이 제출은 이전 버전의 oj.uz에서 채점하였습니다. 현재는 제출 당시와는 다른 서버에서 채점을 하기 때문에, 다시 제출하면 결과가 달라질 수도 있습니다.
#include <bits/stdc++.h>
using namespace std;
//#pragma GCC optimize ("O3")
//#pragma GCC target ("sse4")
#ifndef LOCAL
#define cerr if(false) cerr
#endif
#define endl "\n"
#define out(x) "[" << #x << "=" << x << "]"
struct debug {
debug() { cerr << "DEBUGGER: " << endl; }
~debug() { cerr << endl << "DEBUGGER_END " << endl; }
template<class T>
debug& operator <<(const T x) {
cerr << x << " ";
return *this;
}
};
template<class T> inline ostream &operator <<(ostream &out, const vector<T> &x) {
for(const auto &it : x) {
out << it << " ";
}
return out;
}
template<class T, class T2> inline ostream &operator <<(ostream &out, const pair<T, T2> &x) {
return out << x.first << " " << x.second;
}
template<class T, class T2> inline bool chkmax(T &x, const T2 &y) { return x < y ? x = y, 1 : 0; }
template<class T, class T2> inline bool chkmin(T &x, const T2 &y) { return x > y ? x = y, 1 : 0; }
typedef long long ll;
const ll mod = 1e9 + 7;
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~//
const int MAX_N = 1e5 + 10;
int n, m;
int par[MAX_N], dist[MAX_N], sz[MAX_N];
vector<pair<int, int> > g[MAX_N];
const int LOG = 17;
int lift[MAX_N][LOG];
pair<int, int> edg[MAX_N];
bool used[MAX_N];
int cnt = 0;
void dfs(int x, int p) {
par[x] = par[p];
dist[x] = dist[p] + 1;
lift[x][0] = p;
for(int i = 1; i < LOG; i ++) {
lift[x][i] = lift[lift[x][i - 1]][i - 1];
}
cerr << "Dfs " << x << " " << p << endl;
for(auto it : g[x]) {
if(it.first == p) {continue;}
dfs(it.first, x);
}
}
int lca(int x, int y) {
if(dist[x] < dist[y]) {swap(x, y);}
for(int i = LOG - 1; i >= 0; i --) {
if(dist[lift[x][i]] >= dist[y]) {
x = lift[x][i];
}
}
if(x == y) {
return x;
}
for(int i = LOG - 1; i >= 0; i --) {
if(lift[x][i] != lift[y][i]) {
x = lift[x][i];
y = lift[y][i];
}
}
return lift[x][0];
}
int toRem[MAX_N], toAdd[MAX_N];
int apply(int x, int p) {
ll cnt = toRem[x] + toAdd[x];
cerr << "Applying " << x << " " << p << endl;
for(auto it : g[x]) {
if(it.first == p) {continue;}
int now = apply(it.first, x);
if(now > 0) {
used[it.second] = true;
}
cnt += now;
}
toRem[x] = toAdd[x] = 0;
cerr << "After applying " << x << " " << p << " " << cnt << endl;
return cnt;
}
bool merge(int x, int y) {
int xx = par[x];
int yy = par[y];
if(xx == yy) {
return false;
}
if(sz[xx] < sz[yy]) {
swap(x, y);
swap(xx, yy);
}
cerr << "Merging " << xx << " " << yy << " from comps " << x << " " << y << endl;
apply(y, 0);
sz[xx] += sz[yy];
g[x].push_back({y, cnt});
g[y].push_back({x, cnt});
edg[cnt] = {x, y};
used[cnt] = false;
cnt ++;
dfs(y, x);
return true;
}
signed main() {
#ifndef LOCAL
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#endif
for(int i = 0; i < MAX_N; i ++) {
sz[i] = 1;
par[i] = i;
dist[i] = 0;
for(int j = 0; j < LOG; j ++) {
lift[i][j] = 0;
}
}
cin >> n >> m;
for(int i = 0; i < m; i ++) {
int a, b;
cin >> a >> b;
if(!merge(a, b)) {
int l = lca(a, b);
toRem[l] -= 2;
toAdd[a] ++;
toAdd[b] ++;
cerr << "Found lca " << a << " " << b << " " << l << endl;
}
cerr << "After edge " << a << " " << b << endl;
for(int j = 1; j <= n; j ++) {
cerr << "[" << par[j] << " " << dist[j] << " " << sz[j] << "]" << " ";
}
cerr << endl;
}
for(int i = 1; i <= n; i ++) {
if(par[i] == i) {
apply(i, 0);
}
}
for(int i = 0; i < cnt; i ++) {
if(!used[i]) {
cout << edg[i] << endl;
}
}
return 0;
}
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