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Submission #498030

# Submission time Handle Problem Language Result Execution time Memory
498030 2021-12-24T09:49:07 Z andrei_boaca Star Trek (CEOI20_startrek) C++17
100 / 100
 138 ms 32112 KB 
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const ll mod=1e9+7;
ll n,d,nr[2][2],nrL,nrW,dp[100005][2][2],win[100005],rez[2][2],c[2][2],sol[2][2],parent[100005],nrlose[100005];
ll suma[100005][2][2];
vector<int> muchii[100005];
set<int> losers[100005];
bool use[100005];
void mult(ll a[2][2],ll b[2][2])
{
    for(int i=0;i<=1;i++)
        for(int j=0;j<=1;j++)
        {
            c[i][j]=0;
            for(int k=0;k<=1;k++)
                c[i][j]=(c[i][j]+(a[i][k]*b[k][j])%mod)%mod;
        }
}
void matpw(ll b)
{
    while(b)
    {
        if(b&1)
        {
            mult(rez,nr);
            for(int i=0;i<=1;i++)
                for(int j=0;j<=1;j++)
                    rez[i][j]=c[i][j];
        }
        b/=2;
        mult(nr,nr);
        for(int i=0;i<=1;i++)
            for(int j=0;j<=1;j++)
                nr[i][j]=c[i][j];
    }
}
void dfs(int nod,int par)
{
    parent[nod]=par;
    nrlose[nod]=0;
    win[nod]=0;
    for(int i:muchii[nod])
        if(i!=par)
        {
            dfs(i,nod);
            if(win[i]==0)
            {
                losers[nod].insert(i);
                nrlose[nod]++;
                win[nod]=1;
            }
        }
    for(int i:muchii[nod])
        if(i!=par)
        {
            for(int j=0;j<=1;j++)
                for(int k=0;k<=1;k++)
                    suma[nod][j][k]=(suma[nod][j][k]+dp[i][j][k])%mod;
            if(win[i]==0)
                nrlose[nod]--;
            if(nrlose[nod]==0)
            {
                dp[nod][0][1]=(dp[nod][0][1]+dp[i][1][1])%mod;
                dp[nod][0][0]=(dp[nod][0][0]+dp[i][1][0])%mod;
            }
            else
            {
                dp[nod][1][1]=(dp[nod][1][1]+dp[i][1][1])%mod;
                dp[nod][1][0]=(dp[nod][1][0]+dp[i][1][0])%mod;
            }
            dp[nod][1][1]=(dp[nod][1][1]+dp[i][0][1])%mod;
            dp[nod][1][0]=(dp[nod][1][0]+dp[i][0][0])%mod;
            if(win[i]==0)
                nrlose[nod]++;
        }
    if(nrlose[nod]==0)
    {
        dp[nod][1][0]++;
        dp[nod][1][0]%=mod;
        dp[nod][0][1]++;
        dp[nod][0][1]%=mod;
    }
    else
    {
        dp[nod][1][0]++;
        dp[nod][1][0]%=mod;
        dp[nod][1][1]++;
        dp[nod][1][1]%=mod;
    }
}
void recalc(int nod)
{
    for(int i=0;i<=1;i++)
        for(int j=0;j<=1;j++)
            dp[nod][i][j]=0;
    if(nrlose[nod]>0)
        win[nod]=1;
    else
        win[nod]=0;
    if(nrlose[nod]>1)
    {
        dp[nod][1][1]=(suma[nod][1][1]+suma[nod][0][1])%mod;
        dp[nod][1][0]=(suma[nod][1][0]+suma[nod][0][0])%mod;
    }
    if(nrlose[nod]==1)
    {
        int lose=*losers[nod].begin();
        dp[nod][1][1]=(suma[nod][1][1]+suma[nod][0][1])%mod;
        dp[nod][1][1]-=dp[lose][1][1];
        if(dp[nod][1][1]<0)
            dp[nod][1][1]+=mod;
        dp[nod][1][0]=(suma[nod][1][0]+suma[nod][0][0])%mod;
        dp[nod][1][0]-=dp[lose][1][0];
        if(dp[nod][1][0]<0)
            dp[nod][1][0]+=mod;
        dp[nod][0][1]=dp[lose][1][1];
        dp[nod][0][0]=dp[lose][1][0];
