This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
int lg, n, m;
int unde[300001];
struct T
{
int nr1, nr2;
char cmp;
};
T op[300001];
int tata[300001], rang[300001];
int in[300001], in1[300001];
vector <int> v[300001];
vector <int> trans[300001];
bool viz[300001];
int ans[300001];
int find_tata (int nod)
{
int rez = nod;
while (nod != tata[nod])
nod = tata[nod];
while (rez != nod)
{
int cop = tata[rez];
tata[rez] = nod;
rez = cop;
}
return nod;
}
void uneste (int a, int b)
{
if (rang[a] > rang[b])
tata[b] = a;
else
{
tata[a] = b;
if (rang[a] == rang[b])
rang[a]++;
}
}
int viz1[300001];
int value[300001];
void dfs (int nod, int dist)
{
viz1[nod] = 1;
value[nod] = dist;
for (auto vecin:trans[nod])
if (!viz1[vecin])
dfs(vecin, dist + 1);
}
void dfs1 (int nod, int dist)
{
viz1[nod] = 1;
if (value[nod] + dist == lg)
ans[nod] = value[nod];
for (auto vecin:v[nod])
if (!viz1[vecin])
dfs1(vecin, dist + 1);
}
void solve ()
{
for (int i = 1; i<=n; ++i)
if (in1[unde[i]] == 0 && viz[unde[i]] == 0)
{
dfs(unde[i], 1);
viz[unde[i]] = 1;
}
for (int i = 1;i<=n;++i)
viz[i] = 0, viz1[i] = 0, ans[i] = -1;
for (int i = 1;i<=n;++i)
if (in[unde[i]] == 0 && viz[unde[i]] == 0 && value[unde[i]] == lg)
{
dfs1(unde[i], 0);
viz[unde[i]] = 1;
}
return ;
}
int main ()
{
cin >> lg >> n >> m;
for (int i = 1; i<=m; ++i)
{
int a, b;
char c;
cin >> a >> c >> b;
op[i].nr1 = a;
op[i].nr2 = b;
op[i].cmp = c;
}
for (int i = 1; i<=n; ++i)
tata[i] = i;
for (int i = 1; i<=m; ++i)
if (op[i].cmp == '=')
uneste(find_tata(op[i].nr1), find_tata(op[i].nr2));
for (int i = 1; i<=n; ++i)
unde[i] = find_tata(i);
// use unde[nod] instead of nod
for (int i = 1; i<=m; ++i)
if (op[i].cmp == '<')
{
v[unde[op[i].nr2]].push_back(unde[op[i].nr1]);
in[unde[op[i].nr1]]++;
trans[unde[op[i].nr1]].push_back(unde[op[i].nr2]);
in1[unde[op[i].nr2]]++;
}
else if (op[i].cmp == '>')
{
v[unde[op[i].nr1]].push_back(unde[op[i].nr2]);
in[unde[op[i].nr2]]++;
trans[unde[op[i].nr2]].push_back(unde[op[i].nr1]);
in1[unde[op[i].nr1]]++;
}
solve();
for (int i = 1;i<=n;++i)
if (ans[unde[i]] == -1)
cout << "?\n";
else
cout << "K" << ans[unde[i]] << '\n';
return 0;
}
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