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답안 #588749

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
588749 2022-07-04T02:32:17 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 222 ms 34124 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];
bitset<400002> mat;
int ey[400002];
int parEdge[100002];
bitset<100002> canWin;
bitset<400002> dfsChk;

int group[100002], groupCnt[2];
int res[100002];
ll ans;

bitset<100002> groupVisited;
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=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++) 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

# 결과 실행 시간 메모리 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

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 3 ms 5012 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 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 4948 KB Output is correct
5 Correct 5 ms 4948 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 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 4948 KB Output is correct
5 Correct 5 ms 4948 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 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 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 4948 KB Output is correct
5 Correct 5 ms 4948 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 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 214 ms 25848 KB Output is correct
13 Correct 212 ms 34124 KB Output is correct
14 Correct 187 ms 18680 KB Output is correct
15 Correct 192 ms 18652 KB Output is correct
16 Correct 174 ms 18640 KB Output is correct

Subtask #6
20.0 / 20.0

# 결과 실행 시간 메모리 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 4948 KB Output is correct
5 Correct 5 ms 4948 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 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 3 ms 4992 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 3 ms 4948 KB Output is correct
19 Correct 3 ms 4948 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 4 ms 5220 KB Output is correct
22 Correct 3 ms 5332 KB Output is correct
23 Correct 4 ms 5204 KB Output is correct
24 Correct 3 ms 5204 KB Output is correct
25 Correct 3 ms 5204 KB Output is correct
26 Correct 4 ms 5204 KB Output is correct
27 Correct 3 ms 5332 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 4 ms 5076 KB Output is correct

Subtask #7
20.0 / 20.0

# 결과 실행 시간 메모리 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 4948 KB Output is correct
5 Correct 5 ms 4948 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 5332 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5076 KB Output is correct
12 Correct 214 ms 25848 KB Output is correct
13 Correct 212 ms 34124 KB Output is correct
14 Correct 187 ms 18680 KB Output is correct
15 Correct 192 ms 18652 KB Output is correct
16 Correct 174 ms 18640 KB Output is correct
17 Correct 3 ms 4992 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 3 ms 4948 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 3 ms 4948 KB Output is correct
26 Correct 4 ms 5220 KB Output is correct
27 Correct 3 ms 5332 KB Output is correct
28 Correct 4 ms 5204 KB Output is correct
29 Correct 3 ms 5204 KB Output is correct
30 Correct 3 ms 5204 KB Output is correct
31 Correct 4 ms 5204 KB Output is correct
32 Correct 3 ms 5332 KB Output is correct
33 Correct 3 ms 5076 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 4 ms 5076 KB Output is correct
36 Correct 197 ms 25768 KB Output is correct
37 Correct 222 ms 34096 KB Output is correct
38 Correct 145 ms 18704 KB Output is correct
39 Correct 198 ms 18640 KB Output is correct
40 Correct 186 ms 18576 KB Output is correct
41 Correct 215 ms 30088 KB Output is correct
42 Correct 201 ms 31748 KB Output is correct
43 Correct 146 ms 17104 KB Output is correct
44 Correct 174 ms 18652 KB Output is correct
45 Correct 171 ms 18636 KB Output is correct

Subtask #8
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 3 ms 5076 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5012 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 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 4948 KB Output is correct
12 Correct 5 ms 4948 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 5332 KB Output is correct
16 Correct 3 ms 5204 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 4 ms 5076 KB Output is correct
19 Correct 214 ms 25848 KB Output is correct
20 Correct 212 ms 34124 KB Output is correct
21 Correct 187 ms 18680 KB Output is correct
22 Correct 192 ms 18652 KB Output is correct
23 Correct 174 ms 18640 KB Output is correct
24 Correct 3 ms 4992 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 3 ms 4948 KB Output is correct
31 Correct 3 ms 4948 KB Output is correct
32 Correct 3 ms 4948 KB Output is correct
33 Correct 4 ms 5220 KB Output is correct
34 Correct 3 ms 5332 KB Output is correct
35 Correct 4 ms 5204 KB Output is correct
36 Correct 3 ms 5204 KB Output is correct
37 Correct 3 ms 5204 KB Output is correct
38 Correct 4 ms 5204 KB Output is correct
39 Correct 3 ms 5332 KB Output is correct
40 Correct 3 ms 5076 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 4 ms 5076 KB Output is correct
43 Correct 197 ms 25768 KB Output is correct
44 Correct 222 ms 34096 KB Output is correct
45 Correct 145 ms 18704 KB Output is correct
46 Correct 198 ms 18640 KB Output is correct
47 Correct 186 ms 18576 KB Output is correct
48 Correct 215 ms 30088 KB Output is correct
49 Correct 201 ms 31748 KB Output is correct
50 Correct 146 ms 17104 KB Output is correct
51 Correct 174 ms 18652 KB Output is correct
52 Correct 171 ms 18636 KB Output is correct
53 Correct 222 ms 34092 KB Output is correct
54 Correct 206 ms 30896 KB Output is correct
55 Correct 106 ms 16028 KB Output is correct
56 Correct 199 ms 25812 KB Output is correct
57 Correct 163 ms 18784 KB Output is correct
58 Correct 181 ms 18788 KB Output is correct
59 Correct 201 ms 18720 KB Output is correct
60 Correct 158 ms 18636 KB Output is correct