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;
vector<int> parent;
vector<int> depth;
vector<int> root;
vector<int> union_parent;
vector<vector<int>> children;
int find(int a)
{
if (union_parent[a] == a)
return a;
return union_parent[a] = find(union_parent[a]);
}
bool unite(int a, int b)
{
a = find(a);
b = find(b);
if (a == b)
return false;
if (depth[b] > depth[a])
swap(a, b);
union_parent[a] = b;
return true;
}
vector<vector<int>> adj;
int iter = 0;
int dfs_reconstruct(int i, int d, int p, int r)
{
root[i] = r;
parent[i] = p;
depth[i] = d;
iter++;
int subtree = 1;
// assert(iter < 10000);
for (int c : adj[i])
{
if (c == p)
continue;
subtree += dfs_reconstruct(c, d + 1, i, r);
}
return subtree;
}
signed main()
{
cin.tie(0);
ios_base::sync_with_stdio(false);
int n, m;
cin >> n >> m;
children.resize(n);
adj.resize(n);
parent = root = union_parent = depth = vector<int>(n);
for (int i = 0; i < n; i++)
{
parent[i] = root[i] = union_parent[i] = i;
children[i] = vector<int>{i};
depth[i] = 1;
}
while (m--)
{
int a, b;
cin >> a >> b;
a--, b--;
// for (int i = 0; i < n; i++)
// assert(root[i] == root[parent[i]] && root[i] == root[find(i)] && root[i] == root[parent[find(i)]]);
if (root[a] == root[b])
{
a = find(a);
b = find(b);
while (a != b)
{
// assert(root[a] == root[b]);
if (depth[a] < depth[b])
swap(a, b);
// assert(parent[a] != a);
unite(a, parent[a]);
a = find(a);
b = find(b);
}
}
else
{
if (children[root[a]].size() < children[root[b]].size())
swap(a, b);
vector<pair<int, int>> inserts;
vector<int> new_nodes;
int roots = 0;
for (int i : children[root[b]])
{
int p = parent[i];
new_nodes.push_back(i);
if (i == p)
{
roots++;
continue;
}
inserts.push_back({i, p});
}
assert(roots == 1);
assert(inserts.size() == new_nodes.size() - 1);
children[root[b]].clear();
for (auto [a, b] : inserts)
{
adj[a].push_back(b);
adj[b].push_back(a);
}
iter = 0;
assert(dfs_reconstruct(b, depth[a] + 1, a, root[a]) == new_nodes.size());
for (int node : new_nodes)
{
// assert(root[node] == root[a]);
children[root[a]].push_back(node);
if (depth[node] < depth[find(node)])
union_parent[find(node)] = node;
}
for (auto [a, b] : inserts)
{
adj[a].clear();
adj[b].clear();
}
}
}
for (int i = 0; i < n; i++)
{
if (find(i) != find(parent[i]))
cout << i + 1 << " " << parent[i] + 1 << "\n";
}
}
Compilation message (stderr)
In file included from /usr/include/c++/10/cassert:44,
from /usr/include/x86_64-linux-gnu/c++/10/bits/stdc++.h:33,
from pipes.cpp:1:
pipes.cpp: In function 'int main()':
pipes.cpp:145:56: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
145 | assert(dfs_reconstruct(b, depth[a] + 1, a, root[a]) == new_nodes.size());
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~
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