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Submission #588747

# Submission time Handle Problem Language Result Execution time Memory
588747 2022-07-04T02:29:33 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 225 ms 33836 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[100002];
bitset<400002> dfsChk;

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

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 3 ms 5204 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 4948 KB Output is correct
3 Correct 2 ms 4948 KB Output is correct
4 Correct 2 ms 5056 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 2 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 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 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 2 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 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 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct
12 Correct 206 ms 26256 KB Output is correct
13 Correct 225 ms 33796 KB Output is correct
14 Correct 147 ms 19896 KB Output is correct
15 Correct 172 ms 19788 KB Output is correct
16 Correct 161 ms 19788 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 2 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 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 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 2 ms 4948 KB Output is correct
16 Correct 3 ms 4948 KB Output is correct
17 Correct 2 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 3 ms 5204 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 3 ms 5332 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 3 ms 5204 KB Output is correct
30 Correct 3 ms 5204 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 2 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 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 5204 KB Output is correct
11 Correct 3 ms 5204 KB Output is correct
12 Correct 206 ms 26256 KB Output is correct
13 Correct 225 ms 33796 KB Output is correct
14 Correct 147 ms 19896 KB Output is correct
15 Correct 172 ms 19788 KB Output is correct
16 Correct 161 ms 19788 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 2 ms 4948 KB Output is correct
21 Correct 3 ms 4948 KB Output is correct
22 Correct 2 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 3 ms 5204 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 3 ms 5332 KB Output is correct
33 Correct 3 ms 5076 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 3 ms 5204 KB Output is correct
36 Correct 207 ms 26268 KB Output is correct
37 Correct 211 ms 33760 KB Output is correct
38 Correct 146 ms 19796 KB Output is correct
39 Correct 182 ms 19780 KB Output is correct
40 Correct 168 ms 19816 KB Output is correct
41 Correct 204 ms 30156 KB Output is correct
42 Correct 189 ms 31280 KB Output is correct
43 Correct 124 ms 18148 KB Output is correct
44 Correct 171 ms 19740 KB Output is correct
45 Correct 176 ms 19804 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4948 KB Output is correct
2 Correct 3 ms 5204 KB Output is correct
3 Correct 2 ms 4948 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct
6 Correct 2 ms 5056 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 2 ms 4948 KB Output is correct
9 Correct 2 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 2 ms 4948 KB Output is correct
12 Correct 3 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 5204 KB Output is correct
18 Correct 3 ms 5204 KB Output is correct
19 Correct 206 ms 26256 KB Output is correct
20 Correct 225 ms 33796 KB Output is correct
21 Correct 147 ms 19896 KB Output is correct
22 Correct 172 ms 19788 KB Output is correct
23 Correct 161 ms 19788 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 2 ms 4948 KB Output is correct
28 Correct 3 ms 4948 KB Output is correct
29 Correct 2 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 3 ms 5204 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 3 ms 5332 KB Output is correct
40 Correct 3 ms 5076 KB Output is correct
41 Correct 3 ms 5204 KB Output is correct
42 Correct 3 ms 5204 KB Output is correct
43 Correct 207 ms 26268 KB Output is correct
44 Correct 211 ms 33760 KB Output is correct
45 Correct 146 ms 19796 KB Output is correct
46 Correct 182 ms 19780 KB Output is correct
47 Correct 168 ms 19816 KB Output is correct
48 Correct 204 ms 30156 KB Output is correct
49 Correct 189 ms 31280 KB Output is correct
50 Correct 124 ms 18148 KB Output is correct
51 Correct 171 ms 19740 KB Output is correct
52 Correct 176 ms 19804 KB Output is correct
53 Correct 223 ms 33836 KB Output is correct
54 Correct 203 ms 30952 KB Output is correct
55 Correct 109 ms 17004 KB Output is correct
56 Correct 177 ms 26304 KB Output is correct
57 Correct 165 ms 19896 KB Output is correct
58 Correct 158 ms 19916 KB Output is correct
59 Correct 180 ms 19812 KB Output is correct
60 Correct 170 ms 19860 KB Output is correct