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Submission #588748

# Submission time Handle Problem Language Result Execution time Memory
588748 2022-07-04T02:30:31 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 232 ms 33072 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
const ll MOD = 1000000007;

struct Matrix{
    int n, m;
    ll mat[2][2];
    Matrix(){}
    Matrix(int n, int m): n(n), m(m){
        for(int i=0; i<n; i++) for(int j=0; j<m; j++) mat[i][j] = 0;
    }

    Matrix operator*(const Matrix &r)const{
        assert(m == r.n);
        Matrix ret (n, r.m);
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++){
                for(int k=0; k<r.m; k++){
                    ret.mat[i][k] += mat[i][j] * r.mat[j][k];
                    ret.mat[i][k] %= MOD;
                }
            }
        }
        return ret;
    }
};

ll mpow(ll x, ll y){
    if(!y) return 1;
    if(y%2) return mpow(x, y-1) * x % MOD;
    ll tmp = mpow(x, y/2);
    return tmp*tmp%MOD;
}

Matrix BasicMatrix(int n, int m){
    Matrix mat (n, m);
    assert(n==m);
    for(int i=0; i<n; i++) mat.mat[i][i] = 1;
    return mat;
}

Matrix mpow(Matrix x, ll y){
    if(!y) return BasicMatrix(x.n, x.m);
    if(y&1) return mpow(x, y-1) * x;
    Matrix tmp = mpow(x, y/2);
    return tmp * tmp;
}

int n, lim;
ll k;
vector<int> link[100002][2];
bool mat[400002];
int ey[400002];
int parEdge[100002];
bool canWin[100002];
bitset<400002> dfsChk;

int group[100002], groupCnt[2];
int res[100002];
ll ans;

bool groupVisited[100002];
void groupDfs(int x, int p=-1){
    groupCnt[group[x]]++;
    groupVisited[x] = 1;
    for(auto y: link[x][0]){
        if(ey[y]==p || groupVisited[ey[y]]) continue;
        group[ey[y]] = !group[x];
        groupDfs(ey[y], x);
    }
}

int winCnt[100002];
bool dfs(int pe){
    if(dfsChk[pe]) return mat[pe];
    int x = ey[pe];
    mat[pe] = !!(winCnt[x] - (pe > lim ? 0 : (dfsChk[pe^1] && !mat[pe^1])));
    dfsChk[pe] = 1;
    vector<int> nLink;
    for(auto y: link[x][0]){
        if((y^pe)==1) nLink.push_back(y);
        else if(!dfs(y)) winCnt[x]++, mat[pe] = 1;
    }
    link[x][0].swap(nLink);
    return mat[pe];
}

int find1[400002][2];
int findV[100002][2];
bitset<400002> findChk[2];
int dfsFind(int pe, bool dp){ /// 무조건 지나야 하는 상대 차례 점 개수 찾기
    if(findChk[dp][pe]) return find1[pe][dp];
    int x = ey[pe];
    findChk[dp][pe] = 1;
    if(!dp){ /// my turn
        int cnt = 0;
        for(auto y: link[x][0]){
            if((y^1)!=pe && !mat[y]) cnt++;
        }
        if(cnt > 1) return find1[pe][dp] = 0;
        assert(cnt == 1);
        for(auto y: link[x][0]){
            if((y^1)!=pe && !mat[y]) return find1[pe][dp] = dfsFind(y, !dp);
        }
        exit(1);
    }
    else{ /// your turn
        int ret = 1 + findV[x][1] - ((pe>lim || !findChk[0][pe^1]) ? 0 : find1[pe^1][0]);
        vector<int> v;
        for(auto y: link[x][1]){
            if((y^1)==pe) v.push_back(y);
            else{
                int tmp = dfsFind(y, !dp);
                ret += tmp, findV[x][1] += tmp;
            }
        }
        link[x][1].swap(v);
        return find1[pe][dp] = ret;
    }
}

