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답안 #588745

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
588745 2022-07-04T02:25:46 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 270 ms 34408 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];
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][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[pe^1][0]) ? 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 4 ms 4948 KB Output is correct
2 Correct 4 ms 5204 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 3 ms 4948 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct

Subtask #3
8.0 / 8.0

# 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 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 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 2 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 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 5 ms 5332 KB Output is correct
9 Correct 4 ms 5180 KB Output is correct
10 Correct 5 ms 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct

Subtask #5
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 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 5 ms 5332 KB Output is correct
9 Correct 4 ms 5180 KB Output is correct
10 Correct 5 ms 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct
12 Correct 215 ms 26612 KB Output is correct
13 Correct 232 ms 34120 KB Output is correct
14 Correct 206 ms 20264 KB Output is correct
15 Correct 213 ms 20172 KB Output is correct
16 Correct 177 ms 20156 KB Output is correct

Subtask #6
20.0 / 20.0

# 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 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 5 ms 5332 KB Output is correct
9 Correct 4 ms 5180 KB Output is correct
10 Correct 5 ms 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 3 ms 5204 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 5076 KB Output is correct
19 Correct 4 ms 4992 KB Output is correct
20 Correct 3 ms 5076 KB Output is correct
21 Correct 3 ms 5272 KB Output is correct
22 Correct 3 ms 5332 KB Output is correct
23 Correct 3 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 3 ms 5204 KB Output is correct
27 Correct 4 ms 5332 KB Output is correct
28 Correct 4 ms 5204 KB Output is correct
29 Correct 4 ms 5204 KB Output is correct
30 Correct 3 ms 5204 KB Output is correct

Subtask #7
20.0 / 20.0

# 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 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 2 ms 5076 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 5 ms 5332 KB Output is correct
9 Correct 4 ms 5180 KB Output is correct
10 Correct 5 ms 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct
12 Correct 215 ms 26612 KB Output is correct
13 Correct 232 ms 34120 KB Output is correct
14 Correct 206 ms 20264 KB Output is correct
15 Correct 213 ms 20172 KB Output is correct
16 Correct 177 ms 20156 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 3 ms 5204 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 5076 KB Output is correct
24 Correct 4 ms 4992 KB Output is correct
25 Correct 3 ms 5076 KB Output is correct
26 Correct 3 ms 5272 KB Output is correct
27 Correct 3 ms 5332 KB Output is correct
28 Correct 3 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 3 ms 5204 KB Output is correct
32 Correct 4 ms 5332 KB Output is correct
33 Correct 4 ms 5204 KB Output is correct
34 Correct 4 ms 5204 KB Output is correct
35 Correct 3 ms 5204 KB Output is correct
36 Correct 259 ms 26920 KB Output is correct
37 Correct 245 ms 34408 KB Output is correct
38 Correct 188 ms 20316 KB Output is correct
39 Correct 221 ms 20308 KB Output is correct
40 Correct 205 ms 20424 KB Output is correct
41 Correct 246 ms 30648 KB Output is correct
42 Correct 215 ms 31820 KB Output is correct
43 Correct 162 ms 18684 KB Output is correct
44 Correct 190 ms 20300 KB Output is correct
45 Correct 180 ms 20232 KB Output is correct

Subtask #8
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 4948 KB Output is correct
2 Correct 4 ms 5204 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 2 ms 5076 KB Output is correct
8 Correct 2 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 5076 KB Output is correct
12 Correct 2 ms 5076 KB Output is correct
13 Correct 3 ms 5076 KB Output is correct
14 Correct 3 ms 5204 KB Output is correct
15 Correct 5 ms 5332 KB Output is correct
16 Correct 4 ms 5180 KB Output is correct
17 Correct 5 ms 5204 KB Output is correct
18 Correct 3 ms 5204 KB Output is correct
19 Correct 215 ms 26612 KB Output is correct
20 Correct 232 ms 34120 KB Output is correct
21 Correct 206 ms 20264 KB Output is correct
22 Correct 213 ms 20172 KB Output is correct
23 Correct 177 ms 20156 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 3 ms 5204 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 5076 KB Output is correct
31 Correct 4 ms 4992 KB Output is correct
32 Correct 3 ms 5076 KB Output is correct
33 Correct 3 ms 5272 KB Output is correct
34 Correct 3 ms 5332 KB Output is correct
35 Correct 3 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 3 ms 5204 KB Output is correct
39 Correct 4 ms 5332 KB Output is correct
40 Correct 4 ms 5204 KB Output is correct
41 Correct 4 ms 5204 KB Output is correct
42 Correct 3 ms 5204 KB Output is correct
43 Correct 259 ms 26920 KB Output is correct
44 Correct 245 ms 34408 KB Output is correct
45 Correct 188 ms 20316 KB Output is correct
46 Correct 221 ms 20308 KB Output is correct
47 Correct 205 ms 20424 KB Output is correct
48 Correct 246 ms 30648 KB Output is correct
49 Correct 215 ms 31820 KB Output is correct
50 Correct 162 ms 18684 KB Output is correct
51 Correct 190 ms 20300 KB Output is correct
52 Correct 180 ms 20232 KB Output is correct
53 Correct 270 ms 34256 KB Output is correct
54 Correct 232 ms 31428 KB Output is correct
55 Correct 116 ms 17412 KB Output is correct
56 Correct 227 ms 26700 KB Output is correct
57 Correct 179 ms 20428 KB Output is correct
58 Correct 219 ms 20380 KB Output is correct
59 Correct 221 ms 20248 KB Output is correct
60 Correct 189 ms 20348 KB Output is correct