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Submission #588755

# Submission time Handle Problem Language Result Execution time Memory
588755 2022-07-04T02:48:50 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 231 ms 32084 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];
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++){
        link[i][0].shrink_to_fit();
        link[i][1].shrink_to_fit();
    }
    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]) dfsFind(parEdge[i], 0);
        else 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] + (groupCnt[!group[i]] - find1[parEdge[i]][0])) % MOD;

            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - groupCnt[group[i]] - (groupCnt[!group[i]] - find1[parEdge[i]][0]) + MOD)%MOD;
        }
        else{
            multiplier.mat[1][0] = (multiplier.mat[1][0] + find1[parEdge[i]][1]) % MOD;

            multiplier.mat[0][1] = (multiplier.mat[0][1] + n) % MOD;
            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - find1[parEdge[i]][1]) % 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 * (groupCnt[!group[1]] - find1[parEdge[1]][0])) % MOD;
    }
    else ans = Lsum * find1[parEdge[1]][1] % MOD;

    printf("%lld", ans);
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:126:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  126 |     scanf("%d %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:130:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  130 |         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 5076 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 3 ms 4948 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 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 2 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 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 3 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 4948 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 3 ms 5204 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

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory 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 2 ms 4948 KB Output is correct
5 Correct 3 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 3 ms 5204 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 217 ms 24560 KB Output is correct
13 Correct 211 ms 32016 KB Output is correct
14 Correct 153 ms 18492 KB Output is correct
15 Correct 177 ms 18188 KB Output is correct
16 Correct 165 ms 18140 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 3 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 4948 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 3 ms 5204 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 4948 KB Output is correct
13 Correct 3 ms 5076 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 4948 KB Output is correct
19 Correct 2 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 5260 KB Output is correct
23 Correct 3 ms 5076 KB Output is correct
24 Correct 3 ms 5076 KB Output is correct
25 Correct 3 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 5084 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 3 ms 5076 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 3 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 4948 KB Output is correct
7 Correct 4 ms 5204 KB Output is correct
8 Correct 3 ms 5204 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 217 ms 24560 KB Output is correct
13 Correct 211 ms 32016 KB Output is correct
14 Correct 153 ms 18492 KB Output is correct
15 Correct 177 ms 18188 KB Output is correct
16 Correct 165 ms 18140 KB Output is correct
17 Correct 2 ms 4948 KB Output is correct
18 Correct 3 ms 5076 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 4948 KB Output is correct
24 Correct 2 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 5260 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 3 ms 5204 KB Output is correct
32 Correct 3 ms 5332 KB Output is correct
33 Correct 3 ms 5084 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 213 ms 24572 KB Output is correct
37 Correct 231 ms 32084 KB Output is correct
38 Correct 148 ms 18432 KB Output is correct
39 Correct 179 ms 18188 KB Output is correct
40 Correct 168 ms 18276 KB Output is correct
41 Correct 201 ms 28492 KB Output is correct
42 Correct 186 ms 29836 KB Output is correct
43 Correct 126 ms 16868 KB Output is correct
44 Correct 175 ms 18120 KB Output is correct
45 Correct 167 ms 18200 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 5076 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 3 ms 4948 KB Output is correct
7 Correct 2 ms 4948 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 2 ms 4948 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Correct 4 ms 5204 KB Output is correct
15 Correct 3 ms 5204 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 217 ms 24560 KB Output is correct
20 Correct 211 ms 32016 KB Output is correct
21 Correct 153 ms 18492 KB Output is correct
22 Correct 177 ms 18188 KB Output is correct
23 Correct 165 ms 18140 KB Output is correct
24 Correct 2 ms 4948 KB Output is correct
25 Correct 3 ms 5076 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 4948 KB Output is correct
31 Correct 2 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 5260 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 3 ms 5076 KB Output is correct
37 Correct 3 ms 5076 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 5084 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 3 ms 5076 KB Output is correct
43 Correct 213 ms 24572 KB Output is correct
44 Correct 231 ms 32084 KB Output is correct
45 Correct 148 ms 18432 KB Output is correct
46 Correct 179 ms 18188 KB Output is correct
47 Correct 168 ms 18276 KB Output is correct
48 Correct 201 ms 28492 KB Output is correct
49 Correct 186 ms 29836 KB Output is correct
50 Correct 126 ms 16868 KB Output is correct
51 Correct 175 ms 18120 KB Output is correct
52 Correct 167 ms 18200 KB Output is correct
53 Correct 215 ms 31976 KB Output is correct
54 Correct 207 ms 29420 KB Output is correct
55 Correct 109 ms 15796 KB Output is correct
56 Correct 183 ms 24552 KB Output is correct
57 Correct 163 ms 18304 KB Output is correct
58 Correct 167 ms 18364 KB Output is correct
59 Correct 187 ms 18204 KB Output is correct
60 Correct 171 ms 18160 KB Output is correct