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답안 #588741

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
588741 2022-07-04T02:18:06 Z 79brue Star Trek (CEOI20_startrek) C++17
50 / 100
 1000 ms 38864 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][3];
bool mat[400002];
int ey[400002];
int parEdge[100002];
bool canWin[400002];
bool dfsChk[400002], findChk[400002][2];

int group[400002], groupCnt[2];
int find1[400002][2];
int res[400002];
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 findV[100002][2];
int dfsFind(int pe, bool dp){ /// 무조건 지나야 하는 상대 차례 점 개수 찾기
    if(findChk[pe][dp]) return find1[pe][dp];
    int x = ey[pe];
    findChk[pe][dp] = 1;
    if(!dp){ /// my turn
        int cnt = 0;
        for(auto y: link[x][1]){
            if((y^1)!=pe && !mat[y]) cnt++;
        }
        if(cnt > 1) return find1[pe][dp] = 0;
        assert(cnt == 1);
        for(auto y: link[x][1]){
            if((y^1)!=pe && !mat[y]) return find1[pe][dp] = dfsFind(y, !dp);
        }
        exit(1);
    }
    else{ /// your turn
        int ret = 1;
        for(auto y: link[x][2]){
            if((y^1)==pe) continue;
            ret += dfsFind(y, !dp);
        }
        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[x][2].push_back(i*2-2);
        link[y][0].push_back(i*2-1);
        link[y][1].push_back(i*2-1);
        link[y][2].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++){
        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:121:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  121 |     scanf("%d %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:125:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  125 |         scanf("%d %d", &x, &y);
      |         ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7508 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7412 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 3 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7344 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct
5 Correct 5 ms 7392 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7344 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct
5 Correct 5 ms 7392 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 6 ms 7636 KB Output is correct
9 Correct 7 ms 7588 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7504 KB Output is correct

Subtask #5
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7344 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct
5 Correct 5 ms 7392 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 6 ms 7636 KB Output is correct
9 Correct 7 ms 7588 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7504 KB Output is correct
12 Correct 218 ms 31292 KB Output is correct
13 Correct 254 ms 38864 KB Output is correct
14 Execution timed out 1086 ms 23164 KB Time limit exceeded
15 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7344 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct
5 Correct 5 ms 7392 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 6 ms 7636 KB Output is correct
9 Correct 7 ms 7588 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7504 KB Output is correct
12 Correct 4 ms 7380 KB Output is correct
13 Correct 4 ms 7508 KB Output is correct
14 Correct 4 ms 7380 KB Output is correct
15 Correct 4 ms 7380 KB Output is correct
16 Correct 4 ms 7380 KB Output is correct
17 Correct 4 ms 7380 KB Output is correct
18 Correct 4 ms 7380 KB Output is correct
19 Correct 4 ms 7380 KB Output is correct
20 Correct 4 ms 7380 KB Output is correct
21 Correct 4 ms 7636 KB Output is correct
22 Correct 6 ms 7636 KB Output is correct
23 Correct 5 ms 7508 KB Output is correct
24 Correct 4 ms 7508 KB Output is correct
25 Correct 5 ms 7508 KB Output is correct
26 Correct 5 ms 7508 KB Output is correct
27 Correct 6 ms 7636 KB Output is correct
28 Correct 5 ms 7504 KB Output is correct
29 Correct 5 ms 7508 KB Output is correct
30 Correct 7 ms 7508 KB Output is correct

Subtask #7
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7344 KB Output is correct
4 Correct 3 ms 7380 KB Output is correct
5 Correct 5 ms 7392 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 6 ms 7636 KB Output is correct
9 Correct 7 ms 7588 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7504 KB Output is correct
12 Correct 218 ms 31292 KB Output is correct
13 Correct 254 ms 38864 KB Output is correct
14 Execution timed out 1086 ms 23164 KB Time limit exceeded
15 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7508 KB Output is correct
3 Correct 4 ms 7412 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 3 ms 7380 KB Output is correct
6 Correct 4 ms 7380 KB Output is correct
7 Correct 4 ms 7380 KB Output is correct
8 Correct 4 ms 7380 KB Output is correct
9 Correct 4 ms 7380 KB Output is correct
10 Correct 4 ms 7344 KB Output is correct
11 Correct 3 ms 7380 KB Output is correct
12 Correct 5 ms 7392 KB Output is correct
13 Correct 4 ms 7380 KB Output is correct
14 Correct 5 ms 7636 KB Output is correct
15 Correct 6 ms 7636 KB Output is correct
16 Correct 7 ms 7588 KB Output is correct
17 Correct 5 ms 7508 KB Output is correct
18 Correct 4 ms 7504 KB Output is correct
19 Correct 218 ms 31292 KB Output is correct
20 Correct 254 ms 38864 KB Output is correct
21 Execution timed out 1086 ms 23164 KB Time limit exceeded
22 Halted 0 ms 0 KB -