Submission #1091242

#	Time	Username	Problem	Language	Result	Execution time	Memory
1091242		mispertion	Star Trek (CEOI20_startrek)	C++17	100 / 100	64 ms	42320 KiB

startrek

#include<bits/stdc++.h>

using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef long long ll;
#define int ll
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

#define pb push_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define mispertion ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define F first
#define S second
#define getlast(s) (*s.rbegin())
#define debg cout << "OK\n"

const ld PI = 3.1415926535;
const int N = 1e6 + 6;
const int M = 7e6 + 1;
const int mod = 1e9+7;
const int infi = INT_MAX;
const ll infl = LLONG_MAX;
const int P = 31;

int mult(int a, int b) {
    return a * 1LL * b % mod;
}

int sum(int a, int b) { 
    if (a + b < 0)
        return a + b + mod;
    if (a + b >= mod)
        return a + b - mod;
    return a + b;
}

ll binpow(ll a, ll n) {
    if (n == 0)
        return 1;
    if (n % 2 == 1) {
        return binpow(a, n - 1) * a % mod;
    } else {
        ll b = binpow(a, n / 2);
        return b * b % mod;
    }
}

int n, d, dp[N], ndp[N], cd[N], cu[N], C[N], st[N], ddp[N];
vector<int> g[N];

void dfs(int v, int p){
    int cnt0 = 0;
    for(auto u : g[v]){
        if(u == p) continue;
        dfs(u, v);
        if(dp[u] == 0)
            cnt0++;
    }
    dp[v] = (cnt0 != 0);
    if(dp[v] == 0){
        cd[v] = 1;
        for(auto u : g[v]){
            if(u == p) continue;
            cd[v] += cd[u];
        }
    }else{
        cd[v] = 0;
        if(cnt0 == 1){
            for(auto u : g[v]){
                if(u == p) continue;
                if(dp[u] == 0)
                    cd[v] += cd[u];
            }
        }
    }
}

void dfs1(int v, int p){
    int cnt0 = (ndp[v] == 0), sm0 = 0, sm = cu[v];
    if(ndp[v] == 0){
        sm0 += cu[v];
    }
    for(auto u : g[v]){
        if(u == p) continue;
        cnt0 += (dp[u] == 0);
        sm += cd[u];
        if(dp[u] == 0)
            sm0 += cd[u];
    }
    for(auto u : g[v]){
        if(u == p) continue;
        cnt0 -= (dp[u] == 0);
        sm -= cd[u];
        if(dp[u] == 0)
            sm0 -= cd[u];
        ndp[u] = (cnt0 != 0);
        if(ndp[u] == 0){
            cu[u] = 1 + sm;
        }else{
            if(cnt0 == 1)
                cu[u] = sm0;
        }
        dfs1(u, v);
        cnt0 += (dp[u] == 0);
        sm += cd[u];
        if(dp[u] == 0)
            sm0 += cd[u];
    }
}

void dfs2(int v, int p){
    int cnt0 = (ndp[v] == 0);
    for(auto u : g[v]){
        if(u == p) continue;
        cnt0 += (dp[u] == 0);
    }
    st[v] = (cnt0 != 0);
    if(st[v] == 0){
        C[v] = 1 + cu[v];
        for(auto u : g[v]){
            if(u == p) continue;
            C[v] += cd[u];
        }
    }else{
        if(cnt0 == 1){
            if(ndp[v] == 0)
                C[v] = cu[v];
            for(auto u : g[v]){
                if(u == p) continue;
                if(dp[u] == 0)
                    C[v] += cd[u];
            }
        }
    }
    for(auto u : g[v])
        if(u != p) 
            dfs2(u, v);
}

void solve(){
    cin >> n >> d;
    for(int i = 2; i <= n; i++){
        int u, v;
        cin >> u >> v;
        g[v].pb(u);
        g[u].pb(v);
    }
    dfs(1, 0);
    ndp[1] = 1;
    cu[1] = 0;
    dfs1(1, 0);
    dfs2(1, 0);
    int L = 0;
    for(int i = 1; i <= n; i++)
        L += (st[i] == 0);
    int E = 0;
    for(int i = 1; i <= n; i++){
        if(st[i])
            E += C[i];
        else
            E -= C[i];
    }
    int n2 = mult(n, n);
    int lst = mult(L, mult(sum(binpow(n2, d), -binpow(E, d)), binpow(sum(n2, -E), mod - 2)));
    int ret;
    if(st[1]){
        ret = sum(binpow(n2, d), -mult(C[1], lst));
    }else{
        ret = mult(C[1], lst);
    }
    cout << ret << '\n';
}   

signed main() {
    mispertion;
    int t = 1;
    //cin >> t;
    while(t--){
        solve();
    }
    return 0;
}

• 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