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Submission #947360

# Submission time Handle Problem Language Result Execution time Memory
947360 2024-03-16T02:53:45 Z GrindMachine Star Trek (CEOI20_startrek) C++17
65 / 100
 90 ms 32852 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, 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 3 ms 10584 KB Output is correct
2 Correct 3 ms 10796 KB Output is correct

Subtask #2
7.0 / 7.0

# 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

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 4 ms 10588 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10584 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 4 ms 10588 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10584 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 4 ms 10844 KB Output is correct
8 Correct 3 ms 10800 KB Output is correct
9 Correct 3 ms 10792 KB Output is correct
10 Correct 3 ms 10840 KB Output is correct
11 Correct 4 ms 10844 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 4 ms 10588 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10584 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 4 ms 10844 KB Output is correct
8 Correct 3 ms 10800 KB Output is correct
9 Correct 3 ms 10792 KB Output is correct
10 Correct 3 ms 10840 KB Output is correct
11 Correct 4 ms 10844 KB Output is correct
12 Correct 67 ms 24404 KB Output is correct
13 Correct 90 ms 32852 KB Output is correct
14 Correct 41 ms 17584 KB Output is correct
15 Correct 71 ms 17540 KB Output is correct
16 Correct 85 ms 17528 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 4 ms 10588 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10584 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 4 ms 10844 KB Output is correct
8 Correct 3 ms 10800 KB Output is correct
9 Correct 3 ms 10792 KB Output is correct
10 Correct 3 ms 10840 KB Output is correct
11 Correct 4 ms 10844 KB Output is correct
12 Correct 3 ms 10588 KB Output is correct
13 Correct 3 ms 10844 KB Output is correct
14 Correct 2 ms 10588 KB Output is correct
15 Correct 3 ms 10588 KB Output is correct
16 Correct 3 ms 10588 KB Output is correct
17 Correct 3 ms 10676 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 10792 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 10844 KB Output is correct
24 Correct 4 ms 10844 KB Output is correct
25 Correct 3 ms 10844 KB Output is correct
26 Correct 4 ms 10844 KB Output is correct
27 Correct 3 ms 10840 KB Output is correct
28 Correct 3 ms 10744 KB Output is correct
29 Correct 3 ms 10844 KB Output is correct
30 Correct 4 ms 10840 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10588 KB Output is correct
2 Correct 4 ms 10588 KB Output is correct
3 Correct 4 ms 10588 KB Output is correct
4 Correct 3 ms 10588 KB Output is correct
5 Correct 3 ms 10584 KB Output is correct
6 Correct 3 ms 10588 KB Output is correct
7 Correct 4 ms 10844 KB Output is correct
8 Correct 3 ms 10800 KB Output is correct
9 Correct 3 ms 10792 KB Output is correct
10 Correct 3 ms 10840 KB Output is correct
11 Correct 4 ms 10844 KB Output is correct
12 Correct 67 ms 24404 KB Output is correct
13 Correct 90 ms 32852 KB Output is correct
14 Correct 41 ms 17584 KB Output is correct
15 Correct 71 ms 17540 KB Output is correct
16 Correct 85 ms 17528 KB Output is correct
17 Correct 3 ms 10588 KB Output is correct
18 Correct 3 ms 10844 KB Output is correct
19 Correct 2 ms 10588 KB Output is correct
20 Correct 3 ms 10588 KB Output is correct
21 Correct 3 ms 10588 KB Output is correct
22 Correct 3 ms 10676 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 10792 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 4 ms 10844 KB Output is correct
30 Correct 3 ms 10844 KB Output is correct
31 Correct 4 ms 10844 KB Output is correct
32 Correct 3 ms 10840 KB Output is correct
33 Correct 3 ms 10744 KB Output is correct
34 Correct 3 ms 10844 KB Output is correct
35 Correct 4 ms 10840 KB Output is correct
36 Correct 75 ms 24580 KB Output is correct
37 Correct 89 ms 32840 KB Output is correct
38 Correct 45 ms 17860 KB Output is correct
39 Correct 58 ms 17492 KB Output is correct
40 Correct 54 ms 17564 KB Output is correct
41 Incorrect 69 ms 28764 KB Output isn't correct
42 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 10584 KB Output is correct
2 Correct 3 ms 10796 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 10588 KB Output is correct
8 Correct 3 ms 10588 KB Output is correct
9 Correct 4 ms 10588 KB Output is correct
10 Correct 4 ms 10588 KB Output is correct
11 Correct 3 ms 10588 KB Output is correct
12 Correct 3 ms 10584 KB Output is correct
13 Correct 3 ms 10588 KB Output is correct
14 Correct 4 ms 10844 KB Output is correct
15 Correct 3 ms 10800 KB Output is correct
16 Correct 3 ms 10792 KB Output is correct
17 Correct 3 ms 10840 KB Output is correct
18 Correct 4 ms 10844 KB Output is correct
19 Correct 67 ms 24404 KB Output is correct
20 Correct 90 ms 32852 KB Output is correct
21 Correct 41 ms 17584 KB Output is correct
22 Correct 71 ms 17540 KB Output is correct
23 Correct 85 ms 17528 KB Output is correct
24 Correct 3 ms 10588 KB Output is correct
25 Correct 3 ms 10844 KB Output is correct
26 Correct 2 ms 10588 KB Output is correct
27 Correct 3 ms 10588 KB Output is correct
28 Correct 3 ms 10588 KB Output is correct
29 Correct 3 ms 10676 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 10792 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 10844 KB Output is correct
36 Correct 4 ms 10844 KB Output is correct
37 Correct 3 ms 10844 KB Output is correct
38 Correct 4 ms 10844 KB Output is correct
39 Correct 3 ms 10840 KB Output is correct
40 Correct 3 ms 10744 KB Output is correct
41 Correct 3 ms 10844 KB Output is correct
42 Correct 4 ms 10840 KB Output is correct
43 Correct 75 ms 24580 KB Output is correct
44 Correct 89 ms 32840 KB Output is correct
45 Correct 45 ms 17860 KB Output is correct
46 Correct 58 ms 17492 KB Output is correct
47 Correct 54 ms 17564 KB Output is correct
48 Incorrect 69 ms 28764 KB Output isn't correct
49 Halted 0 ms 0 KB -