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Submission #947078

# Submission time Handle Problem Language Result Execution time Memory
947078 2024-03-15T13:26:07 Z GrindMachine Star Trek (CEOI20_startrek) C++17
50 / 100
 1000 ms 23296 KB 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

refs:
edi
https://youtu.be/Tjv78ZThV5c

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

struct Matrix {
    vector<vector<ll>> a;
    int n, m;

    Matrix() {

    }

    Matrix(int row, int col) {
        n = row, m = col;
        a = vector<vector<ll>>(row, vector<ll>(col));
    }

    Matrix operator*(const Matrix &mat2) {
        int n2 = mat2.n, m2 = mat2.m;
        Matrix res(n, m2);

        rep(i, n) {
            rep(j, m2) {
                rep(k, m) {
                    ll temp = (a[i][k] * mat2.a[k][j]) % MOD;
                    res.a[i][j] = (res.a[i][j] + temp) % MOD;
                }
            }
        }

        return res;
    }

    void exp(ll b) {
        Matrix res(n, m);
        Matrix curr = *this;
        rep(i, n) res.a[i][i] = 1;

        while (b) {
            if (b & 1) res = res * curr;
            curr = curr * curr;
            b /= 2;
        }

        a = res.a;
    }
};

vector<ll> adj[N];
vector<ll> dp1(N), dp2(N), dp3(N);

void dfs1(ll u, ll p){
    dp1[u] = 0;
    trav(v,adj[u]){
        if(v == p) conts;
        dfs1(v,u);
        dp1[u] += (dp1[v] == 0);
    }
}

void dfs2(ll u, ll p){
    trav(v,adj[u]){
        if(v == p) conts;
        ll val = dp2[u]-(dp1[v] == 0);
        dp2[v] += (val == 0);
        dfs2(v,u);
    }
}

void dfs3(ll u, ll p, ll depth, ll r){
    if(!dp1[u]){
        ll val = 1;
        if(depth&1) val = 0;
        dp3[r] -= dp2[r];
        dp3[r] += val;
    }

    vector<ll> win,lose;
    trav(v,adj[u]){
        if(v == p) conts;
        if(dp1[v]) win.pb(v);
        else lose.pb(v);
    }

    if(sz(lose) == 0){
        trav(v,win){
            dfs3(v,u,depth+1,r);
        }
    }
    else if(sz(lose) == 1){
        dfs3(lose[0],u,depth+1,r);
    }
}

void solve(int test_case)
{
    ll n,d; cin >> n >> d;
    rep1(i,n-1){
        ll u,v; cin >> u >> v;
        adj[u].pb(v), adj[v].pb(u);
    }

    dfs1(1,-1);
    rep1(i,n) dp2[i] = dp1[i];
    dfs2(1,-1);

    rep1(i,n){
        amin(dp1[i],1ll);
        amin(dp2[i],1ll);
    }

    rep1(r,n){
        dfs1(r,-1);
        dp3[r] = dp2[r]*n;
        dfs3(r,-1,0,r);
    }

    ll win_ways_w = 0, lose_ways_w = 0;
    rep1(r,n){
        if(dp2[r]){
            win_ways_w += n;
        }
        else{
            lose_ways_w += n;
        }
    }

    ll win_ways_l = 0, lose_ways_l = 0;
    rep1(r,n){
        win_ways_l += dp3[r];
        lose_ways_l += n-dp3[r];
    }

    Matrix base(1,2);
    rep1(i,n){
        base.a[0][dp2[i]]++;
    }

    Matrix mat(2,2);
    mat.a = {
        {lose_ways_l, win_ways_l},
        {lose_ways_w, win_ways_w}
    };

    mat.exp(d-1);
    base = base*mat;

    ll ans = 0;
    if(dp2[1]){
        ans += n*base.a[0][1];
    }
    
    ans += dp3[1]*base.a[0][0];
    ans %= MOD;

    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

Compilation message

startrek.cpp: In member function 'Matrix Matrix::operator*(const Matrix&)':
startrek.cpp:76:13: warning: unused variable 'n2' [-Wunused-variable]
   76 |         int n2 = mat2.n, m2 = mat2.m;
      |             ^~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 9 ms 5220 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 1 ms 4952 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4956 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4992 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4992 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 18 ms 5312 KB Output is correct
8 Correct 32 ms 5212 KB Output is correct
9 Correct 16 ms 5208 KB Output is correct
10 Correct 10 ms 5208 KB Output is correct
11 Correct 23 ms 5212 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4992 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 18 ms 5312 KB Output is correct
8 Correct 32 ms 5212 KB Output is correct
9 Correct 16 ms 5208 KB Output is correct
10 Correct 10 ms 5208 KB Output is correct
11 Correct 23 ms 5212 KB Output is correct
12 Execution timed out 1051 ms 23296 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4992 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 18 ms 5312 KB Output is correct
8 Correct 32 ms 5212 KB Output is correct
9 Correct 16 ms 5208 KB Output is correct
10 Correct 10 ms 5208 KB Output is correct
11 Correct 23 ms 5212 KB Output is correct
12 Correct 2 ms 5156 KB Output is correct
13 Correct 9 ms 5208 KB Output is correct
14 Correct 2 ms 4952 KB Output is correct
15 Correct 2 ms 4952 KB Output is correct
16 Correct 2 ms 4956 KB Output is correct
17 Correct 2 ms 4952 KB Output is correct
18 Correct 2 ms 4956 KB Output is correct
19 Correct 2 ms 4956 KB Output is correct
20 Correct 2 ms 4952 KB Output is correct
21 Correct 18 ms 5212 KB Output is correct
22 Correct 31 ms 5212 KB Output is correct
23 Correct 16 ms 5212 KB Output is correct
24 Correct 9 ms 5212 KB Output is correct
25 Correct 23 ms 4956 KB Output is correct
26 Correct 11 ms 5268 KB Output is correct
27 Correct 32 ms 5212 KB Output is correct
28 Correct 11 ms 4956 KB Output is correct
29 Correct 10 ms 5212 KB Output is correct
30 Correct 25 ms 5440 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 5208 KB Output is correct
2 Correct 2 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4992 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 18 ms 5312 KB Output is correct
8 Correct 32 ms 5212 KB Output is correct
9 Correct 16 ms 5208 KB Output is correct
10 Correct 10 ms 5208 KB Output is correct
11 Correct 23 ms 5212 KB Output is correct
12 Execution timed out 1051 ms 23296 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 9 ms 5220 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 1 ms 4952 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 2 ms 4956 KB Output is correct
8 Correct 2 ms 5208 KB Output is correct
9 Correct 2 ms 4956 KB Output is correct
10 Correct 2 ms 4956 KB Output is correct
11 Correct 2 ms 4956 KB Output is correct
12 Correct 2 ms 4992 KB Output is correct
13 Correct 2 ms 4956 KB Output is correct
14 Correct 18 ms 5312 KB Output is correct
15 Correct 32 ms 5212 KB Output is correct
16 Correct 16 ms 5208 KB Output is correct
17 Correct 10 ms 5208 KB Output is correct
18 Correct 23 ms 5212 KB Output is correct
19 Execution timed out 1051 ms 23296 KB Time limit exceeded
20 Halted 0 ms 0 KB -