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Submission #947361

# Submission time Handle Problem Language Result Execution time Memory
947361 2024-03-16T02:54:59 Z GrindMachine Star Trek (CEOI20_startrek) C++17
100 / 100
 88 ms 32744 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);
vector<ll> win_cnt(N), lose_cnt(N);
ll win_sum[N][2], lose_sum[N][2];

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);
            win_cnt[u]++;
            rep(j,2){
                win_sum[u][j] += dp3[v][j];
            }
        }
        else{
            lose.pb(v);
            lose_cnt[u]++;
            rep(j,2){
                lose_sum[u][j] += dp3[v][j];
            }
        }
    }

    if(sz(lose) == 0){
        rep(j,2){
            dp3[u][j] += win_sum[u][j^1];
        }
    }
    else if(sz(lose) == 1){
        rep(j,2){
            dp3[u][j] += lose_sum[u][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 = win_cnt[u], lose = lose_cnt[u];
        array<ll,2> wsum,lsum;
        wsum.fill(0), lsum.fill(0);

        rep(j,2){
            wsum[j] = win_sum[u][j];
            lsum[j] = lose_sum[u][j];
        }

        if(dp1[v]){
            win--;
            rep(j,2){
                wsum[j] -= dp3[v][j];
            }
        }
        else{
            lose--;
            rep(j,2){
                lsum[j] -= dp3[v][j];
            }
        }

        array<ll,2> dpu;
        dpu.fill(0);
        dpu[0] = 1;

        if(lose == 0){
            rep(j,2){
                dpu[j] += wsum[j^1];
            }
        }
        else if(lose == 1){
            rep(j,2){
                dpu[j] += lsum[j^1];
            }
        }

        ll val = dp2[u];
        val -= (dp1[v] == 0);

        if(val){
            win_cnt[v]++;
            rep(j,2){
                win_sum[v][j] += dpu[j];
            }
        }
        else{
            lose_cnt[v]++;
            rep(j,2){
                lose_sum[v][j] += dpu[j]; 
            }
        }

        dp4[v][0] = 1, dp4[v][1] = 0;

        if(lose_cnt[v] == 0){
            rep(j,2){
                dp4[v][j] += win_sum[v][j^1];
            }
        }
        else if(lose_cnt[v] == 1){
            rep(j,2){
                dp4[v][j] += lose_sum[v][j^1];
            }
        }

        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%MOD, win_ways_l%MOD},
        {lose_ways_w%MOD, win_ways_w%MOD}
    };

