Submission #107849

#	Time	Username	Problem	Language	Result	Execution time	Memory
107849		qkxwsm	Hard route (IZhO17_road)	C++14	100 / 100	1949 ms	92820 KiB

road

//clever
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();

struct custom_hash
{
	template<class T>
	unsigned long long operator()(T v) const
	{
		unsigned long long x = v;
		x += FIXED_RANDOM;
		// x += 11400714819323198485ull;
		// x = (x ^ (x >> 30)) * 13787848793156543929ull;
		x = (x ^ (x >> 27)) * 10723151780598845931ull;
		return x ^ (x >> 31);
	}
};

template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;

template<class T>
T randomize(T mod)
{
	return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
	x = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
	{
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		x = x * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		x = -x;
	}
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int buf[20], n = 0;
	while(output)
	{
		buf[n] = ((output % 10));
		output /= 10;
		n++;
	}
	for (n--; n >= 0; n--)
	{
		putchar(buf[n] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
	return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
	if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
	return (b ? gcd(b, a % b) : a);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 500013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;

int N;
vi edge[MAXN];
pll ans = {0, 0};
int depth[MAXN];
pll dp[MAXN];
int dist[2][MAXN];
int parent[MAXN];
int S, T;
bool flag;
bitset<MAXN> diam;

void comb(pll &p, pll q)
{
	if (q.se == 0) return;
	if (q.fi > p.fi) p = q;
	else if (q.fi == p.fi) p.se += q.se;
}
void gendist(int u)
{
	FOR(i, 0, N) depth[i] = INF;
	depth[u] = 0;
	vi nodes;
	nodes.PB(u);
	while(!nodes.empty())
	{
		int v = nodes.back();
		nodes.pop_back();
		for (int w : edge[v])
		{
			if (depth[w] != INF) continue;
			depth[w] = depth[v] + 1;
			nodes.PB(w);
		}
	}
	return;
}
void dfs(int u, int p)
{
	parent[u] = p;
	if (SZ(edge[u]) == 1)
	{
		dp[u] = MP(dist[flag][u], 1);
		return;
	}
	dp[u] = MP(0, 0);
	for (int v : edge[u])
	{
		if (v == p) continue;
		dfs(v, u);
		comb(dp[u], dp[v]);
	}
	ll tot = 0; int freq = 0;
	for (int v : edge[u])
	{
		if (v == p) continue;
		if (dp[v].fi == dp[u].fi)
		{
			freq++;
			tot += dp[v].se;
		}
	}
	pll opt = {0, 0};
	if (freq > 1)
	{
		opt.fi = 1ll * dist[flag][u] * (dp[u].fi + dp[u].fi - 2 * dist[flag][u]);
		for (int v : edge[u])
		{
			if (v == p) continue;
			if (dp[v].fi == dp[u].fi)
			{
				opt.se += (tot - dp[v].se) * (dp[v].se);
			}
		}
		opt.se /= 2;
	}
	else if (freq == 1)
	{
		for (int v : edge[u])
		{
			if (v == p) continue;
			if (dp[v].fi != dp[u].fi)
			{
				comb(opt, dp[v]);
			}
		}
		opt.se *= tot;
		opt.fi = 1ll * dist[flag][u] * (opt.fi + dp[u].fi - 2 * dist[flag][u]);
	}
	comb(ans, opt);
}
void dfs3(int u)
{
	if (SZ(edge[u]) == 1)
	{
		dp[u] = MP(dist[flag][u], 1);
		return;
	}
	dp[u] = MP(0, 0);
	for (int v : edge[u])
	{
		if (diam[v] || v == parent[u]) continue;
		parent[v] = u;
		dfs3(v);
		comb(dp[u], dp[v]);
	}
	if (dist[0][u] == dist[1][u])
	{
		ll tot = 0; int freq = 0;
		for (int v : edge[u])
		{
			if (diam[v] || v == parent[u]) continue;
			if (dp[v].fi == dp[u].fi)
			{
				freq++;
				tot += dp[v].se;
			}
		}
		pll opt = {0, 0};
		if (freq > 1)
		{
			opt.fi = 1ll * dist[flag][u] * (dp[u].fi + dp[u].fi - 2 * dist[flag][u]);
			for (int v : edge[u])
			{
				if (diam[v] || v == parent[u]) continue;
				if (dp[v].fi == dp[u].fi)
				{
					opt.se += (tot - dp[v].se) * (dp[v].se);
				}
			}
			opt.se /= 2;
		}
		else if (freq == 1)
		{
			//find the second biggest!
			for (int v : edge[u])
			{
				if (diam[v] || v == parent[u]) continue;
				if (dp[v].fi != dp[u].fi)
				{
					comb(opt, dp[v]);
				}
			}
			opt.se *= tot;
			opt.fi = 1ll * dist[flag][u] * (opt.fi + dp[u].fi - 2 * dist[flag][u]);
		}
		if (opt.fi == ans.fi) ans.se -= opt.se;
	}
}
void mark(int u, int p)
{
	for (int v : edge[u])
	{
		if (diam[v] || v == p) continue;
		depth[v] = depth[u] + 1;
		mark(v, u);
	}
}

