Submission #578540

#	Time	Username	Problem	Language	Result	Execution time	Memory
578540		amunduzbaev	Star Trek (CEOI20_startrek)	C++17	100 / 100	108 ms	20172 KiB

startrek

#include "bits/stdc++.h"
using namespace std;
 
#define ar array
typedef int64_t ll;
#define int ll
 
const int N = 1e5 + 5;
const int mod = 1e9 + 7;
vector<int> edges[N];
int dp[N], up[N], cnt[N], n;
int sub[N], rev[N], tot[N], tmp[N];

void dfs(int u, int p = -1){
	for(auto x : edges[u]){
		if(x == p) continue;
		dfs(x, u);
		if(dp[x] == 0){
			dp[u] = 1, 
			tmp[u] += sub[x], 
			cnt[u]++;
		} 
		
		tot[u] += sub[x];
	}
	
	if(cnt[u] > 1) sub[u] = 0;
	if(cnt[u] == 1) sub[u] = tmp[u];
	if(cnt[u] == 0) sub[u] = tot[u] + 1;
}

void re(int u, int p = -1){
	tot[u] += rev[u];
	if(up[u] == 0){
		tmp[u] += rev[u];
		dp[u] = 1, cnt[u]++;
	}
	if(cnt[u] > 1) sub[u] = 0;
	if(cnt[u] == 1) sub[u] = tmp[u];
	if(cnt[u] == 0) sub[u] = tot[u] + 1;
	
	for(auto x : edges[u]){
		if(x == p) continue;
		tot[u] -= sub[x];
		if(!dp[x]){
			cnt[u]--, tmp[u] -= sub[x];
		}
		
		if(cnt[u]) up[x] = 1;
		if(cnt[u] > 1) rev[x] = 0;
		if(cnt[u] == 1) rev[x] = tmp[u];
		if(cnt[u] == 0) rev[x] = tot[u] + 1;
		
		tot[u] += sub[x];
		if(!dp[x]){
			cnt[u]++, tmp[u] += sub[x];
		}
		
		re(x, u);
	}
}

int bp(int a, int b){
	int c=1;
	while(b){
		if(b&1) c = c * 1ll * a % mod;
		a = a * 1ll * a % mod, b >>= 1;
	} return c;
}

signed main(){
	ios::sync_with_stdio(0); cin.tie(0);
	
	int d; cin>>n>>d;
	for(int i=1;i<n;i++){
		int a, b; cin>>a>>b;
		edges[a].push_back(b);
		edges[b].push_back(a);
	}
	
	dfs(1);
	up[1] = 1;
	re(1);
	int E = 0, L = 0;
	for(int i=1;i<=n;i++){
		if(dp[i] == 1) E = (E + sub[i]) % mod;
		else E = (E - sub[i] + mod) % mod, L++;
	}
	
	int F = n * 1ll * n % mod;
	int res = (bp(F, d) - bp(E, d) + mod) % mod * 1ll * bp((F - E + mod) % mod, mod - 2) % mod;
	res = res * 1ll * L % mod;
	if(dp[1]){
		res = res * 1ll * sub[1] % mod;
	} else {
		res = (bp(F, d) - res * 1ll * sub[1] % mod + mod) % mod;
	}
	
	res = (bp(F, d) - res + mod) % mod;
	res = (res % mod + mod) % mod;
	cout<<res<<"\n";
}
 
/*

5 2
1 2
1 3
2 4
3 5

*/

• Subtask 1: 0 / 0
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 15 / 15
• Subtask 6: 20 / 20
• Subtask 7: 20 / 20
• Subtask 8: 15 / 15