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Submission #578517

# Submission time Handle Problem Language Result Execution time Memory
578517 2022-06-17T07:55:49 Z amunduzbaev Star Trek (CEOI20_startrek) C++17
0 / 100
 2 ms 2772 KB 
#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++;
	}
	
	//~ for(int i=1;i<=n;i++){
		//~ cout<<sub[i]<<" ";
	//~ } cout<<"\n";
	
	int F = n * 1ll * n % mod;
	
	//~ vector<int> e(d + 1), f(d + 1);
	//~ e[0] = f[0] = 1;
	//~ for(int i=1;i<=d;i++){
		//~ e[i] = e[i-1] * 1ll * E % mod;
		//~ f[i] = f[i-1] * 1ll * n % mod * n % mod;
	//~ }
	
	//~ d--;
	//~ int res = 0;
	//~ for(int i=0;i<=d;i++){
		//~ res = (res + f[d-i] * 1ll * e[i]) % mod;
	//~ }
	//~ res = res * 1ll * L % mod;
	int res = (bp(F, d) - bp(E, d) + mod) * 1ll * bp((F - E + mod) % mod, mod - 2) % mod * L % mod;
	if(dp[1]){
		res = res * 1ll * sub[1] % mod;
	} else {
		res = (bp(F, d + 1) - res * 1ll * sub[1] % mod + mod) % mod;
	}
	res = (bp(F, d + 1) - res + mod) % mod;
	cout<<res<<"\n";
}
 
/*
 
5 1
1 2
2 3
2 4
1 5
 
*/

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2772 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Incorrect 2 ms 2644 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #3
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 1 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 1 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 1 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 1 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 1 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2772 KB Output is correct
3 Incorrect 2 ms 2644 KB Output isn't correct
4 Halted 0 ms 0 KB -