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Submission #588753

# Submission time Handle Problem Language Result Execution time Memory
588753 2022-07-04T02:37:09 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 248 ms 32472 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[300002];
int ey[300002];
int parEdge[100002];
bool canWin[100002];
bool dfsChk[300002];

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[300002][2];
int findV[100002][2];
bool findChk[2][300002];
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=1; i<=n; i++){
        ey[lim+i] = i;
        parEdge[i] = lim+i;
    }

    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 3 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 3 ms 4948 KB Output is correct
4 Correct 2 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5044 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5024 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 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5044 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5024 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 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 4 ms 5204 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5044 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5024 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 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 4 ms 5204 KB Output is correct
12 Correct 229 ms 25008 KB Output is correct
13 Correct 208 ms 32472 KB Output is correct
14 Correct 150 ms 18592 KB Output is correct
15 Correct 231 ms 18508 KB Output is correct
16 Correct 209 ms 18628 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5044 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5024 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 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 4 ms 5204 KB Output is correct
12 Correct 2 ms 4948 KB Output is correct
13 Correct 3 ms 5204 KB Output is correct
14 Correct 2 ms 4948 KB Output is correct
15 Correct 2 ms 4948 KB Output is correct
16 Correct 2 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 4948 KB Output is correct
20 Correct 4 ms 5076 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 5216 KB Output is correct
24 Correct 4 ms 5204 KB Output is correct
25 Correct 3 ms 5204 KB Output is correct
26 Correct 3 ms 5184 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 3 ms 4948 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 3 ms 5044 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5024 KB Output is correct
6 Correct 3 ms 5076 KB Output is correct
7 Correct 4 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 4 ms 5204 KB Output is correct
12 Correct 229 ms 25008 KB Output is correct
13 Correct 208 ms 32472 KB Output is correct
14 Correct 150 ms 18592 KB Output is correct
15 Correct 231 ms 18508 KB Output is correct
16 Correct 209 ms 18628 KB Output is correct
17 Correct 2 ms 4948 KB Output is correct
18 Correct 3 ms 5204 KB Output is correct
19 Correct 2 ms 4948 KB Output is correct
20 Correct 2 ms 4948 KB Output is correct
21 Correct 2 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 4948 KB Output is correct
25 Correct 4 ms 5076 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 5216 KB Output is correct
29 Correct 4 ms 5204 KB Output is correct
30 Correct 3 ms 5204 KB Output is correct
31 Correct 3 ms 5184 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 202 ms 25016 KB Output is correct
37 Correct 248 ms 32436 KB Output is correct
38 Correct 209 ms 18708 KB Output is correct
39 Correct 185 ms 18512 KB Output is correct
40 Correct 183 ms 18660 KB Output is correct
41 Correct 237 ms 29088 KB Output is correct
42 Correct 199 ms 30088 KB Output is correct
43 Correct 140 ms 17108 KB Output is correct
44 Correct 187 ms 18632 KB Output is correct
45 Correct 164 ms 18600 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 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 3 ms 4948 KB Output is correct
6 Correct 2 ms 4948 KB Output is correct
7 Correct 3 ms 4948 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 2 ms 5076 KB Output is correct
10 Correct 3 ms 5044 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 3 ms 5024 KB Output is correct
13 Correct 3 ms 5076 KB Output is correct
14 Correct 4 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 4 ms 5204 KB Output is correct
19 Correct 229 ms 25008 KB Output is correct
20 Correct 208 ms 32472 KB Output is correct
21 Correct 150 ms 18592 KB Output is correct
22 Correct 231 ms 18508 KB Output is correct
23 Correct 209 ms 18628 KB Output is correct
24 Correct 2 ms 4948 KB Output is correct
25 Correct 3 ms 5204 KB Output is correct
26 Correct 2 ms 4948 KB Output is correct
27 Correct 2 ms 4948 KB Output is correct
28 Correct 2 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 4948 KB Output is correct
32 Correct 4 ms 5076 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 5216 KB Output is correct
36 Correct 4 ms 5204 KB Output is correct
37 Correct 3 ms 5204 KB Output is correct
38 Correct 3 ms 5184 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 202 ms 25016 KB Output is correct
44 Correct 248 ms 32436 KB Output is correct
45 Correct 209 ms 18708 KB Output is correct
46 Correct 185 ms 18512 KB Output is correct
47 Correct 183 ms 18660 KB Output is correct
48 Correct 237 ms 29088 KB Output is correct
49 Correct 199 ms 30088 KB Output is correct
50 Correct 140 ms 17108 KB Output is correct
51 Correct 187 ms 18632 KB Output is correct
52 Correct 164 ms 18600 KB Output is correct
53 Correct 221 ms 32376 KB Output is correct
54 Correct 240 ms 29644 KB Output is correct
55 Correct 114 ms 15924 KB Output is correct
56 Correct 178 ms 25036 KB Output is correct
57 Correct 204 ms 18788 KB Output is correct
58 Correct 167 ms 18740 KB Output is correct
59 Correct 196 ms 18532 KB Output is correct
60 Correct 197 ms 18644 KB Output is correct