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Submission #585821

# Submission time Handle Problem Language Result Execution time Memory
585821 2022-06-29T11:38:20 Z 79brue Star Trek (CEOI20_startrek) C++17
50 / 100
 32 ms 8320 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;
}

ll n;
ll k;
vector<int> link[1002];
ll mat[1002][1002];
ll depth[1002];
ll group[1002], groupCnt[2];
ll ans;

ll DP[2][1002];
ll find1[1002], find2[1002];

void dfs(int x, int p, int r){
    if(r==1){
        group[x] = depth[x]%2;
        groupCnt[group[x]]++;
    }
    for(auto y: link[x]){
        if(y==p) continue;
        depth[y] = depth[x] + 1;
        dfs(y, x, r);
        if(!mat[r][y]) mat[r][x] = 1;
    }
}

int dfsFind(int x, int p, int dp, int r){ /// 무조건 지나야 하는 상대 차례 점 개수 찾기
    if(dp % 2 == 0){ /// my turn
        int cnt = 0;
        for(auto y: link[x]){
            if(y!=p && !mat[r][y]) cnt++;
        }
        if(cnt > 1) return 0;
        assert(cnt == 1);
        for(auto y: link[x]){
            if(y!=p && !mat[r][y]) return dfsFind(y, x, dp+1, r);
        }
        exit(1);
    }
    else{ /// your turn
        int ret = 1;
        for(auto y: link[x]){
            if(y==p) continue;
            ret += dfsFind(y, x, dp+1, r);
        }
        return ret;
    }
}

int dfsFind2(int x, int p, int dp, int r){
    if(dp % 2 == 0){ /// my turn
        int ret = 1;
        for(auto y: link[x]){
            if(y==p) continue;
            ret += dfsFind2(y, x, dp+1, r);
        }
        return ret;
    }
    else{ /// your turn
        int cnt = 0;
        for(auto y: link[x]){
            if(y!=p && !mat[r][y]) cnt++;
        }
        if(cnt > 1) return 0;
        assert(cnt == 1);
        for(auto y: link[x]){
            if(y!=p && !mat[r][y]) return dfsFind2(y, x, dp+1, r);
        }
        exit(1);
    }
}

int main(){
    scanf("%lld %lld", &n, &k);
    for(int i=1; i<n; i++){
        int x, y;
        scanf("%d %d", &x, &y);
        link[x].push_back(y);
        link[y].push_back(x);
    }
//    for(int i=n; i>=1; i--){
//        for(int x=0; x<=n+1; x++) depth[x] = DP[x] = 0;
//        dfs(i), DProot[i] = DP[i];
//    }
//    for(int i=1; i<=n; i++) printf("%d ", DProot[i]);

    for(int i=1; i<=n; i++){
        dfs(i, -1, i);
        if(mat[i][i]) find1[i] = groupCnt[!group[i]] - dfsFind(i, -1, 0, i);
        else find2[i] = dfsFind2(i, -1, 0, i);
        DP[0][i] = mat[i][i];
    }

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

            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - groupCnt[group[i]] - find1[i] + MOD)%MOD;
        }
        else{
            multiplier.mat[1][0] = (multiplier.mat[1][0] + find2[i]) % MOD;

            multiplier.mat[0][1] = (multiplier.mat[0][1] + n) % MOD;
            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - find2[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(mat[1][1]){
        ans = (Wsum * n + groupCnt[group[1]] * Lsum + find1[1] * Lsum) % MOD;
    }
    else ans = find2[1] * Lsum % MOD;

//        int b = turn%2;
//
//        /// 전처리
//        ll Wsum = 0; /// 이기는 가짓수
//        for(int i=1; i<=n; i++) Wsum = (Wsum + DP[!b][i]) % MOD;
//        ll Lsum = (mpow(n, 2*turn-1) - Wsum + MOD) % MOD; /// 지는 가짓수
//
//        /// 실제 계산
//        for(int i=1; i<=n; i++){
//            DP[b][i] = 0;
//            if(mat[i][i]){ /// 여기서 시작하면 이기는 경우
//                /// ? -> W
//                DP[b][i] = (DP[b][i] + Wsum * n) % MOD;
//                /// my turn -> L
//                DP[b][i] = (DP[b][i] + groupCnt[group[i]] * Lsum) % MOD;
//                /// your turn -> L
//                DP[b][i] = (DP[b][i] + find1[i] * Lsum) % MOD;
//            }
//            else{
//                DP[b][i] = (DP[b][i] + find2[i] * Lsum) % MOD;
//            }
//        }
//    }

