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 <iostream>
#include <vector>
#include <queue>
#include <set>
#define MAXN 500000
using namespace std;
struct Path {
vector<int> path;
Path(vector<int> p) {
path = p;
}
int size() {
return (int)path.size();
}
};
set<int> leafs; // leaf nodes sorted by depth
int mxleaf[MAXN + 1]; // max number leaf in any path for each as root
vector<Path> paths;
set<pair<int, int>> erase; // nodes to delete
vector<int> adj[MAXN + 1];
int root;
struct c {
bool operator() (Path x, Path y) {
return x.size() < y.size();
}
};
int dfs1(int y, int x) {
int count = 0;
if (leafs.count(x))count++;
int mx = 0;
for (int e : adj[x]) {
if (e == y)continue;
int c = dfs1(x, e);
count += c;
mx = max(mx, c);
}
mxleaf[x] = max(mx, (int)leafs.size() - count);
return count;
}
vector<int> dfs2(int y, int x) {
vector<int> total;
for (int e : adj[x]) {
if (e == y)continue;
vector<int> child = dfs2(x, e);
for (int l : child) total.push_back(l);
}
if (leafs.count(x)) total.push_back(x);
return total;
}
int main() {
int N;
cin >> N;
for (int i = 1; i < N; i++) {
int a, b;
cin >> a >> b;
adj[a].push_back(b);
adj[b].push_back(a);
}
for (int i = 1; i <= N; i++) {
if (adj[i].size() == 1) {
leafs.insert(i);
}
}
dfs1(0, 1);
root = 1;
for (int i = 1; i <= N; i++) {
if (mxleaf[i] < mxleaf[root]) root = i;
}
int total = 0;
priority_queue<Path, vector<Path>, c> pq;
for (int e : adj[root]) {
Path childpath(dfs2(root, e));
total += (int)childpath.size();
paths.push_back(childpath);
pq.push(childpath);
}
cout << (total + 1) / 2 << endl;
while (!pq.empty()) {
Path fir = pq.top(); pq.pop();
if (pq.empty()) {
cout << fir.path[0] << " " << root;
break;
}
Path sec = pq.top(); pq.pop();
int fs = fir.size();
int ss = sec.size();
int mn = min(fs, ss);
for (int i = 1; i <= mn; i++) {
cout << fir.path[fs - i] << " " << sec.path[ss - i] << endl;
fir.path.pop_back();
sec.path.pop_back();
}
if (fir.size()>0) {
pq.push(fir);
}
if(sec.size() > 0) {
pq.push(sec);
}
}
}
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