Submission #659654

#	Time	Username	Problem	Language	Result	Execution time	Memory
659654		Lobo	Star Trek (CEOI20_startrek)	C++17	100 / 100	177 ms	69576 KiB

startrek

#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
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 15 / 15
• Subtask 6: 20 / 20
• Subtask 7: 20 / 20
• Subtask 8: 15 / 15