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Submission #588419

# Submission time Handle Problem Language Result Execution time Memory
588419 2022-07-03T09:15:10 Z 79brue Star Trek (CEOI20_startrek) C++17
30 / 100
 1000 ms 22672 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;
ll k;
vector<int> link[100002];
bool mat[400002];
int ex[400002], 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;

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

bool dfs(int x, int pe){
    if(dfsChk[pe]) return mat[pe];
    dfsChk[pe] = 1;
    for(auto y: link[x]){
        if((y^pe)==1) continue;
        if(!dfs(ey[y], y)) mat[pe] = 1;
    }
    return mat[pe];
}

int dfsFind(int x, int pe, bool dp){ /// 무조건 지나야 하는 상대 차례 점 개수 찾기
    if(findChk[pe][dp]) return find1[pe][dp];
    findChk[pe][dp] = 1;
    if(!dp){ /// my turn
        int cnt = 0;
        for(auto y: link[x]){
            if((y^1)!=pe && !mat[y]) cnt++;
        }
        if(cnt > 1) return find1[pe][dp] = 0;
        assert(cnt == 1);
        for(auto y: link[x]){
            if((y^1)!=pe && !mat[y]) return find1[pe][dp] = dfsFind(ey[y], y, !dp);
        }
        exit(1);
    }
    else{ /// your turn
        int ret = 1;
        for(auto y: link[x]){
            if((y^1)==pe) continue;
            ret += dfsFind(ey[y], y, !dp);
        }
        return find1[pe][dp] = ret;
    }
}

int main(){
    scanf("%d %lld", &n, &k);
    for(int i=1; i<n; i++){
        int x, y;
        scanf("%d %d", &x, &y);
        link[x].push_back(i*2-2);
        link[y].push_back(i*2-1);
        ex[i*2-2] = x, ey[i*2-2] = y;
        ex[i*2-1] = y, ey[i*2-1] = x;
    }
    for(int i=n; i<n+n; i++){
        ex[i*2-2] = -1, ey[i*2-2] = i-n+1;
        ex[i*2-1] = i-n+1, ey[i*2-1] = -1;
        parEdge[i-n+1] = i*2-2;
    }

    groupDfs(1);
    for(int i=1; i<=n; i++){
        canWin[i] = dfs(i, parEdge[i]);
    }
    for(int i=1; i<=n; i++){
        if(canWin[i]) res[i] = groupCnt[!group[i]] - dfsFind(i, parEdge[i], 0);
        else res[i] = dfsFind(i, 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] + find1[i][0]) % 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:111:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  111 |     scanf("%d %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:114:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  114 |         scanf("%d %d", &x, &y);
      |         ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 2 ms 2772 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 1 ms 2644 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 4 ms 2840 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 4 ms 2840 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct
12 Correct 112 ms 18404 KB Output is correct
13 Correct 120 ms 22672 KB Output is correct
14 Execution timed out 1085 ms 10600 KB Time limit exceeded
15 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 4 ms 2840 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Incorrect 2 ms 2772 KB Output isn't correct
14 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 3 ms 2900 KB Output is correct
9 Correct 4 ms 2840 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct
12 Correct 112 ms 18404 KB Output is correct
13 Correct 120 ms 22672 KB Output is correct
14 Execution timed out 1085 ms 10600 KB Time limit exceeded
15 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 2 ms 2772 KB Output isn't correct
3 Halted 0 ms 0 KB -