    }
    if(nrlose[nod]==0)
    {
        dp[nod][0][0]=suma[nod][1][0];
        dp[nod][0][1]=suma[nod][1][1];
        dp[nod][1][0]=suma[nod][0][0];
        dp[nod][1][1]=suma[nod][0][1];
    }
    if(nrlose[nod]==0)
    {
        dp[nod][1][0]++;
        dp[nod][1][0]%=mod;
        dp[nod][0][1]++;
        dp[nod][0][1]%=mod;
    }
    else
    {
        dp[nod][1][0]++;
        dp[nod][1][0]%=mod;
        dp[nod][1][1]++;
        dp[nod][1][1]%=mod;
    }
}
void reroot(int par,int fiu)
{
    if(win[fiu]==0)
    {
        nrlose[par]--;
        losers[par].erase(fiu);
    }
    for(int i=0;i<=1;i++)
        for(int j=0;j<=1;j++)
        {
            suma[par][i][j]-=dp[fiu][i][j];
            if(suma[par][i][j]<0)
                suma[par][i][j]+=mod;
        }
    recalc(par);
    for(int i=0;i<=1;i++)
        for(int j=0;j<=1;j++)
        {
            suma[fiu][i][j]+=dp[par][i][j];
            if(suma[fiu][i][j]>=mod)
                suma[fiu][i][j]-=mod;
        }
    if(win[par]==0)
    {
        nrlose[fiu]++;
        losers[fiu].insert(par);
    }
    recalc(fiu);
}
void calcdp(int nod)
{
    use[nod]=1;
    for(int i:muchii[nod])
        if(!use[i])
        {
            reroot(nod,i);
            int root=i;
            for(int k=0;k<=1;k++)
                for(int j=0;j<=1;j++)
                {
                    nr[j][k]=(nr[j][k]+dp[root][k][j]);
                    if(nr[j][k]>=mod)
                        nr[j][k]-=mod;
                }
            if(win[root]==0)
                nrL++;
            if(win[root]==1)
                nrW++;
            calcdp(i);
            reroot(i,nod);
        }
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin>>n>>d;
    for(int i=1;i<n;i++)
    {
        int a,b;
        cin>>a>>b;
        muchii[a].push_back(b);
        muchii[b].push_back(a);
    }
    for(int root=1;root<=1;root++)
    {
        for(int i=1;i<=n;i++)
        {
            win[i]=0;
            for(int j=0;j<=1;j++)
                for(int k=0;k<=1;k++)
                    dp[i][j][k]=0;
        }
        dfs(root,0);
        for(int i=0;i<=1;i++)
            for(int j=0;j<=1;j++)
            {
                nr[j][i]=(nr[j][i]+dp[root][i][j]);
                if(nr[j][i]>=mod)
                    nr[j][i]-=mod;
            }
        if(win[root]==0)
            nrL++;
        if(win[root]==1)
            nrW++;
        if(root==1)
        {
            for(int i=0;i<=1;i++)
                for(int j=0;j<=1;j++)
                    sol[i][j]=dp[root][i][j];
        }
    }
    calcdp(1);
    rez[0][0]=nrL;
    rez[0][1]=nrW;
    if(d>1)
        matpw(d-1);
    ll ans=(sol[1][0]*rez[0][0])%mod;
    ans=(ans+sol[1][1]*rez[0][1]%mod)%mod;
    cout<<ans;
    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7352 KB Output is correct
2 Correct 5 ms 7496 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7372 KB Output is correct
2 Correct 4 ms 7368 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 4 ms 7372 KB Output is correct
5 Correct 3 ms 7368 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7368 KB Output is correct
2 Correct 4 ms 7312 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 3 ms 7372 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7368 KB Output is correct
