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D.cpp
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D.cpp
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/*
. . , ,
|` \/ \/ \,',
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/._______,|__________,'\
`--.____,'|_________,-'
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/ ,-._/`---' /
/ (____)(----. ) ,'
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: / \ .__/
\ (__ \ |_
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`-._ / `--'/ \
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,-' | /
/ | -'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp> // Including
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;
//typedef __int128_t bigint;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<vpi> vvpi;
typedef vector<vpl> vvpl;
typedef set<int> si;
typedef multiset<int> msi;
typedef set<ll> sl;
typedef multiset<ll> msl;
typedef tree<
pl,
null_type,
less<pl>,
rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;
typedef long double ld;
#define clrcin cin.ignore(numeric_limits<streamsize>::max(),'\n');
#define GOGOGO ios::sync_with_stdio(false); cin.tie(nullptr);
#define BYEBYE return 0;
#define all(cn) (cn).begin(), (cn).end()
#define rep(i, n) for (int i = 0; i < n; ++i)
#define repk(i, k, n) for(int i = k; i < n; ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define popcnt __builtin_popcount
#define gcd std::__detail::__gcd
#define lcm std::__detail::__lcm
const int INFI = 1e9 + 5;
const ll INFL = 1e18 + 5;
template<class T> using func = function<T>;
/************************************ general.hpp begin ************************************/
namespace CompetitiveProgramming
{
using bigint = long long int;
using ll = long long int;
using ftype = long double;
using ld = long double;
namespace IO
{
template<class ElementType> inline void output_array(ElementType* array, uint32_t size)
{
if(size)
{
cout << *array++;
size--;
while(size)
{
cout << ' ' << *array++;
--size;
}
}
cout << '\n';
}
template<class Iterator> inline void output_iterator_range(Iterator begin, const Iterator& end)
{
if(begin != end)
{
cout << *begin++;
while(begin != end)
{
cout << ' ' << *begin++;
}
}
cout << '\n';
}
template<class Container> inline void output_container(const Container& container)
{
output_iterator_range(container.begin(), container.end());
}
template<class ElementType> inline void read_array(ElementType* array, uint32_t size)
{
while(size)
{
cin >> *array++;
--size;
}
}
template<class Iterator> inline void read_iterator_range(Iterator begin, const Iterator& end)
{
while(begin != end)
{
cin >> *begin++;
}
}
template<class Container> inline void read_container(Container& container) // I dont think this will work for set etc, only std::array, std::vector etc
{
read_iterator_range(container.begin(), container.end());
}
}
}
using namespace CompetitiveProgramming;
using namespace IO;
/************************************ general.hpp end ************************************/
#define BRUH_WHY_TESTCASES
//#define PREC 10
//#define USACO "sleepy"
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
auto DIST = uniform_int_distribution<ll>(0, INFL);
ll grnd()
{
return DIST(rng);
}
#define NO -1
const int maxn = 1e5 +5;
int n;
vi g[maxn];
int sdp[maxn] = { 0 };
pi sn[maxn];
int cdp[maxn] = { 0 };
int cn[maxn] = { 0 };
int par[maxn];
//vector<pi> cnc;
pi chain[maxn];
int tail = -1;
void dfs(int c, int p = 0) {
int odeg = 0;
par[c] = p;
for(auto e : g[c]) {
if(e!=p) {
dfs(e, c);
odeg++;
}
}
if(odeg == 0) {
sn[c] = {NO, NO}; cn[c] = NO;
if(c!= 1) {
sdp[c] = 1;
} else {
sdp[c] = 0;
}
cdp[c] = 0; return;
}
// c - connected to papa
int who = NO;
int sm = 0;
for(auto e : g[c]) {
if(e!=p) {
sm += sdp[e];
if(who == NO || cdp[who] - sdp[who] > cdp[e] - sdp[e]) {
who = e;
}
}
}
if(cdp[who] - sdp[who] < 0) {
cdp[c] = sm - sdp[who] + cdp[who]; cn[c] = who;
} else {
cdp[c] = sm; cn[c] = NO;
}
// s - self
// we can connect up to 2 things
vector<pi> val;
for(auto e : g[c]) {
if(e!=p) {
val.emplace_back(e, cdp[e] - sdp[e]);
}
}
sort(all(val), [&](const pi& x, const pi& y) {
return x.se < y.se;
});
if(val.size() > 0 && val[0].se < 0) {
if(val.size() > 1 && val[1].se < 0) {
// both
sdp[c] = 1 + sm + val[0].se + val[1].se;
sn[c] = {val[0].fi, val[1].fi};
} else {
sdp[c] = 1 + sm + val[0].se;
sn[c] = {val[0].fi, NO};
}
} else {
sdp[c] = 1 + sm; sn[c] = {NO, NO};
}
}
void dfs2(int c, bool st=false, int p = 0, int head=-1, bool zr = false) {
if(st == false) {
if(sn[c].fi == NO) {
chain[c] = {c, c};
} else if(sn[c].se == NO) {
chain[c].se = c;
}
for(auto e : g[c]) {
if(e != p) {
if(e == sn[c].fi) {
dfs2(e, true, c, c, true);
}
else if(e == sn[c].se) {
dfs2(e, true, c, c, false);
} else {
dfs2(e, false, c);
}
}
}
} else {
if(cn[c] == NO) {
if(zr) {
chain[head].fi = c;
} else {
chain[head].se = c;
}
}
for(auto e : g[c]) {
if(e!=p) {
if(e== cn[c]) {
dfs2(e, true, c, head, zr);
} else {
dfs2(e, false, c);
}
}
}
}
}
void solve() {
cin >> n;
rep(i, n-1) {
int s, t; cin >> s >> t;
g[s].pb(t); g[t].pb(s);
}
dfs(1);
for(int i = 1; i <= n; ++i) {
chain[i] = {NO, NO};
}
dfs2(1, false);
vector<pair<pi, pi>> res;
int lst = chain[1].fi;
assert(lst != -1);
for(int i = 2; i <= n; ++i) {
if(chain[i].fi != NO) {
res.pb({{i, par[i]}, {chain[i].fi, lst}});
lst = chain[i].se;
}
}
cout << res.size() << '\n';
for(auto e : res) {
cout << e.fi.fi << ' ' << e.fi.se << ' ' << e.se.fi << ' ' << e.se.se << '\n';
}
for(int i = 1; i <= n; ++i) {
g[i].clear(); sn[i] = {NO, NO}; cn[i] = NO; chain[i] = {NO, NO};
}
}
signed main()
{
#ifdef USACO
freopen(USACO ".in", "r", stdin);
freopen(USACO ".out", "w", stdout);
#endif
GOGOGO
#ifdef PREC
cout << fixed << setprecision(PREC);
#endif
int t=1;
#ifdef BRUH_WHY_TESTCASES
cin >> t;
#endif
while(t--)
{
solve();
}
BYEBYE
}
/* PLEASE READ THIS
* N = 1
* GUESS A!!!!!!!
* DO SOMETHING INSTEAD OF NOTHING
*/