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Submission #588750

# Submission time Handle Problem Language Result Execution time Memory
588750 2022-07-04T02:35:31 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 254 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[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=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 2 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 2 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 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 3 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 4972 KB Output is correct
5 Correct 3 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 3 ms 5076 KB Output is correct
4 Correct 3 ms 4972 KB Output is correct
5 Correct 3 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 3 ms 5128 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 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 3 ms 5076 KB Output is correct
4 Correct 3 ms 4972 KB Output is correct
5 Correct 3 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 3 ms 5128 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 204 ms 24196 KB Output is correct
13 Correct 207 ms 31820 KB Output is correct
14 Correct 186 ms 17876 KB Output is correct
15 Correct 196 ms 17960 KB Output is correct
16 Correct 181 ms 17824 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 3 ms 5076 KB Output is correct
4 Correct 3 ms 4972 KB Output is correct
5 Correct 3 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 3 ms 5128 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 4 ms 4948 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 3 ms 5076 KB Output is correct
18 Correct 2 ms 5076 KB Output is correct
19 Correct 2 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 3 ms 5204 KB Output is correct
23 Correct 4 ms 5076 KB Output is correct
24 Correct 5 ms 5076 KB Output is correct
25 Correct 3 ms 5076 KB Output is correct
26 Correct 4 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 3 ms 5076 KB Output is correct
30 Correct 3 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 3 ms 5076 KB Output is correct
4 Correct 3 ms 4972 KB Output is correct
5 Correct 3 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 3 ms 5128 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 204 ms 24196 KB Output is correct
13 Correct 207 ms 31820 KB Output is correct
14 Correct 186 ms 17876 KB Output is correct
15 Correct 196 ms 17960 KB Output is correct
16 Correct 181 ms 17824 KB Output is correct
17 Correct 4 ms 4948 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 3 ms 5076 KB Output is correct
23 Correct 2 ms 5076 KB Output is correct
24 Correct 2 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 3 ms 5204 KB Output is correct
28 Correct 4 ms 5076 KB Output is correct
29 Correct 5 ms 5076 KB Output is correct
30 Correct 3 ms 5076 KB Output is correct
31 Correct 4 ms 5204 KB Output is correct
32 Correct 3 ms 5204 KB Output is correct
33 Correct 3 ms 5076 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 201 ms 24372 KB Output is correct
37 Correct 215 ms 31756 KB Output is correct
38 Correct 158 ms 17892 KB Output is correct
39 Correct 175 ms 17776 KB Output is correct
40 Correct 166 ms 17784 KB Output is correct
41 Correct 247 ms 28296 KB Output is correct
42 Correct 195 ms 29488 KB Output is correct
43 Correct 125 ms 16392 KB Output is correct
44 Correct 210 ms 17884 KB Output is correct
45 Correct 173 ms 17772 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 3 ms 5076 KB Output is correct
3 Correct 2 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 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 3 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 4972 KB Output is correct
12 Correct 3 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 3 ms 5128 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 204 ms 24196 KB Output is correct
20 Correct 207 ms 31820 KB Output is correct
21 Correct 186 ms 17876 KB Output is correct
22 Correct 196 ms 17960 KB Output is correct
23 Correct 181 ms 17824 KB Output is correct
24 Correct 4 ms 4948 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 3 ms 5076 KB Output is correct
30 Correct 2 ms 5076 KB Output is correct
31 Correct 2 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 3 ms 5204 KB Output is correct
35 Correct 4 ms 5076 KB Output is correct
36 Correct 5 ms 5076 KB Output is correct
37 Correct 3 ms 5076 KB Output is correct
38 Correct 4 ms 5204 KB Output is correct
39 Correct 3 ms 5204 KB Output is correct
40 Correct 3 ms 5076 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 3 ms 5076 KB Output is correct
43 Correct 201 ms 24372 KB Output is correct
44 Correct 215 ms 31756 KB Output is correct
45 Correct 158 ms 17892 KB Output is correct
46 Correct 175 ms 17776 KB Output is correct
47 Correct 166 ms 17784 KB Output is correct
48 Correct 247 ms 28296 KB Output is correct
49 Correct 195 ms 29488 KB Output is correct
50 Correct 125 ms 16392 KB Output is correct
51 Correct 210 ms 17884 KB Output is correct
52 Correct 173 ms 17772 KB Output is correct
53 Correct 225 ms 31728 KB Output is correct
54 Correct 254 ms 29052 KB Output is correct
55 Correct 110 ms 15392 KB Output is correct
56 Correct 235 ms 24424 KB Output is correct
57 Correct 193 ms 17936 KB Output is correct
58 Correct 168 ms 17960 KB Output is correct
59 Correct 175 ms 17864 KB Output is correct
60 Correct 210 ms 17868 KB Output is correct