2 Correct 4 ms 7312 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 3 ms 7372 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct
7 Correct 6 ms 7500 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7500 KB Output is correct
10 Correct 4 ms 7500 KB Output is correct
11 Correct 5 ms 7500 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7368 KB Output is correct
2 Correct 4 ms 7312 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 3 ms 7372 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct
7 Correct 6 ms 7500 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7500 KB Output is correct
10 Correct 4 ms 7500 KB Output is correct
11 Correct 5 ms 7500 KB Output is correct
12 Correct 138 ms 27104 KB Output is correct
13 Correct 135 ms 31968 KB Output is correct
14 Correct 107 ms 22612 KB Output is correct
15 Correct 120 ms 22888 KB Output is correct
16 Correct 129 ms 22944 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7368 KB Output is correct
2 Correct 4 ms 7312 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 3 ms 7372 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct
7 Correct 6 ms 7500 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7500 KB Output is correct
10 Correct 4 ms 7500 KB Output is correct
11 Correct 5 ms 7500 KB Output is correct
12 Correct 4 ms 7400 KB Output is correct
13 Correct 5 ms 7504 KB Output is correct
14 Correct 4 ms 7372 KB Output is correct
15 Correct 4 ms 7368 KB Output is correct
16 Correct 4 ms 7372 KB Output is correct
17 Correct 3 ms 7372 KB Output is correct
18 Correct 4 ms 7344 KB Output is correct
19 Correct 4 ms 7372 KB Output is correct
20 Correct 4 ms 7372 KB Output is correct
21 Correct 6 ms 7504 KB Output is correct
22 Correct 4 ms 7628 KB Output is correct
23 Correct 4 ms 7500 KB Output is correct
24 Correct 4 ms 7500 KB Output is correct
25 Correct 4 ms 7508 KB Output is correct
26 Correct 4 ms 7500 KB Output is correct
27 Correct 4 ms 7632 KB Output is correct
28 Correct 4 ms 7500 KB Output is correct
29 Correct 4 ms 7508 KB Output is correct
30 Correct 4 ms 7500 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7368 KB Output is correct
2 Correct 4 ms 7312 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 3 ms 7372 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct
7 Correct 6 ms 7500 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7500 KB Output is correct
10 Correct 4 ms 7500 KB Output is correct
11 Correct 5 ms 7500 KB Output is correct
12 Correct 138 ms 27104 KB Output is correct
13 Correct 135 ms 31968 KB Output is correct
14 Correct 107 ms 22612 KB Output is correct
15 Correct 120 ms 22888 KB Output is correct
16 Correct 129 ms 22944 KB Output is correct
17 Correct 4 ms 7400 KB Output is correct
18 Correct 5 ms 7504 KB Output is correct
19 Correct 4 ms 7372 KB Output is correct
20 Correct 4 ms 7368 KB Output is correct
21 Correct 4 ms 7372 KB Output is correct
22 Correct 3 ms 7372 KB Output is correct
23 Correct 4 ms 7344 KB Output is correct
24 Correct 4 ms 7372 KB Output is correct
25 Correct 4 ms 7372 KB Output is correct
26 Correct 6 ms 7504 KB Output is correct
27 Correct 4 ms 7628 KB Output is correct
28 Correct 4 ms 7500 KB Output is correct
29 Correct 4 ms 7500 KB Output is correct
