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Submission #659652

# Submission time Handle Problem Language Result Execution time Memory
659652 2022-11-18T21:30:25 Z Lobo Star Trek (CEOI20_startrek) C++17
78 / 100
 1000 ms 68472 KB 
#include<bits/stdc++.h>
using namespace std;
const long long inf = (long long) 1e18 + 10;
const int inf1 = (int) 1e9 + 10;
#define int long long
#define dbl long double
#define endl '\n'
#define sc second
#define fr first
#define mp make_pair
#define pb push_back
#define all(x) x.begin(), x.end()

const int maxn = 5e5+10;
const int mod = 1e9+7;

int n, d, dpw[maxn][2], dpl[maxn][2], dpwup[maxn][2], dplup[maxn][2];
vector<int> g[maxn];
int SL, SW, SL0, SW0, SWb, SLb;

void dfs1(int u, int ant) {
    dpw[u][1] = SW*dpw[u][0] + SL*(dpw[u][0]+dpl[u][0]); dpw[u][1]%= mod;
    dpl[u][1] = SW*dpl[u][0]; dpl[u][1]%= mod;

    int qtl = 0;
    for(auto v : g[u]) if(v != ant) {
        qtl+= dpl[v][0];
        dfs1(v,u);
    }

    for(auto v : g[u]) if(v != ant) {
        qtl-= dpl[v][0];
        if(qtl) {
            dpw[u][1]+= dpw[v][1]+dpl[v][1]; dpw[u][1]%= mod;
            dpl[u][1]+= 0;
        }
        else {
            dpw[u][1]+= dpl[v][1]; dpw[u][1]%= mod;
            dpl[u][1]+= dpw[v][1]; dpl[u][1]%= mod;
        }
        qtl+= dpl[v][0];
    }
}

int dw[maxn][2], dl[maxn][2], sdw[maxn][2], sdl[maxn][2], sbsz[maxn];
set<int> dl0s[maxn];

void calc(int u) {
    if(sdl[u][0] >= 1) {
        dw[u][0] = 1;
    }
    else {
        dw[u][0] = 0;
    }

    if(sdl[u][0] >= 2) {
        dw[u][1] = 1+sdw[u][1]+sdl[u][1];
    }
    else if(sdl[u][0] == 1) {
        dw[u][1] = 1+sdw[u][1]+sdl[u][1];
        int v1 = *dl0s[u].begin();
        dw[u][1]-= dw[v1][1];
    }
    else {
        dw[u][1] = 1+sdl[u][1];
    }
    dl[u][0] = 1-dw[u][0];
    dl[u][1] = sbsz[u]-dw[u][1];
}
void sol(int u, int ant) {
    dw[u][0] = 0;
    dl[u][0] = 0;
    sdw[u][0] = 0;
    sdl[u][0] = 0;
    dw[u][1] = 0;
    dl[u][1] = 0;
    sdw[u][1] = 0;
    sdl[u][1] = 0;
    sbsz[u] = 1;
    dl0s[u].clear();
    for(auto v : g[u]) if(v != ant) {
        sol(v,u);
        sdw[u][0]+= dw[v][0];
        sdw[u][1]+= dw[v][1];
        sdl[u][0]+= dl[v][0];
        sdl[u][1]+= dl[v][1];
        sbsz[u]+= sbsz[v];
        if(dl[v][0]) {
            dl0s[u].insert(v);
        }
    }

    calc(u);
}

void dfsrrt(int u, int ant) {
    SWb+= dw[u][1];
    for(auto v : g[u]) if(v != ant) {
        // take v off u
        sdw[u][0]-= dw[v][0];
        sdw[u][1]-= dw[v][1];
        sdl[u][0]-= dl[v][0];
        sdl[u][1]-= dl[v][1];
        sbsz[u]-= sbsz[v];
        if(dl[v][0]) {
            dl0s[u].erase(v);
        }
        calc(u);

        // put u into v
        sdw[v][0]+= dw[u][0];
        sdw[v][1]+= dw[u][1];
        sdl[v][0]+= dl[u][0];
        sdl[v][1]+= dl[u][1];
        sbsz[v]+= sbsz[u];
        if(dl[u][0]) {
            dl0s[v].insert(u);
        }
        calc(v);
        dfsrrt(v,u);

        // take u off v
        sdw[v][0]-= dw[u][0];
        sdw[v][1]-= dw[u][1];
        sdl[v][0]-= dl[u][0];
        sdl[v][1]-= dl[u][1];
        sbsz[v]-= sbsz[u];
        if(dl[u][0]) {
            dl0s[v].erase(u);
        }
        calc(v);

