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Submission #588746

# Submission time Handle Problem Language Result Execution time Memory
588746 2022-07-04T02:26:46 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 269 ms 34224 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];
bool dfsChk[400002];

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 3 ms 4948 KB Output is correct
2 Correct 4 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 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 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 4 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 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 4 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 5332 KB Output is correct
9 Correct 4 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5148 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 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 4 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 5332 KB Output is correct
9 Correct 4 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5148 KB Output is correct
12 Correct 201 ms 26516 KB Output is correct
13 Correct 267 ms 34144 KB Output is correct
14 Correct 211 ms 20316 KB Output is correct
15 Correct 185 ms 20160 KB Output is correct
16 Correct 197 ms 20096 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 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 4 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 5332 KB Output is correct
9 Correct 4 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5148 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 4 ms 5204 KB Output is correct
14 Correct 3 ms 4948 KB Output is correct
15 Correct 3 ms 4948 KB Output is correct
16 Correct 2 ms 4948 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 2 ms 4948 KB Output is correct
21 Correct 4 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 4 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 3 ms 4948 KB Output is correct
2 Correct 3 ms 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 4 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 5332 KB Output is correct
9 Correct 4 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 ms 5148 KB Output is correct
12 Correct 201 ms 26516 KB Output is correct
13 Correct 267 ms 34144 KB Output is correct
14 Correct 211 ms 20316 KB Output is correct
15 Correct 185 ms 20160 KB Output is correct
16 Correct 197 ms 20096 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 4 ms 5204 KB Output is correct
19 Correct 3 ms 4948 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 2 ms 4948 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 2 ms 4948 KB Output is correct
26 Correct 4 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 4 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 269 ms 26560 KB Output is correct
37 Correct 218 ms 34036 KB Output is correct
38 Correct 160 ms 20244 KB Output is correct
39 Correct 204 ms 20100 KB Output is correct
40 Correct 185 ms 20152 KB Output is correct
41 Correct 203 ms 30488 KB Output is correct
42 Correct 190 ms 31516 KB Output is correct
43 Correct 179 ms 18468 KB Output is correct
44 Correct 180 ms 20080 KB Output is correct
45 Correct 230 ms 20188 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 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 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 4948 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 4 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 5332 KB Output is correct
16 Correct 4 ms 5204 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 4 ms 5148 KB Output is correct
19 Correct 201 ms 26516 KB Output is correct
20 Correct 267 ms 34144 KB Output is correct
21 Correct 211 ms 20316 KB Output is correct
22 Correct 185 ms 20160 KB Output is correct
23 Correct 197 ms 20096 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 4 ms 5204 KB Output is correct
26 Correct 3 ms 4948 KB Output is correct
27 Correct 3 ms 4948 KB Output is correct
28 Correct 2 ms 4948 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 2 ms 4948 KB Output is correct
33 Correct 4 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 4 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 269 ms 26560 KB Output is correct
44 Correct 218 ms 34036 KB Output is correct
45 Correct 160 ms 20244 KB Output is correct
46 Correct 204 ms 20100 KB Output is correct
47 Correct 185 ms 20152 KB Output is correct
48 Correct 203 ms 30488 KB Output is correct
49 Correct 190 ms 31516 KB Output is correct
50 Correct 179 ms 18468 KB Output is correct
51 Correct 180 ms 20080 KB Output is correct
52 Correct 230 ms 20188 KB Output is correct
53 Correct 254 ms 34224 KB Output is correct
54 Correct 208 ms 31264 KB Output is correct
55 Correct 126 ms 17228 KB Output is correct
56 Correct 244 ms 26552 KB Output is correct
57 Correct 171 ms 20320 KB Output is correct
58 Correct 181 ms 20236 KB Output is correct
59 Correct 198 ms 20156 KB Output is correct
60 Correct 228 ms 20128 KB Output is correct