int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	// cout << fixed << setprecision(10);
	// cerr << fixed << setprecision(10);
	// if (fopen("file.in", "r"))
	// {
	// 	freopen ("file.in", "r", stdin);
	// 	freopen ("file.out", "w", stdout);
	// }
	cin >> N;
	FOR(i, 0, N - 1)
	{
		int u, v;
		cin >> u >> v;
		u--; v--;
		edge[u].PB(v); edge[v].PB(u);
	}
	gendist(0);
	FOR(i, 0, N)
	{
		if (depth[i] > depth[S])
		{
			S = i;
		}
	}
	vi nodes;
	nodes.PB(S);
	while(!nodes.empty())
	{
		int v = nodes.back();
		nodes.pop_back();
		for (int w : edge[v])
		{
			if (w == S || dist[0][w]) continue;
			dist[0][w] = dist[0][v] + 1;
			nodes.PB(w);
		}
	}
	FOR(i, 0, N)
	{
		if (dist[0][i] > dist[0][T]) T = i;
	}
	nodes.PB(T);
	while(!nodes.empty())
	{
		int v = nodes.back();
		nodes.pop_back();
		for (int w : edge[v])
		{
			if (w == T || dist[1][w]) continue;
			dist[1][w] = dist[1][v] + 1;
			nodes.PB(w);
		}
	}
	flag = true;
	for (int v : edge[T])
	{
		dfs(v, T);
	}
	parent[S] = N;
	flag = false;
	for (int v : edge[S])
	{
		dfs(v, S);
	}
	vi lol;
	int tmp = T;
	while(tmp != S)
	{
		diam[tmp] = true;
		lol.PB(tmp);
		tmp = parent[tmp];
	}
	diam[tmp] = true;
	lol.PB(tmp);
	FOR(i, 0, N) depth[i] = 0;
	FOR(i, 0, N)
	{
		if (!diam[i]) continue;
		for (int v : edge[i])
		{
			if (diam[v]) continue;
			depth[v] = 1;
			mark(v, i);
		}
	}
	tmp = 0;
	FOR(i, 0, N) ckmax(tmp, depth[i]);
	comb(ans, {1ll * dist[0][T] * tmp, 1});
	if (SZ(lol) % 2)
	{
		int mid = lol[SZ(lol) / 2];
		diam[mid] = false;
		FOR(i, 0, N) parent[i] = N;
		dfs3(mid);
	}
	cout << ans.fi << ' ' << ans.se << '\n';
	// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/

• Subtask 1: 19 / 19
• Subtask 2: 33 / 33
• Subtask 3: 48 / 48