int main(){
//    freopen("input.txt", "r", stdin);
    scanf("%d %lld", &n, &k);
    lim = (n-1)*2-1;
    for(int i=1; i<n; i++){
        int x, y;
        scanf("%d %d", &x, &y);
        link[x][0].push_back(i*2-2);
        link[x][1].push_back(i*2-2);
        link[y][0].push_back(i*2-1);
        link[y][1].push_back(i*2-1);
        ey[i*2-2] = y;
        ey[i*2-1] = x;
    }
    for(int i=n; i<n+n; i++){
        ey[i*2-2] = i-n+1;
        parEdge[i-n+1] = i*2-2;
    }

    groupDfs(1);
    for(int i=1; i<=n; i++){
        canWin[i] = dfs(parEdge[i]);
    }
    for(int i=1; i<=n; i++) link[i][0] = link[i][1];
    for(int i=1; i<=n; i++){
        if(canWin[i]) res[i] = groupCnt[!group[i]] - dfsFind(parEdge[i], 0);
        else res[i] = dfsFind(parEdge[i], 1);
    }

    Matrix first (1, 2);
    first.mat[0][0] = first.mat[0][1] = 0;
    for(int i=1; i<=n; i++){
        if(canWin[i]) first.mat[0][0]++;
        else first.mat[0][1]++;
    }

    Matrix multiplier (2, 2); /// 0: WIN, 1: LOSE
    for(int i=1; i<=n; i++){
        if(canWin[i]){
            multiplier.mat[0][0] = (multiplier.mat[0][0] + n) % MOD;
            multiplier.mat[1][0] = (multiplier.mat[1][0] + groupCnt[group[i]]) % MOD;
            multiplier.mat[1][0] = (multiplier.mat[1][0] + res[i]) % MOD;

            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - groupCnt[group[i]] - res[i] + MOD)%MOD;
        }
        else{
            multiplier.mat[1][0] = (multiplier.mat[1][0] + res[i]) % MOD;

            multiplier.mat[0][1] = (multiplier.mat[0][1] + n) % MOD;
            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - res[i]) % MOD;
        }
    }
    multiplier = mpow(multiplier, k-1);
    first = first * multiplier;
    ll Wsum = first.mat[0][0], Lsum = first.mat[0][1];
    ll ans = 0;
    if(canWin[1]){
        ans = (Wsum * n + Lsum * groupCnt[group[1]] + Lsum * res[1]) % MOD;
    }
    else ans = Lsum * res[1] % MOD;

