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Submission #588751

# Submission time Handle Problem Language Result Execution time Memory
588751 2022-07-04T02:35:58 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 242 ms 31820 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[300002];
int ey[300002];
int parEdge[100002];
bool canWin[100002];
bitset<300002> 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[300002][2];
int findV[100002][2];
bitset<300002> 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=1; i<=n; i++){
        ey[lim+i] = i;
        parEdge[i] = lim+i;
    }

    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 3 ms 5076 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 4948 KB Output is correct
3 Correct 2 ms 4948 KB Output is correct
4 Correct 2 ms 5076 KB Output is correct
5 Correct 3 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 3 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 4 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 3 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 4 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 4 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 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 3 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 4 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 4 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 206 ms 24368 KB Output is correct
13 Correct 215 ms 31708 KB Output is correct
14 Correct 175 ms 17852 KB Output is correct
15 Correct 203 ms 17752 KB Output is correct
16 Correct 170 ms 17740 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 3 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 4 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 4 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 4 ms 5076 KB Output is correct
13 Correct 3 ms 5076 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 3 ms 4948 KB Output is correct
16 Correct 3 ms 5076 KB Output is correct
17 Correct 4 ms 5036 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 3 ms 5076 KB Output is correct
21 Correct 3 ms 5204 KB Output is correct
22 Correct 3 ms 5204 KB Output is correct
23 Correct 3 ms 5076 KB Output is correct
24 Correct 4 ms 5076 KB Output is correct
25 Correct 3 ms 5076 KB Output is correct
26 Correct 3 ms 5204 KB Output is correct
27 Correct 3 ms 5332 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 4 ms 5076 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 3 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 4 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 4 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 206 ms 24368 KB Output is correct
13 Correct 215 ms 31708 KB Output is correct
14 Correct 175 ms 17852 KB Output is correct
15 Correct 203 ms 17752 KB Output is correct
16 Correct 170 ms 17740 KB Output is correct
17 Correct 4 ms 5076 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 3 ms 4948 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 3 ms 5076 KB Output is correct
22 Correct 4 ms 5036 KB Output is correct
23 Correct 3 ms 5076 KB Output is correct
24 Correct 3 ms 5076 KB Output is correct
25 Correct 3 ms 5076 KB Output is correct
26 Correct 3 ms 5204 KB Output is correct
27 Correct 3 ms 5204 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 4 ms 5076 KB Output is correct
30 Correct 3 ms 5076 KB Output is correct
31 Correct 3 ms 5204 KB Output is correct
32 Correct 3 ms 5332 KB Output is correct
33 Correct 3 ms 5076 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 4 ms 5076 KB Output is correct
36 Correct 223 ms 24240 KB Output is correct
37 Correct 212 ms 31820 KB Output is correct
38 Correct 161 ms 17868 KB Output is correct
39 Correct 208 ms 17736 KB Output is correct
40 Correct 163 ms 17808 KB Output is correct
41 Correct 211 ms 28276 KB Output is correct
42 Correct 212 ms 29372 KB Output is correct
43 Correct 129 ms 16412 KB Output is correct
44 Correct 171 ms 17808 KB Output is correct
45 Correct 187 ms 17792 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 3 ms 5076 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct
6 Correct 2 ms 5076 KB Output is correct
7 Correct 3 ms 5076 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 3 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 4 ms 5076 KB Output is correct
13 Correct 3 ms 5076 KB Output is correct
14 Correct 3 ms 5204 KB Output is correct
15 Correct 3 ms 5204 KB Output is correct
16 Correct 4 ms 5076 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 4 ms 5076 KB Output is correct
19 Correct 206 ms 24368 KB Output is correct
20 Correct 215 ms 31708 KB Output is correct
21 Correct 175 ms 17852 KB Output is correct
22 Correct 203 ms 17752 KB Output is correct
23 Correct 170 ms 17740 KB Output is correct
24 Correct 4 ms 5076 KB Output is correct
25 Correct 3 ms 5076 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 3 ms 4948 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 4 ms 5036 KB Output is correct
30 Correct 3 ms 5076 KB Output is correct
31 Correct 3 ms 5076 KB Output is correct
32 Correct 3 ms 5076 KB Output is correct
33 Correct 3 ms 5204 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 4 ms 5076 KB Output is correct
37 Correct 3 ms 5076 KB Output is correct
38 Correct 3 ms 5204 KB Output is correct
39 Correct 3 ms 5332 KB Output is correct
40 Correct 3 ms 5076 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 4 ms 5076 KB Output is correct
43 Correct 223 ms 24240 KB Output is correct
44 Correct 212 ms 31820 KB Output is correct
45 Correct 161 ms 17868 KB Output is correct
46 Correct 208 ms 17736 KB Output is correct
47 Correct 163 ms 17808 KB Output is correct
48 Correct 211 ms 28276 KB Output is correct
49 Correct 212 ms 29372 KB Output is correct
50 Correct 129 ms 16412 KB Output is correct
51 Correct 171 ms 17808 KB Output is correct
52 Correct 187 ms 17792 KB Output is correct
53 Correct 242 ms 31788 KB Output is correct
54 Correct 212 ms 28960 KB Output is correct
55 Correct 124 ms 15404 KB Output is correct
56 Correct 187 ms 24268 KB Output is correct
57 Correct 185 ms 17996 KB Output is correct
58 Correct 196 ms 17912 KB Output is correct
59 Correct 193 ms 17864 KB Output is correct
60 Correct 193 ms 17916 KB Output is correct