        // put v into u
        sdw[u][0]+= dw[v][0];
        sdw[u][1]+= dw[v][1];
        sdl[u][0]+= dl[v][0];
        sdl[u][1]+= dl[v][1];
        sbsz[u]+= sbsz[v];
        if(dl[v][0]) {
            dl0s[u].insert(v);
        }
        calc(u);
    }
}

void dfs0(int u, int ant) {
    dpw[u][0] = 0;
    int qtl = 0;
    for(auto v : g[u]) if(v != ant) {
        dfs0(v,u);
        qtl+= dpl[v][0];
    }

    if(qtl) dpw[u][0] = 1;
    dpl[u][0] = 1-dpw[u][0];
}

void dfs0up(int u, int ant) {
    int qtl = 0;
    for(auto v : g[u]) if(v != ant) {
        qtl+= dpl[v][0];
    }

    for(auto v : g[u]) if(v != ant) {
        qtl-= dpl[v][0];
        if(qtl || dpwup[u][0]) {
            dpwup[v][0] = 0;
            dplup[v][0] = 1-dpwup[v][0];
        }
        else {
            dpwup[v][0] = 1;
            dplup[v][0] = 1-dpwup[v][0];
        }
        qtl+= dpl[v][0];
    }

    for(auto v : g[u]) if(v != ant) {
        dfs0up(v,u);
    }
}

void solve() {
    cin >> n >> d;

    for(int i = 1; i <= n-1; i++) {
        int u,v; cin >> u >> v;
        g[u].pb(v);
        g[v].pb(u);
    }

    dfs0(1,0);
    dpwup[1][0] = 0;
    dplup[1][0] = 1;
    dfs0up(1,0);
    for(int i = 1; i <= n; i++) {
        if(dpw[i][0] || dpwup[i][0]) SW0++;
        else SL0++;
    }

    sol(1,0);
    dfsrrt(1,0);
    SLb = n*n-SWb;

    // cout << SWb << " " << SLb << endl;
    // cout << SW0 << " " << SL0 << endl;
    SWb%= mod;
    SLb%= mod;
    SW = SW0;
    SL = SL0;
    // for(int i = 1; i <= d-1; i++) {
    //     int newSW = n*(SW*SW0%mod)%mod + SL*SWb; newSW%= mod;
    //     int newSL = n*(SW*SL0%mod)%mod + SL*SLb; newSL%= mod;
    //     SW = newSW;
    //     SL = newSL;
    // }

    int r[1][2];
    r[0][0] = SW;
    r[0][1] = SL;
    int b[2][2];
    b[0][0] = n*SW0%mod;
    b[0][1] = n*SL0%mod;
    b[1][0] = SWb;
    b[1][1] = SLb;

    for(int wtf = 1; wtf <= d-1; wtf++) {
        int a[1][2];
        a[0][0] = r[0][0];
        a[0][1] = r[0][1];

        r[0][0] = 0;
        r[0][1] = 0;
        for(int k = 0; k <= 1; k++) {
            for(int i = 0; i <= 0; i++) {
                for(int j = 0; j <= 1; j++) {
                    r[i][j]+= a[i][k]*b[k][j];
                    r[i][j]%= mod;
                }
            }
        }
    }

    SW = r[0][0];
    SL = r[0][1];


    dfs1(1,0);
    // cout << SW << " " << SL << endl;
    cout << dpw[1][1] << endl;
}

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(0);

    // freopen("in.in", "r", stdin);
    // freopen("out.out", "w", stdout);
    int tt = 1;
    // cin >> tt;
    while(tt--) {
        solve();
    }