30 Correct 4 ms 7508 KB Output is correct
31 Correct 4 ms 7500 KB Output is correct
32 Correct 4 ms 7632 KB Output is correct
33 Correct 4 ms 7500 KB Output is correct
34 Correct 4 ms 7508 KB Output is correct
35 Correct 4 ms 7500 KB Output is correct
36 Correct 132 ms 27100 KB Output is correct
37 Correct 132 ms 32112 KB Output is correct
38 Correct 101 ms 22660 KB Output is correct
39 Correct 112 ms 22724 KB Output is correct
40 Correct 113 ms 23012 KB Output is correct
41 Correct 128 ms 29672 KB Output is correct
42 Correct 118 ms 29932 KB Output is correct
43 Correct 89 ms 20928 KB Output is correct
44 Correct 115 ms 22988 KB Output is correct
45 Correct 116 ms 22872 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7352 KB Output is correct
2 Correct 5 ms 7496 KB Output is correct
3 Correct 4 ms 7372 KB Output is correct
4 Correct 4 ms 7368 KB Output is correct
5 Correct 4 ms 7372 KB Output is correct
6 Correct 4 ms 7372 KB Output is correct
7 Correct 3 ms 7368 KB Output is correct
8 Correct 4 ms 7368 KB Output is correct
9 Correct 4 ms 7312 KB Output is correct
10 Correct 4 ms 7372 KB Output is correct
11 Correct 3 ms 7372 KB Output is correct
12 Correct 4 ms 7372 KB Output is correct
13 Correct 4 ms 7372 KB Output is correct
14 Correct 6 ms 7500 KB Output is correct
15 Correct 4 ms 7636 KB Output is correct
16 Correct 4 ms 7500 KB Output is correct
17 Correct 4 ms 7500 KB Output is correct
18 Correct 5 ms 7500 KB Output is correct
19 Correct 138 ms 27104 KB Output is correct
20 Correct 135 ms 31968 KB Output is correct
21 Correct 107 ms 22612 KB Output is correct
22 Correct 120 ms 22888 KB Output is correct
23 Correct 129 ms 22944 KB Output is correct
24 Correct 4 ms 7400 KB Output is correct
25 Correct 5 ms 7504 KB Output is correct
26 Correct 4 ms 7372 KB Output is correct
27 Correct 4 ms 7368 KB Output is correct
28 Correct 4 ms 7372 KB Output is correct
29 Correct 3 ms 7372 KB Output is correct
30 Correct 4 ms 7344 KB Output is correct
31 Correct 4 ms 7372 KB Output is correct
32 Correct 4 ms 7372 KB Output is correct
33 Correct 6 ms 7504 KB Output is correct
34 Correct 4 ms 7628 KB Output is correct
35 Correct 4 ms 7500 KB Output is correct
36 Correct 4 ms 7500 KB Output is correct
37 Correct 4 ms 7508 KB Output is correct
38 Correct 4 ms 7500 KB Output is correct
39 Correct 4 ms 7632 KB Output is correct
40 Correct 4 ms 7500 KB Output is correct
41 Correct 4 ms 7508 KB Output is correct
42 Correct 4 ms 7500 KB Output is correct
43 Correct 132 ms 27100 KB Output is correct
44 Correct 132 ms 32112 KB Output is correct
45 Correct 101 ms 22660 KB Output is correct
46 Correct 112 ms 22724 KB Output is correct
47 Correct 113 ms 23012 KB Output is correct
48 Correct 128 ms 29672 KB Output is correct
49 Correct 118 ms 29932 KB Output is correct
50 Correct 89 ms 20928 KB Output is correct
51 Correct 115 ms 22988 KB Output is correct
52 Correct 116 ms 22872 KB Output is correct
53 Correct 135 ms 32068 KB Output is correct
54 Correct 137 ms 30156 KB Output is correct
55 Correct 77 ms 19660 KB Output is correct
56 Correct 126 ms 27340 KB Output is correct
57 Correct 109 ms 23212 KB Output is correct
58 Correct 120 ms 23248 KB Output is correct
59 Correct 123 ms 22712 KB Output is correct
60 Correct 112 ms 22736 KB Output is correct