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>
#define Loop(x,l,r) for (ll x = (l); x < (ll)(r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (ll)(l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;
const int N = 100010;
const int lg = 18;
int sz[N];
int anc[N][lg];
int height[N];
struct edge_node {
int v, e;
int nxt;
} pool[2*N];
int A[N];
int new_edge_node(int v, int e, int a)
{
static int nxt = 1;
pool[nxt].v = v;
pool[nxt].e = e;
pool[nxt].nxt = a;
return nxt++;
}
bool ans[N];
int buf[N];
vector<pii> edges;
int nd[N];
int n, m;
void dfs(int v)
{
height[v] = anc[v][0] >= 0? height[anc[v][0]]+1: 0;
Loop (i,0,lg-1)
anc[v][i+1] = anc[anc[v][i]][i];
nd[v] = A[v];
while (nd[v]) {
if (pool[nd[v]].v != anc[v][0]) {
anc[pool[nd[v]].v][0] = v;
dfs(pool[nd[v]].v);
}
nd[v] = pool[nd[v]].nxt;
}
}
int lca(int v, int u)
{
if (height[v] < height[u])
swap(v, u);
int dif = height[v] - height[u];
Loop (i,0,lg) {
if (dif & (1<<i))
v = anc[v][i];
}
if (v == u)
return v;
LoopR (i,0,lg) {
if (anc[v][i] != anc[u][i]) {
v = anc[v][i];
u = anc[u][i];
}
}
return anc[v][0];
}
int flush(int v)
{
nd[v] = A[v];
while (nd[v]) {
if (pool[nd[v]].v != anc[v][0]) {
auto tmp = flush(pool[nd[v]].v);
::ans[pool[nd[v]].e] |= tmp;
buf[v] += tmp;
}
nd[v] = pool[nd[v]].nxt;
}
auto tmp = buf[v];
buf[v] = 0;
return tmp;
}
int main()
{
cin.tie(0) -> sync_with_stdio(false);
cin >> n >> m;
Loop (i,0,n) {
Loop (j,0,lg)
anc[i][j] = i;
sz[i] = 1;
}
Loop (i,0,m) {
int v, u;
cin >> v >> u;
--v; --u;
if (anc[v][lg-1] == anc[u][lg-1]) {
buf[v] += 1;
buf[u] += 1;
buf[lca(v, u)] -= 2;
} else {
if (sz[anc[v][lg-1]] < sz[anc[u][lg-1]])
swap(v, u);
flush(anc[u][lg-1]);
A[v] = new_edge_node(u, edges.size(), A[v]);
A[u] = new_edge_node(v, edges.size(), A[u]);
edges.push_back({v, u});
sz[anc[v][lg-1]] += sz[anc[u][lg-1]];
anc[u][0] = v; dfs(u);
}
}
Loop (i,0,n)
if (anc[i][lg-1] == i)
flush(i);
Loop (i,0,edges.size()) {
if (!ans[i]) {
cout << edges[i].first+1 << ' ';
cout << edges[i].second+1 << '\n';
}
}
}
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