}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 17 ms 35808 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35596 KB Output is correct
2 Correct 16 ms 35504 KB Output is correct
3 Execution timed out 1086 ms 35572 KB Time limit exceeded
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 18 ms 35580 KB Output is correct
3 Correct 19 ms 35564 KB Output is correct
4 Correct 17 ms 35572 KB Output is correct
5 Correct 18 ms 35540 KB Output is correct
6 Correct 18 ms 35540 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 18 ms 35580 KB Output is correct
3 Correct 19 ms 35564 KB Output is correct
4 Correct 17 ms 35572 KB Output is correct
5 Correct 18 ms 35540 KB Output is correct
6 Correct 18 ms 35540 KB Output is correct
7 Correct 20 ms 35796 KB Output is correct
8 Correct 18 ms 35908 KB Output is correct
9 Correct 17 ms 35804 KB Output is correct
10 Correct 19 ms 35808 KB Output is correct
11 Correct 18 ms 35740 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 18 ms 35580 KB Output is correct
3 Correct 19 ms 35564 KB Output is correct
4 Correct 17 ms 35572 KB Output is correct
5 Correct 18 ms 35540 KB Output is correct
6 Correct 18 ms 35540 KB Output is correct
7 Correct 20 ms 35796 KB Output is correct
8 Correct 18 ms 35908 KB Output is correct
9 Correct 17 ms 35804 KB Output is correct
10 Correct 19 ms 35808 KB Output is correct
11 Correct 18 ms 35740 KB Output is correct
12 Correct 188 ms 60956 KB Output is correct
13 Correct 175 ms 68472 KB Output is correct
14 Correct 151 ms 54708 KB Output is correct
15 Correct 181 ms 54844 KB Output is correct
16 Correct 195 ms 55104 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 18 ms 35580 KB Output is correct
3 Correct 19 ms 35564 KB Output is correct
4 Correct 17 ms 35572 KB Output is correct
5 Correct 18 ms 35540 KB Output is correct
6 Correct 18 ms 35540 KB Output is correct
7 Correct 20 ms 35796 KB Output is correct
8 Correct 18 ms 35908 KB Output is correct
9 Correct 17 ms 35804 KB Output is correct
10 Correct 19 ms 35808 KB Output is correct
11 Correct 18 ms 35740 KB Output is correct
12 Correct 18 ms 35540 KB Output is correct
13 Correct 19 ms 35736 KB Output is correct
14 Correct 17 ms 35616 KB Output is correct
15 Correct 17 ms 35544 KB Output is correct
16 Correct 22 ms 35528 KB Output is correct
17 Correct 20 ms 35552 KB Output is correct
18 Correct 20 ms 35592 KB Output is correct
19 Correct 17 ms 35540 KB Output is correct
20 Correct 21 ms 35628 KB Output is correct
21 Correct 17 ms 35796 KB Output is correct
22 Correct 19 ms 35924 KB Output is correct
23 Correct 19 ms 35808 KB Output is correct
24 Correct 19 ms 35796 KB Output is correct
25 Correct 20 ms 35752 KB Output is correct
26 Correct 24 ms 35872 KB Output is correct
27 Correct 21 ms 35924 KB Output is correct
28 Correct 23 ms 35648 KB Output is correct
29 Correct 22 ms 35708 KB Output is correct
30 Correct 19 ms 35788 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 18 ms 35580 KB Output is correct
3 Correct 19 ms 35564 KB Output is correct
4 Correct 17 ms 35572 KB Output is correct
5 Correct 18 ms 35540 KB Output is correct
6 Correct 18 ms 35540 KB Output is correct
7 Correct 20 ms 35796 KB Output is correct
8 Correct 18 ms 35908 KB Output is correct
9 Correct 17 ms 35804 KB Output is correct
10 Correct 19 ms 35808 KB Output is correct
11 Correct 18 ms 35740 KB Output is correct
12 Correct 188 ms 60956 KB Output is correct
13 Correct 175 ms 68472 KB Output is correct
14 Correct 151 ms 54708 KB Output is correct
15 Correct 181 ms 54844 KB Output is correct
16 Correct 195 ms 55104 KB Output is correct
17 Correct 18 ms 35540 KB Output is correct
18 Correct 19 ms 35736 KB Output is correct
19 Correct 17 ms 35616 KB Output is correct
20 Correct 17 ms 35544 KB Output is correct
21 Correct 22 ms 35528 KB Output is correct
22 Correct 20 ms 35552 KB Output is correct
23 Correct 20 ms 35592 KB Output is correct
24 Correct 17 ms 35540 KB Output is correct
25 Correct 21 ms 35628 KB Output is correct
26 Correct 17 ms 35796 KB Output is correct
27 Correct 19 ms 35924 KB Output is correct
28 Correct 19 ms 35808 KB Output is correct
29 Correct 19 ms 35796 KB Output is correct
30 Correct 20 ms 35752 KB Output is correct
31 Correct 24 ms 35872 KB Output is correct
32 Correct 21 ms 35924 KB Output is correct
33 Correct 23 ms 35648 KB Output is correct
34 Correct 22 ms 35708 KB Output is correct
35 Correct 19 ms 35788 KB Output is correct
36 Correct 185 ms 61060 KB Output is correct
37 Correct 174 ms 68424 KB Output is correct
38 Correct 126 ms 54756 KB Output is correct
39 Correct 151 ms 54980 KB Output is correct
40 Correct 157 ms 55020 KB Output is correct
41 Correct 163 ms 65068 KB Output is correct
42 Correct 149 ms 65476 KB Output is correct
43 Correct 107 ms 52456 KB Output is correct
44 Correct 185 ms 55092 KB Output is correct
45 Correct 169 ms 54740 KB Output is correct

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 17 ms 35808 KB Output is correct
3 Correct 16 ms 35596 KB Output is correct
4 Correct 16 ms 35504 KB Output is correct
5 Execution timed out 1086 ms 35572 KB Time limit exceeded
6 Halted 0 ms 0 KB -