    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 4 ms 10584 KB Output is correct
2 Correct 3 ms 10840 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10588 KB Output is correct
2 Correct 2 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10664 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 3 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 3 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 3 ms 10844 KB Output is correct
8 Correct 3 ms 10844 KB Output is correct
9 Correct 3 ms 11096 KB Output is correct
10 Correct 3 ms 10844 KB Output is correct
11 Correct 3 ms 10864 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 3 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 3 ms 10844 KB Output is correct
8 Correct 3 ms 10844 KB Output is correct
9 Correct 3 ms 11096 KB Output is correct
10 Correct 3 ms 10844 KB Output is correct
11 Correct 3 ms 10864 KB Output is correct
12 Correct 67 ms 23380 KB Output is correct
13 Correct 78 ms 31772 KB Output is correct
14 Correct 62 ms 16460 KB Output is correct
15 Correct 59 ms 16472 KB Output is correct
16 Correct 68 ms 16592 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 3 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 3 ms 10844 KB Output is correct
8 Correct 3 ms 10844 KB Output is correct
9 Correct 3 ms 11096 KB Output is correct
10 Correct 3 ms 10844 KB Output is correct
11 Correct 3 ms 10864 KB Output is correct
12 Correct 3 ms 10588 KB Output is correct
13 Correct 3 ms 10844 KB Output is correct
14 Correct 3 ms 10588 KB Output is correct
15 Correct 3 ms 10588 KB Output is correct
16 Correct 3 ms 10584 KB Output is correct
17 Correct 3 ms 10584 KB Output is correct
18 Correct 3 ms 10584 KB Output is correct
19 Correct 3 ms 10588 KB Output is correct
20 Correct 3 ms 10800 KB Output is correct
21 Correct 3 ms 10844 KB Output is correct
22 Correct 3 ms 10844 KB Output is correct
23 Correct 3 ms 10840 KB Output is correct
24 Correct 4 ms 10844 KB Output is correct
25 Correct 3 ms 10844 KB Output is correct
26 Correct 3 ms 10844 KB Output is correct
27 Correct 3 ms 10844 KB Output is correct
28 Correct 3 ms 10844 KB Output is correct
29 Correct 3 ms 10840 KB Output is correct
30 Correct 3 ms 10840 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 3 ms 10588 KB Output is correct
3 Correct 3 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 3 ms 10844 KB Output is correct
8 Correct 3 ms 10844 KB Output is correct
9 Correct 3 ms 11096 KB Output is correct
10 Correct 3 ms 10844 KB Output is correct
11 Correct 3 ms 10864 KB Output is correct
12 Correct 67 ms 23380 KB Output is correct
13 Correct 78 ms 31772 KB Output is correct
14 Correct 62 ms 16460 KB Output is correct
15 Correct 59 ms 16472 KB Output is correct
16 Correct 68 ms 16592 KB Output is correct
17 Correct 3 ms 10588 KB Output is correct
18 Correct 3 ms 10844 KB Output is correct
19 Correct 3 ms 10588 KB Output is correct
20 Correct 3 ms 10588 KB Output is correct
21 Correct 3 ms 10584 KB Output is correct
22 Correct 3 ms 10584 KB Output is correct
23 Correct 3 ms 10584 KB Output is correct
24 Correct 3 ms 10588 KB Output is correct
25 Correct 3 ms 10800 KB Output is correct
26 Correct 3 ms 10844 KB Output is correct
27 Correct 3 ms 10844 KB Output is correct
28 Correct 3 ms 10840 KB Output is correct
29 Correct 4 ms 10844 KB Output is correct
30 Correct 3 ms 10844 KB Output is correct
31 Correct 3 ms 10844 KB Output is correct
32 Correct 3 ms 10844 KB Output is correct
33 Correct 3 ms 10844 KB Output is correct
34 Correct 3 ms 10840 KB Output is correct
35 Correct 3 ms 10840 KB Output is correct
36 Correct 72 ms 23388 KB Output is correct
37 Correct 77 ms 31568 KB Output is correct
38 Correct 60 ms 16464 KB Output is correct
39 Correct 53 ms 16464 KB Output is correct
40 Correct 71 ms 16460 KB Output is correct
41 Correct 88 ms 27780 KB Output is correct
42 Correct 65 ms 31180 KB Output is correct
43 Correct 36 ms 17608 KB Output is correct
44 Correct 54 ms 17500 KB Output is correct
45 Correct 56 ms 17488 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 10584 KB Output is correct
2 Correct 3 ms 10840 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 2 ms 10588 KB Output is correct
5 Correct 3 ms 10588 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 3 ms 10664 KB Output is correct
8 Correct 3 ms 10588 KB Output is correct
9 Correct 3 ms 10588 KB Output is correct
10 Correct 3 ms 10588 KB Output is correct
11 Correct 3 ms 10588 KB Output is correct
12 Correct 3 ms 10588 KB Output is correct
13 Correct 3 ms 10588 KB Output is correct
14 Correct 3 ms 10844 KB Output is correct
15 Correct 3 ms 10844 KB Output is correct
16 Correct 3 ms 11096 KB Output is correct
17 Correct 3 ms 10844 KB Output is correct
18 Correct 3 ms 10864 KB Output is correct
19 Correct 67 ms 23380 KB Output is correct
20 Correct 78 ms 31772 KB Output is correct
21 Correct 62 ms 16460 KB Output is correct
22 Correct 59 ms 16472 KB Output is correct
23 Correct 68 ms 16592 KB Output is correct
24 Correct 3 ms 10588 KB Output is correct
25 Correct 3 ms 10844 KB Output is correct
26 Correct 3 ms 10588 KB Output is correct
27 Correct 3 ms 10588 KB Output is correct
28 Correct 3 ms 10584 KB Output is correct
29 Correct 3 ms 10584 KB Output is correct
30 Correct 3 ms 10584 KB Output is correct
31 Correct 3 ms 10588 KB Output is correct
32 Correct 3 ms 10800 KB Output is correct
33 Correct 3 ms 10844 KB Output is correct
34 Correct 3 ms 10844 KB Output is correct
35 Correct 3 ms 10840 KB Output is correct
36 Correct 4 ms 10844 KB Output is correct
37 Correct 3 ms 10844 KB Output is correct
38 Correct 3 ms 10844 KB Output is correct
39 Correct 3 ms 10844 KB Output is correct
40 Correct 3 ms 10844 KB Output is correct
41 Correct 3 ms 10840 KB Output is correct
42 Correct 3 ms 10840 KB Output is correct
43 Correct 72 ms 23388 KB Output is correct
44 Correct 77 ms 31568 KB Output is correct
45 Correct 60 ms 16464 KB Output is correct
46 Correct 53 ms 16464 KB Output is correct
47 Correct 71 ms 16460 KB Output is correct
48 Correct 88 ms 27780 KB Output is correct
49 Correct 65 ms 31180 KB Output is correct
50 Correct 36 ms 17608 KB Output is correct
51 Correct 54 ms 17500 KB Output is correct
52 Correct 56 ms 17488 KB Output is correct
53 Correct 71 ms 32744 KB Output is correct
54 Correct 77 ms 29780 KB Output is correct
55 Correct 31 ms 17260 KB Output is correct
56 Correct 66 ms 24484 KB Output is correct
57 Correct 60 ms 17820 KB Output is correct
58 Correct 83 ms 17872 KB Output is correct
59 Correct 56 ms 17620 KB Output is correct
60 Correct 67 ms 17520 KB Output is correct