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Submission #588743

# Submission time Handle Problem Language Result Execution time Memory
588743 2022-07-04T02:23:42 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 296 ms 40836 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];

int group[400002], groupCnt[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 find1[400002][2];
int findV[100002][2];
bool findChk[400002][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 + findV[x][1] - ((pe>lim || !findChk[pe^1][0]) ? 0 : find1[pe^1][0]);
        vector<int> v;
        for(auto y: link[x][2]){
            if((y^1)==pe) v.push_back(y);
            else{
                int tmp = dfsFind(y, !dp);
                ret += tmp, findV[x][1] += tmp;
            }
        }
        link[x][2].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[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: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 7380 KB Output is correct
2 Correct 5 ms 7508 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 5 ms 7380 KB Output is correct
3 Correct 4 ms 7416 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

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 4 ms 7468 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 4 ms 7468 KB Output is correct
7 Correct 4 ms 7636 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7508 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 4 ms 7468 KB Output is correct
7 Correct 4 ms 7636 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7508 KB Output is correct
12 Correct 236 ms 32028 KB Output is correct
13 Correct 296 ms 39620 KB Output is correct
14 Correct 176 ms 25756 KB Output is correct
15 Correct 207 ms 25656 KB Output is correct
16 Correct 240 ms 25712 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 4 ms 7468 KB Output is correct
7 Correct 4 ms 7636 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7508 KB Output is correct
12 Correct 4 ms 7380 KB Output is correct
13 Correct 4 ms 7508 KB Output is correct
14 Correct 3 ms 7380 KB Output is correct
15 Correct 3 ms 7380 KB Output is correct
16 Correct 3 ms 7380 KB Output is correct
17 Correct 5 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 5 ms 7636 KB Output is correct
22 Correct 5 ms 7636 KB Output is correct
23 Correct 4 ms 7508 KB Output is correct
24 Correct 4 ms 7508 KB Output is correct
25 Correct 4 ms 7508 KB Output is correct
26 Correct 5 ms 7636 KB Output is correct
27 Correct 4 ms 7636 KB Output is correct
28 Correct 4 ms 7580 KB Output is correct
29 Correct 5 ms 7508 KB Output is correct
30 Correct 4 ms 7508 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 4 ms 7380 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct
6 Correct 4 ms 7468 KB Output is correct
7 Correct 4 ms 7636 KB Output is correct
8 Correct 4 ms 7636 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 5 ms 7508 KB Output is correct
11 Correct 4 ms 7508 KB Output is correct
12 Correct 236 ms 32028 KB Output is correct
13 Correct 296 ms 39620 KB Output is correct
14 Correct 176 ms 25756 KB Output is correct
15 Correct 207 ms 25656 KB Output is correct
16 Correct 240 ms 25712 KB Output is correct
17 Correct 4 ms 7380 KB Output is correct
18 Correct 4 ms 7508 KB Output is correct
19 Correct 3 ms 7380 KB Output is correct
20 Correct 3 ms 7380 KB Output is correct
21 Correct 3 ms 7380 KB Output is correct
22 Correct 5 ms 7380 KB Output is correct
23 Correct 4 ms 7380 KB Output is correct
24 Correct 4 ms 7380 KB Output is correct
25 Correct 4 ms 7380 KB Output is correct
26 Correct 5 ms 7636 KB Output is correct
27 Correct 5 ms 7636 KB Output is correct
28 Correct 4 ms 7508 KB Output is correct
29 Correct 4 ms 7508 KB Output is correct
30 Correct 4 ms 7508 KB Output is correct
31 Correct 5 ms 7636 KB Output is correct
32 Correct 4 ms 7636 KB Output is correct
33 Correct 4 ms 7580 KB Output is correct
34 Correct 5 ms 7508 KB Output is correct
35 Correct 4 ms 7508 KB Output is correct
36 Correct 267 ms 33260 KB Output is correct
37 Correct 252 ms 40744 KB Output is correct
38 Correct 203 ms 26668 KB Output is correct
39 Correct 222 ms 26888 KB Output is correct
40 Correct 224 ms 26972 KB Output is correct
41 Correct 289 ms 37136 KB Output is correct
42 Correct 223 ms 37816 KB Output is correct
43 Correct 144 ms 24432 KB Output is correct
44 Correct 208 ms 26804 KB Output is correct
45 Correct 224 ms 26832 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 7380 KB Output is correct
2 Correct 5 ms 7508 KB Output is correct
3 Correct 4 ms 7380 KB Output is correct
4 Correct 5 ms 7380 KB Output is correct
5 Correct 4 ms 7416 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 7380 KB Output is correct
11 Correct 4 ms 7380 KB Output is correct
12 Correct 4 ms 7380 KB Output is correct
13 Correct 4 ms 7468 KB Output is correct
14 Correct 4 ms 7636 KB Output is correct
15 Correct 4 ms 7636 KB Output is correct
16 Correct 4 ms 7508 KB Output is correct
17 Correct 5 ms 7508 KB Output is correct
18 Correct 4 ms 7508 KB Output is correct
19 Correct 236 ms 32028 KB Output is correct
20 Correct 296 ms 39620 KB Output is correct
21 Correct 176 ms 25756 KB Output is correct
22 Correct 207 ms 25656 KB Output is correct
23 Correct 240 ms 25712 KB Output is correct
24 Correct 4 ms 7380 KB Output is correct
25 Correct 4 ms 7508 KB Output is correct
26 Correct 3 ms 7380 KB Output is correct
27 Correct 3 ms 7380 KB Output is correct
28 Correct 3 ms 7380 KB Output is correct
29 Correct 5 ms 7380 KB Output is correct
30 Correct 4 ms 7380 KB Output is correct
31 Correct 4 ms 7380 KB Output is correct
32 Correct 4 ms 7380 KB Output is correct
33 Correct 5 ms 7636 KB Output is correct
34 Correct 5 ms 7636 KB Output is correct
35 Correct 4 ms 7508 KB Output is correct
36 Correct 4 ms 7508 KB Output is correct
37 Correct 4 ms 7508 KB Output is correct
38 Correct 5 ms 7636 KB Output is correct
39 Correct 4 ms 7636 KB Output is correct
40 Correct 4 ms 7580 KB Output is correct
41 Correct 5 ms 7508 KB Output is correct
42 Correct 4 ms 7508 KB Output is correct
43 Correct 267 ms 33260 KB Output is correct
44 Correct 252 ms 40744 KB Output is correct
45 Correct 203 ms 26668 KB Output is correct
46 Correct 222 ms 26888 KB Output is correct
47 Correct 224 ms 26972 KB Output is correct
48 Correct 289 ms 37136 KB Output is correct
49 Correct 223 ms 37816 KB Output is correct
50 Correct 144 ms 24432 KB Output is correct
51 Correct 208 ms 26804 KB Output is correct
52 Correct 224 ms 26832 KB Output is correct
53 Correct 255 ms 40836 KB Output is correct
54 Correct 253 ms 38044 KB Output is correct
55 Correct 137 ms 22864 KB Output is correct
56 Correct 227 ms 33420 KB Output is correct
57 Correct 211 ms 27144 KB Output is correct
58 Correct 204 ms 26924 KB Output is correct
59 Correct 240 ms 26844 KB Output is correct
60 Correct 238 ms 26828 KB Output is correct