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Submission #659654

# Submission time Handle Problem Language Result Execution time Memory
659654 2022-11-18T21:33:06 Z Lobo Star Trek (CEOI20_startrek) C++17
100 / 100
 177 ms 69576 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 pt = 0; pt <= 60; pt++) {
        if((1LL<<pt)&(d-1)) {
            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;
                    }
                }
            }
        }
        int rb[2][2];
        for(int i = 0; i <= 1; i++) {
            for(int j = 0; j <= 1; j++) {
                rb[i][j] = 0;
            }
        }

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

    }

    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 16 ms 35796 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 17 ms 35704 KB Output is correct
2 Correct 16 ms 35504 KB Output is correct
3 Correct 17 ms 35540 KB Output is correct
4 Correct 16 ms 35512 KB Output is correct
5 Correct 17 ms 35512 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 17 ms 35540 KB Output is correct
3 Correct 16 ms 35640 KB Output is correct
4 Correct 17 ms 35540 KB Output is correct
5 Correct 17 ms 35608 KB Output is correct
6 Correct 17 ms 35600 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 17 ms 35540 KB Output is correct
3 Correct 16 ms 35640 KB Output is correct
4 Correct 17 ms 35540 KB Output is correct
5 Correct 17 ms 35608 KB Output is correct
6 Correct 17 ms 35600 KB Output is correct
7 Correct 16 ms 35796 KB Output is correct
8 Correct 19 ms 35924 KB Output is correct
9 Correct 17 ms 35796 KB Output is correct
10 Correct 18 ms 35784 KB Output is correct
11 Correct 18 ms 35752 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 17 ms 35540 KB Output is correct
3 Correct 16 ms 35640 KB Output is correct
4 Correct 17 ms 35540 KB Output is correct
5 Correct 17 ms 35608 KB Output is correct
6 Correct 17 ms 35600 KB Output is correct
7 Correct 16 ms 35796 KB Output is correct
8 Correct 19 ms 35924 KB Output is correct
9 Correct 17 ms 35796 KB Output is correct
10 Correct 18 ms 35784 KB Output is correct
11 Correct 18 ms 35752 KB Output is correct
12 Correct 162 ms 61060 KB Output is correct
13 Correct 167 ms 68420 KB Output is correct
14 Correct 123 ms 54776 KB Output is correct
15 Correct 142 ms 54764 KB Output is correct
16 Correct 141 ms 55100 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 17 ms 35540 KB Output is correct
3 Correct 16 ms 35640 KB Output is correct
4 Correct 17 ms 35540 KB Output is correct
5 Correct 17 ms 35608 KB Output is correct
6 Correct 17 ms 35600 KB Output is correct
7 Correct 16 ms 35796 KB Output is correct
8 Correct 19 ms 35924 KB Output is correct
9 Correct 17 ms 35796 KB Output is correct
10 Correct 18 ms 35784 KB Output is correct
11 Correct 18 ms 35752 KB Output is correct
12 Correct 17 ms 35588 KB Output is correct
13 Correct 18 ms 35740 KB Output is correct
14 Correct 17 ms 35492 KB Output is correct
15 Correct 17 ms 35600 KB Output is correct
16 Correct 17 ms 35572 KB Output is correct
17 Correct 20 ms 35556 KB Output is correct
18 Correct 17 ms 35540 KB Output is correct
19 Correct 18 ms 35540 KB Output is correct
20 Correct 18 ms 35668 KB Output is correct
21 Correct 24 ms 35752 KB Output is correct
22 Correct 17 ms 35944 KB Output is correct
23 Correct 17 ms 35684 KB Output is correct
24 Correct 17 ms 35796 KB Output is correct
25 Correct 18 ms 35796 KB Output is correct
26 Correct 18 ms 35768 KB Output is correct
27 Correct 17 ms 35924 KB Output is correct
28 Correct 21 ms 35768 KB Output is correct
29 Correct 17 ms 35708 KB Output is correct
30 Correct 17 ms 35796 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 17 ms 35540 KB Output is correct
3 Correct 16 ms 35640 KB Output is correct
4 Correct 17 ms 35540 KB Output is correct
5 Correct 17 ms 35608 KB Output is correct
6 Correct 17 ms 35600 KB Output is correct
7 Correct 16 ms 35796 KB Output is correct
8 Correct 19 ms 35924 KB Output is correct
9 Correct 17 ms 35796 KB Output is correct
10 Correct 18 ms 35784 KB Output is correct
11 Correct 18 ms 35752 KB Output is correct
