oj.uz

Submission #947125

# Submission time Handle Problem Language Result Execution time Memory
947125 2024-03-15T14:21:47 Z GrindMachine Star Trek (CEOI20_startrek) C++17
45 / 100
 82 ms 25372 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);

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);
    }
}

ll dp3[N][2], dp4[N][2];
vector<ll> dp5(N);

void dfs3(ll u, ll p){
    dp3[u][0] = 1;

    trav(v,adj[u]){
        if(v == p) conts;
        dfs3(v,u);
    }

    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){
            rep(j,2){
                dp3[u][j] += dp3[v][j^1];
            }
        }
    }
    else if(sz(lose) == 1){
        trav(v,lose){
            rep(j,2){
                dp3[u][j] += dp3[v][j^1];
            }
        }
    }

    rep(j,2){
        dp4[u][j] = dp3[u][j];
    }
}

void dfs4(ll u, ll p){
    trav(v,adj[u]){
        if(v == p) conts;
        ll win = 0, lose = 0;
        trav(w,adj[v]){
            if(w == u) conts;
            if(dp1[w]) win++;
            else lose++;
        }

        ll val = dp2[u];
        val -= (dp1[v] == 0);
        
        if(val){
            if(lose == 0){
                array<ll,2> add;
                rep(j,2){
                    add[j] = dp4[u][j^1]-dp3[v][j];
                }
                rep(j,2){
                    dp4[v][j] += add[j];
                }
            }
        }
        else{
            if(lose == 0){
                dp4[v][0] = 1;
                dp4[v][1] = 0;
                
                array<ll,2> add;
                rep(j,2){
                    add[j] = dp4[u][j^1]-dp3[v][j];
                }
                rep(j,2){
                    dp4[v][j] += add[j];
                }
            }
            else{
                dp4[v][0] = 1;
                dp4[v][1] = 0;
            }
        }

        dfs4(v,u);
    }
}

void dfs5(ll u, ll p, ll depth, ll r){
    if(!dp1[u]){
        ll val = 1;
        if(depth&1) val = 0;
        dp5[r] -= dp2[r];
        dp5[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){
            dfs5(v,u,depth+1,r);
        }
    }
    else if(sz(lose) == 1){
        dfs5(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);

    dfs3(1,-1);
    dfs4(1,-1);

    rep1(i,n){
        amin(dp1[i],1ll);
        amin(dp2[i],1ll);
    }
    
    rep1(i,n){
        dp5[i] = n*dp2[i];
        dp5[i] -= (dp4[i][0]+dp4[i][1])*dp2[i];
        dp5[i] += dp4[i][0];
    }

    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 += dp5[r];
        lose_ways_l += n-dp5[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 += dp5[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 8024 KB Output is correct
2 Incorrect 3 ms 8028 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8024 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 3 ms 8028 KB Output is correct
4 Correct 3 ms 8028 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8064 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 2 ms 8028 KB Output is correct
4 Correct 3 ms 8120 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct
6 Correct 2 ms 8028 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8064 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 2 ms 8028 KB Output is correct
4 Correct 3 ms 8120 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct
6 Correct 2 ms 8028 KB Output is correct
7 Correct 3 ms 8028 KB Output is correct
8 Correct 3 ms 8284 KB Output is correct
9 Correct 2 ms 8028 KB Output is correct
10 Correct 3 ms 8172 KB Output is correct
11 Correct 3 ms 8028 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8064 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 2 ms 8028 KB Output is correct
4 Correct 3 ms 8120 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct
6 Correct 2 ms 8028 KB Output is correct
7 Correct 3 ms 8028 KB Output is correct
8 Correct 3 ms 8284 KB Output is correct
9 Correct 2 ms 8028 KB Output is correct
10 Correct 3 ms 8172 KB Output is correct
11 Correct 3 ms 8028 KB Output is correct
12 Correct 69 ms 17928 KB Output is correct
13 Correct 82 ms 25372 KB Output is correct
14 Correct 41 ms 12356 KB Output is correct
15 Correct 43 ms 11612 KB Output is correct
16 Correct 44 ms 11868 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8064 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 2 ms 8028 KB Output is correct
4 Correct 3 ms 8120 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct
6 Correct 2 ms 8028 KB Output is correct
7 Correct 3 ms 8028 KB Output is correct
8 Correct 3 ms 8284 KB Output is correct
9 Correct 2 ms 8028 KB Output is correct
10 Correct 3 ms 8172 KB Output is correct
11 Correct 3 ms 8028 KB Output is correct
12 Correct 3 ms 8024 KB Output is correct
13 Incorrect 3 ms 8028 KB Output isn't correct
14 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 8064 KB Output is correct
2 Correct 2 ms 8028 KB Output is correct
3 Correct 2 ms 8028 KB Output is correct
4 Correct 3 ms 8120 KB Output is correct
5 Correct 3 ms 8028 KB Output is correct
6 Correct 2 ms 8028 KB Output is correct
7 Correct 3 ms 8028 KB Output is correct
8 Correct 3 ms 8284 KB Output is correct
9 Correct 2 ms 8028 KB Output is correct
10 Correct 3 ms 8172 KB Output is correct
11 Correct 3 ms 8028 KB Output is correct
12 Correct 69 ms 17928 KB Output is correct
13 Correct 82 ms 25372 KB Output is correct
14 Correct 41 ms 12356 KB Output is correct
15 Correct 43 ms 11612 KB Output is correct
16 Correct 44 ms 11868 KB Output is correct
17 Correct 3 ms 8024 KB Output is correct
18 Incorrect 3 ms 8028 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 8024 KB Output is correct
2 Incorrect 3 ms 8028 KB Output isn't correct
3 Halted 0 ms 0 KB -