    printf("%lld", ans);
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:123:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  123 |     scanf("%lld %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~~~
startrek.cpp:126:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  126 |         scanf("%d %d", &x, &y);
      |         ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 17 ms 8148 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 0 ms 340 KB Output is correct
5 Correct 0 ms 332 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 724 KB Output is correct
3 Correct 1 ms 840 KB Output is correct
4 Correct 1 ms 724 KB Output is correct
5 Correct 1 ms 724 KB Output is correct
6 Correct 1 ms 724 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 724 KB Output is correct
3 Correct 1 ms 840 KB Output is correct
4 Correct 1 ms 724 KB Output is correct
5 Correct 1 ms 724 KB Output is correct
6 Correct 1 ms 724 KB Output is correct
7 Correct 24 ms 8200 KB Output is correct
8 Correct 32 ms 8228 KB Output is correct
9 Correct 19 ms 8148 KB Output is correct
10 Correct 22 ms 8196 KB Output is correct
11 Correct 24 ms 8188 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 724 KB Output is correct
3 Correct 1 ms 840 KB Output is correct
4 Correct 1 ms 724 KB Output is correct
5 Correct 1 ms 724 KB Output is correct
6 Correct 1 ms 724 KB Output is correct
7 Correct 24 ms 8200 KB Output is correct
8 Correct 32 ms 8228 KB Output is correct
9 Correct 19 ms 8148 KB Output is correct
10 Correct 22 ms 8196 KB Output is correct
11 Correct 24 ms 8188 KB Output is correct
12 Runtime error 1 ms 468 KB Execution killed with signal 11
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 724 KB Output is correct
3 Correct 1 ms 840 KB Output is correct
4 Correct 1 ms 724 KB Output is correct
5 Correct 1 ms 724 KB Output is correct
6 Correct 1 ms 724 KB Output is correct
7 Correct 24 ms 8200 KB Output is correct
8 Correct 32 ms 8228 KB Output is correct
9 Correct 19 ms 8148 KB Output is correct
10 Correct 22 ms 8196 KB Output is correct
11 Correct 24 ms 8188 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 17 ms 8160 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 724 KB Output is correct
17 Correct 1 ms 848 KB Output is correct
18 Correct 1 ms 724 KB Output is correct
19 Correct 2 ms 724 KB Output is correct
20 Correct 1 ms 724 KB Output is correct
21 Correct 27 ms 8272 KB Output is correct
22 Correct 31 ms 8216 KB Output is correct
23 Correct 20 ms 8180 KB Output is correct
24 Correct 18 ms 8140 KB Output is correct
25 Correct 24 ms 8152 KB Output is correct
26 Correct 19 ms 8240 KB Output is correct
27 Correct 29 ms 8320 KB Output is correct
28 Correct 12 ms 6612 KB Output is correct
29 Correct 19 ms 8140 KB Output is correct
30 Correct 22 ms 8176 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 724 KB Output is correct
3 Correct 1 ms 840 KB Output is correct
4 Correct 1 ms 724 KB Output is correct
5 Correct 1 ms 724 KB Output is correct
6 Correct 1 ms 724 KB Output is correct
7 Correct 24 ms 8200 KB Output is correct
8 Correct 32 ms 8228 KB Output is correct
9 Correct 19 ms 8148 KB Output is correct
10 Correct 22 ms 8196 KB Output is correct
11 Correct 24 ms 8188 KB Output is correct
12 Runtime error 1 ms 468 KB Execution killed with signal 11
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 17 ms 8148 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 340 KB Output is correct
9 Correct 1 ms 724 KB Output is correct
10 Correct 1 ms 840 KB Output is correct
11 Correct 1 ms 724 KB Output is correct
12 Correct 1 ms 724 KB Output is correct
13 Correct 1 ms 724 KB Output is correct
14 Correct 24 ms 8200 KB Output is correct
15 Correct 32 ms 8228 KB Output is correct
16 Correct 19 ms 8148 KB Output is correct
17 Correct 22 ms 8196 KB Output is correct
18 Correct 24 ms 8188 KB Output is correct
19 Runtime error 1 ms 468 KB Execution killed with signal 11
20 Halted 0 ms 0 KB -