
/**
fiecare muchie devine defapt doua muchii, una x -> y cu cost s[y] si una y -> x cu cost s[x]
iau grupul cu macar un nod alive cu cei mai putini oameni si muchia lui spre un nod cu s cat mai mic
daca nu le pot conecta, marchez ca not alive toate nodurile alive din grup
daca le pot conecta, fac un small to large pe noduri (nu conteaza daca alive sau nu) pentru a le uni
ok, idee penala, acum ramane cum implementez
tin un dsu pentru grupuri, iar in tatal grupului tin:
-nodurile alive din grup
-cate alive am
-cati oameni am
-muchiile, sortate dupa cost
imi pot tine un set cu tatii grupurilor cu macar un nod alive, pentru fiecare retinand:
-ofc nodul tata
-numarul de oameni
o sa am ceva gen:
while (setul mai are >= 2 grupuri alive)
{
iau si eu grupul din set cu numar minim de oameni
lui ii iau muchia minima pentru care nu sunt ambele noduri conectate de muchie in grupul lui nod
daca pe muchia asta nu pot conecta, atunci scot din set nodul nod (si atat)
daca pe muchia asta pot conecta, am doua cazuri:
1. nodul de care conectez nu e alive -> il scot pe asta din set, le dau join si bag combinata lor in set
2. nodul de care conectez e alive -> ii scot pe ambii din set, le dau join si bag combinata lor in set
}
apoi, din grupul care mi-a mai ramas singur in set, afisez alea alive
**/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1020 ms |
24920 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1036 ms |
24920 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
24924 KB |
Output is correct |
| 2 |
Execution timed out |
1083 ms |
75560 KB |
Time limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
24924 KB |
Output is correct |
| 2 |
Execution timed out |
1090 ms |
76116 KB |
Time limit exceeded |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1020 ms |
24920 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