    printf("%lld", ans);
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:127:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  127 |     scanf("%d %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:131:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  131 |         scanf("%d %d", &x, &y);
      |         ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 5204 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 2 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 2 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 4 ms 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5204 KB Output is correct
11 Correct 4 ms 5204 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 2 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 4 ms 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5204 KB Output is correct
11 Correct 4 ms 5204 KB Output is correct
12 Correct 212 ms 25476 KB Output is correct
13 Correct 225 ms 33012 KB Output is correct
14 Correct 192 ms 19172 KB Output is correct
15 Correct 181 ms 19068 KB Output is correct
16 Correct 176 ms 19164 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 2 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 4 ms 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5204 KB Output is correct
11 Correct 4 ms 5204 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 3 ms 5204 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 4 ms 4948 KB Output is correct
16 Correct 3 ms 5076 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 2 ms 5076 KB Output is correct
21 Correct 3 ms 5204 KB Output is correct
22 Correct 5 ms 5288 KB Output is correct
23 Correct 3 ms 5204 KB Output is correct
24 Correct 3 ms 5204 KB Output is correct
25 Correct 4 ms 5192 KB Output is correct
26 Correct 3 ms 5204 KB Output is correct
27 Correct 3 ms 5332 KB Output is correct
28 Correct 4 ms 5076 KB Output is correct
29 Correct 3 ms 5204 KB Output is correct
30 Correct 3 ms 5204 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 2 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 4 ms 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5204 KB Output is correct
11 Correct 4 ms 5204 KB Output is correct
12 Correct 212 ms 25476 KB Output is correct
13 Correct 225 ms 33012 KB Output is correct
14 Correct 192 ms 19172 KB Output is correct
15 Correct 181 ms 19068 KB Output is correct
16 Correct 176 ms 19164 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 3 ms 5204 KB Output is correct
19 Correct 3 ms 4948 KB Output is correct
20 Correct 4 ms 4948 KB Output is correct
21 Correct 3 ms 5076 KB Output is correct
22 Correct 3 ms 5076 KB Output is correct
23 Correct 3 ms 5076 KB Output is correct
24 Correct 3 ms 5076 KB Output is correct
25 Correct 2 ms 5076 KB Output is correct
26 Correct 3 ms 5204 KB Output is correct
27 Correct 5 ms 5288 KB Output is correct
28 Correct 3 ms 5204 KB Output is correct
29 Correct 3 ms 5204 KB Output is correct
30 Correct 4 ms 5192 KB Output is correct
31 Correct 3 ms 5204 KB Output is correct
32 Correct 3 ms 5332 KB Output is correct
33 Correct 4 ms 5076 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 3 ms 5204 KB Output is correct
36 Correct 213 ms 25532 KB Output is correct
37 Correct 212 ms 33072 KB Output is correct
38 Correct 157 ms 19388 KB Output is correct
39 Correct 176 ms 19128 KB Output is correct
40 Correct 207 ms 19060 KB Output is correct
41 Correct 232 ms 29472 KB Output is correct
42 Correct 192 ms 30604 KB Output is correct
43 Correct 145 ms 17608 KB Output is correct
44 Correct 221 ms 19136 KB Output is correct
45 Correct 176 ms 19096 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 5204 KB Output is correct
3 Correct 2 ms 4948 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 2 ms 5076 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 2 ms 5076 KB Output is correct
10 Correct 2 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 2 ms 5076 KB Output is correct
13 Correct 3 ms 5076 KB Output is correct
14 Correct 4 ms 5204 KB Output is correct
15 Correct 4 ms 5332 KB Output is correct
16 Correct 3 ms 5204 KB Output is correct
17 Correct 3 ms 5204 KB Output is correct
18 Correct 4 ms 5204 KB Output is correct
19 Correct 212 ms 25476 KB Output is correct
20 Correct 225 ms 33012 KB Output is correct
21 Correct 192 ms 19172 KB Output is correct
22 Correct 181 ms 19068 KB Output is correct
23 Correct 176 ms 19164 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 3 ms 5204 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 4 ms 4948 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 3 ms 5076 KB Output is correct
31 Correct 3 ms 5076 KB Output is correct
32 Correct 2 ms 5076 KB Output is correct
33 Correct 3 ms 5204 KB Output is correct
34 Correct 5 ms 5288 KB Output is correct
35 Correct 3 ms 5204 KB Output is correct
36 Correct 3 ms 5204 KB Output is correct
37 Correct 4 ms 5192 KB Output is correct
38 Correct 3 ms 5204 KB Output is correct
39 Correct 3 ms 5332 KB Output is correct
40 Correct 4 ms 5076 KB Output is correct
41 Correct 3 ms 5204 KB Output is correct
42 Correct 3 ms 5204 KB Output is correct
43 Correct 213 ms 25532 KB Output is correct
44 Correct 212 ms 33072 KB Output is correct
45 Correct 157 ms 19388 KB Output is correct
46 Correct 176 ms 19128 KB Output is correct
47 Correct 207 ms 19060 KB Output is correct
48 Correct 232 ms 29472 KB Output is correct
49 Correct 192 ms 30604 KB Output is correct
50 Correct 145 ms 17608 KB Output is correct
51 Correct 221 ms 19136 KB Output is correct
52 Correct 176 ms 19096 KB Output is correct
53 Correct 207 ms 33024 KB Output is correct
54 Correct 212 ms 30268 KB Output is correct
55 Correct 114 ms 16332 KB Output is correct
56 Correct 189 ms 25548 KB Output is correct
57 Correct 184 ms 19204 KB Output is correct
58 Correct 162 ms 19276 KB Output is correct
59 Correct 211 ms 19140 KB Output is correct
60 Correct 180 ms 19096 KB Output is correct