12 Correct 162 ms 61060 KB Output is correct
13 Correct 167 ms 68420 KB Output is correct
14 Correct 123 ms 54776 KB Output is correct
15 Correct 142 ms 54764 KB Output is correct
16 Correct 141 ms 55100 KB Output is correct
17 Correct 17 ms 35588 KB Output is correct
18 Correct 18 ms 35740 KB Output is correct
19 Correct 17 ms 35492 KB Output is correct
20 Correct 17 ms 35600 KB Output is correct
21 Correct 17 ms 35572 KB Output is correct
22 Correct 20 ms 35556 KB Output is correct
23 Correct 17 ms 35540 KB Output is correct
24 Correct 18 ms 35540 KB Output is correct
25 Correct 18 ms 35668 KB Output is correct
26 Correct 24 ms 35752 KB Output is correct
27 Correct 17 ms 35944 KB Output is correct
28 Correct 17 ms 35684 KB Output is correct
29 Correct 17 ms 35796 KB Output is correct
30 Correct 18 ms 35796 KB Output is correct
31 Correct 18 ms 35768 KB Output is correct
32 Correct 17 ms 35924 KB Output is correct
33 Correct 21 ms 35768 KB Output is correct
34 Correct 17 ms 35708 KB Output is correct
35 Correct 17 ms 35796 KB Output is correct
36 Correct 163 ms 61048 KB Output is correct
37 Correct 172 ms 68428 KB Output is correct
38 Correct 127 ms 54832 KB Output is correct
39 Correct 139 ms 54736 KB Output is correct
40 Correct 141 ms 55116 KB Output is correct
41 Correct 159 ms 65068 KB Output is correct
42 Correct 143 ms 65472 KB Output is correct
43 Correct 102 ms 52516 KB Output is correct
44 Correct 149 ms 55084 KB Output is correct
45 Correct 138 ms 54824 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 35540 KB Output is correct
2 Correct 16 ms 35796 KB Output is correct
3 Correct 17 ms 35704 KB Output is correct
4 Correct 16 ms 35504 KB Output is correct
5 Correct 17 ms 35540 KB Output is correct
6 Correct 16 ms 35512 KB Output is correct
7 Correct 17 ms 35512 KB Output is correct
8 Correct 16 ms 35540 KB Output is correct
9 Correct 17 ms 35540 KB Output is correct
10 Correct 16 ms 35640 KB Output is correct
11 Correct 17 ms 35540 KB Output is correct
12 Correct 17 ms 35608 KB Output is correct
13 Correct 17 ms 35600 KB Output is correct
14 Correct 16 ms 35796 KB Output is correct
15 Correct 19 ms 35924 KB Output is correct
16 Correct 17 ms 35796 KB Output is correct
17 Correct 18 ms 35784 KB Output is correct
18 Correct 18 ms 35752 KB Output is correct
19 Correct 162 ms 61060 KB Output is correct
20 Correct 167 ms 68420 KB Output is correct
21 Correct 123 ms 54776 KB Output is correct
22 Correct 142 ms 54764 KB Output is correct
23 Correct 141 ms 55100 KB Output is correct
24 Correct 17 ms 35588 KB Output is correct
25 Correct 18 ms 35740 KB Output is correct
26 Correct 17 ms 35492 KB Output is correct
27 Correct 17 ms 35600 KB Output is correct
28 Correct 17 ms 35572 KB Output is correct
29 Correct 20 ms 35556 KB Output is correct
30 Correct 17 ms 35540 KB Output is correct
31 Correct 18 ms 35540 KB Output is correct
32 Correct 18 ms 35668 KB Output is correct
33 Correct 24 ms 35752 KB Output is correct
34 Correct 17 ms 35944 KB Output is correct
35 Correct 17 ms 35684 KB Output is correct
36 Correct 17 ms 35796 KB Output is correct
37 Correct 18 ms 35796 KB Output is correct
38 Correct 18 ms 35768 KB Output is correct
39 Correct 17 ms 35924 KB Output is correct
40 Correct 21 ms 35768 KB Output is correct
41 Correct 17 ms 35708 KB Output is correct
42 Correct 17 ms 35796 KB Output is correct
43 Correct 163 ms 61048 KB Output is correct
44 Correct 172 ms 68428 KB Output is correct
45 Correct 127 ms 54832 KB Output is correct
46 Correct 139 ms 54736 KB Output is correct
47 Correct 141 ms 55116 KB Output is correct
48 Correct 159 ms 65068 KB Output is correct
49 Correct 143 ms 65472 KB Output is correct
50 Correct 102 ms 52516 KB Output is correct
51 Correct 149 ms 55084 KB Output is correct
52 Correct 138 ms 54824 KB Output is correct
53 Correct 177 ms 69576 KB Output is correct
54 Correct 166 ms 66848 KB Output is correct
55 Correct 95 ms 51760 KB Output is correct
56 Correct 154 ms 62464 KB Output is correct
57 Correct 140 ms 56652 KB Output is correct
58 Correct 139 ms 56556 KB Output is correct
59 Correct 145 ms 55848 KB Output is correct
60 Correct 168 ms 55824 KB Output is correct