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답안 #588742

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
588742 2022-07-04T02:22:22 Z 79brue Star Trek (CEOI20_startrek) C++17
45 / 100
 248 ms 39588 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][2] - (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);
      |         ~~~~~^~~~~~~~~~~~~~~~~
startrek.cpp: In function 'int dfsFind(int, bool)':
startrek.cpp:111:33: warning: array subscript 2 is above array bounds of 'int [2]' [-Warray-bounds]
  111 |         int ret = 1 + findV[x][2] - (pe>lim || !findChk[pe^1][0] ? 0 : find1[pe^1][0]);
      |                       ~~~~~~~~~~^

Subtask #1
0.0 / 0.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Incorrect 4 ms 7508 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 3 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 4 ms 7416 KB Output is correct
4 Correct 4 ms 7424 KB Output is correct
5 Correct 4 ms 7380 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 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 7344 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 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 7344 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 4 ms 7672 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 4 ms 7508 KB Output is correct
11 Correct 4 ms 7568 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 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 7344 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 4 ms 7672 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 4 ms 7508 KB Output is correct
11 Correct 4 ms 7568 KB Output is correct
12 Correct 231 ms 32044 KB Output is correct
13 Correct 248 ms 39588 KB Output is correct
14 Correct 162 ms 25704 KB Output is correct
15 Correct 216 ms 27012 KB Output is correct
16 Correct 195 ms 26856 KB Output is correct

Subtask #6
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 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 7344 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 4 ms 7672 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 4 ms 7508 KB Output is correct
11 Correct 4 ms 7568 KB Output is correct
12 Correct 4 ms 7380 KB Output is correct
13 Incorrect 5 ms 7508 KB Output isn't correct
14 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Correct 4 ms 7380 KB Output is correct
3 Correct 5 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 7344 KB Output is correct
7 Correct 5 ms 7636 KB Output is correct
8 Correct 4 ms 7672 KB Output is correct
9 Correct 4 ms 7508 KB Output is correct
10 Correct 4 ms 7508 KB Output is correct
11 Correct 4 ms 7568 KB Output is correct
12 Correct 231 ms 32044 KB Output is correct
13 Correct 248 ms 39588 KB Output is correct
14 Correct 162 ms 25704 KB Output is correct
15 Correct 216 ms 27012 KB Output is correct
16 Correct 195 ms 26856 KB Output is correct
17 Correct 4 ms 7380 KB Output is correct
18 Incorrect 5 ms 7508 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 4 ms 7380 KB Output is correct
2 Incorrect 4 ms 7508 KB Output isn't correct
3 Halted 0 ms 0 KB -