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Submission #590827

# Submission time Handle Problem Language Result Execution time Memory
590827 2022-07-06T12:01:52 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 258 ms 32844 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];
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;
    }

    groupDfs(1);
    for(int i=1; i<=n; i++){
        canWin[i] = dfs(lim+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(lim+i, 0);
        else dfsFind(lim+i, 1);
    }
    for(int i=1; i<=n; i++){
        link[i][0].clear();
        link[i][0].shrink_to_fit();
        link[i][1].clear();
        link[i][1].shrink_to_fit();
    }

    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[lim+i][0])) % MOD;

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

            multiplier.mat[0][1] = (multiplier.mat[0][1] + n) % MOD;
            multiplier.mat[1][1] = (multiplier.mat[1][1] + n - find1[lim+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[lim+1][0])) % MOD;
    }
    else ans = Lsum * find1[lim+1][1] % MOD;

    printf("%lld", ans);
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:125:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  125 |     scanf("%d %lld", &n, &k);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:129:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  129 |         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 4 ms 5280 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 2 ms 5012 KB Output is correct
3 Correct 2 ms 4948 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 3 ms 5076 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 5012 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct
6 Correct 3 ms 5064 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 5012 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct
6 Correct 3 ms 5064 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 4 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 3 ms 5012 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct
6 Correct 3 ms 5064 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 4 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 240 ms 25336 KB Output is correct
13 Correct 249 ms 32788 KB Output is correct
14 Correct 156 ms 19056 KB Output is correct
15 Correct 221 ms 19000 KB Output is correct
16 Correct 206 ms 19072 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 5012 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct
6 Correct 3 ms 5064 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 4 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 3 ms 5012 KB Output is correct
16 Correct 4 ms 5076 KB Output is correct
17 Correct 4 ms 5076 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 3 ms 5076 KB Output is correct
20 Correct 3 ms 5076 KB Output is correct
21 Correct 4 ms 5204 KB Output is correct
22 Correct 4 ms 5272 KB Output is correct
23 Correct 4 ms 5144 KB Output is correct
24 Correct 4 ms 5168 KB Output is correct
25 Correct 5 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 5076 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 4 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 3 ms 5012 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 ms 5076 KB Output is correct
5 Correct 3 ms 5076 KB Output is correct
6 Correct 3 ms 5064 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 4 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 240 ms 25336 KB Output is correct
13 Correct 249 ms 32788 KB Output is correct
14 Correct 156 ms 19056 KB Output is correct
15 Correct 221 ms 19000 KB Output is correct
16 Correct 206 ms 19072 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 3 ms 5012 KB Output is correct
21 Correct 4 ms 5076 KB Output is correct
22 Correct 4 ms 5076 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 4 ms 5204 KB Output is correct
27 Correct 4 ms 5272 KB Output is correct
28 Correct 4 ms 5144 KB Output is correct
29 Correct 4 ms 5168 KB Output is correct
30 Correct 5 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 5076 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 4 ms 5204 KB Output is correct
36 Correct 224 ms 25216 KB Output is correct
37 Correct 257 ms 32796 KB Output is correct
38 Correct 148 ms 19060 KB Output is correct
39 Correct 197 ms 18976 KB Output is correct
40 Correct 204 ms 18968 KB Output is correct
41 Correct 245 ms 29276 KB Output is correct
42 Correct 198 ms 30408 KB Output is correct
43 Correct 128 ms 17368 KB Output is correct
44 Correct 201 ms 18996 KB Output is correct
45 Correct 201 ms 18996 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 4 ms 5280 KB Output is correct
3 Correct 3 ms 4948 KB Output is correct
4 Correct 2 ms 5012 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 5076 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 3 ms 5012 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 3 ms 5076 KB Output is correct
13 Correct 3 ms 5064 KB Output is correct
14 Correct 3 ms 5204 KB Output is correct
15 Correct 4 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 240 ms 25336 KB Output is correct
20 Correct 249 ms 32788 KB Output is correct
21 Correct 156 ms 19056 KB Output is correct
22 Correct 221 ms 19000 KB Output is correct
23 Correct 206 ms 19072 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 3 ms 5012 KB Output is correct
28 Correct 4 ms 5076 KB Output is correct
29 Correct 4 ms 5076 KB Output is correct
30 Correct 3 ms 5076 KB Output is correct
31 Correct 3 ms 5076 KB Output is correct
32 Correct 3 ms 5076 KB Output is correct
33 Correct 4 ms 5204 KB Output is correct
34 Correct 4 ms 5272 KB Output is correct
35 Correct 4 ms 5144 KB Output is correct
36 Correct 4 ms 5168 KB Output is correct
37 Correct 5 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 5076 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 4 ms 5204 KB Output is correct
43 Correct 224 ms 25216 KB Output is correct
44 Correct 257 ms 32796 KB Output is correct
45 Correct 148 ms 19060 KB Output is correct
46 Correct 197 ms 18976 KB Output is correct
47 Correct 204 ms 18968 KB Output is correct
48 Correct 245 ms 29276 KB Output is correct
49 Correct 198 ms 30408 KB Output is correct
50 Correct 128 ms 17368 KB Output is correct
51 Correct 201 ms 18996 KB Output is correct
52 Correct 201 ms 18996 KB Output is correct
53 Correct 258 ms 32844 KB Output is correct
54 Correct 244 ms 30072 KB Output is correct
55 Correct 137 ms 16184 KB Output is correct
56 Correct 234 ms 25316 KB Output is correct
57 Correct 182 ms 19132 KB Output is correct
58 Correct 171 ms 19064 KB Output is correct
59 Correct 192 ms 18996 KB Output is correct
60 Correct 217 ms 19000 KB Output is correct