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Submission #588754

# Submission time Handle Problem Language Result Execution time Memory
588754 2022-07-04T02:41:46 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 267 ms 32020 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++){
        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 2 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 3 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 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 4 ms 5076 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 3 ms 5016 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 4 ms 5076 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 3 ms 5016 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5204 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 4948 KB Output is correct
3 Correct 4 ms 5076 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 3 ms 5016 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 213 ms 24628 KB Output is correct
13 Correct 267 ms 31972 KB Output is correct
14 Correct 148 ms 18188 KB Output is correct
15 Correct 206 ms 18164 KB Output is correct
16 Correct 196 ms 18228 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 4 ms 5076 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 3 ms 5016 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 4 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 3 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 2 ms 4948 KB Output is correct
21 Correct 3 ms 5204 KB Output is correct
22 Correct 3 ms 5204 KB Output is correct
23 Correct 3 ms 5076 KB Output is correct
24 Correct 4 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 5204 KB Output is correct
28 Correct 3 ms 5076 KB Output is correct
29 Correct 3 ms 5076 KB Output is correct
30 Correct 5 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 4948 KB Output is correct
3 Correct 4 ms 5076 KB Output is correct
4 Correct 3 ms 4948 KB Output is correct
5 Correct 4 ms 4948 KB Output is correct
6 Correct 3 ms 5016 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5204 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5076 KB Output is correct
12 Correct 213 ms 24628 KB Output is correct
13 Correct 267 ms 31972 KB Output is correct
14 Correct 148 ms 18188 KB Output is correct
15 Correct 206 ms 18164 KB Output is correct
16 Correct 196 ms 18228 KB Output is correct
17 Correct 4 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 3 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 2 ms 4948 KB Output is correct
26 Correct 3 ms 5204 KB Output is correct
27 Correct 3 ms 5204 KB Output is correct
28 Correct 3 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 5204 KB Output is correct
32 Correct 3 ms 5204 KB Output is correct
33 Correct 3 ms 5076 KB Output is correct
34 Correct 3 ms 5076 KB Output is correct
35 Correct 5 ms 5076 KB Output is correct
36 Correct 195 ms 24620 KB Output is correct
37 Correct 227 ms 32020 KB Output is correct
38 Correct 165 ms 18236 KB Output is correct
39 Correct 177 ms 18152 KB Output is correct
40 Correct 177 ms 18312 KB Output is correct
41 Correct 232 ms 28632 KB Output is correct
42 Correct 190 ms 29756 KB Output is correct
43 Correct 134 ms 16800 KB Output is correct
44 Correct 191 ms 18156 KB Output is correct
45 Correct 167 ms 18180 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 5076 KB Output is correct
3 Correct 3 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 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 4 ms 5076 KB Output is correct
11 Correct 3 ms 4948 KB Output is correct
12 Correct 4 ms 4948 KB Output is correct
13 Correct 3 ms 5016 KB Output is correct
14 Correct 3 ms 5204 KB Output is correct
15 Correct 3 ms 5204 KB Output is correct
16 Correct 3 ms 5204 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 3 ms 5076 KB Output is correct
19 Correct 213 ms 24628 KB Output is correct
20 Correct 267 ms 31972 KB Output is correct
21 Correct 148 ms 18188 KB Output is correct
22 Correct 206 ms 18164 KB Output is correct
23 Correct 196 ms 18228 KB Output is correct
24 Correct 4 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 3 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 2 ms 4948 KB Output is correct
33 Correct 3 ms 5204 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 4 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 5204 KB Output is correct
40 Correct 3 ms 5076 KB Output is correct
41 Correct 3 ms 5076 KB Output is correct
42 Correct 5 ms 5076 KB Output is correct
43 Correct 195 ms 24620 KB Output is correct
44 Correct 227 ms 32020 KB Output is correct
45 Correct 165 ms 18236 KB Output is correct
46 Correct 177 ms 18152 KB Output is correct
47 Correct 177 ms 18312 KB Output is correct
48 Correct 232 ms 28632 KB Output is correct
49 Correct 190 ms 29756 KB Output is correct
50 Correct 134 ms 16800 KB Output is correct
51 Correct 191 ms 18156 KB Output is correct
52 Correct 167 ms 18180 KB Output is correct
53 Correct 227 ms 31984 KB Output is correct
54 Correct 215 ms 29252 KB Output is correct
55 Correct 108 ms 15584 KB Output is correct
56 Correct 208 ms 24656 KB Output is correct
57 Correct 184 ms 18260 KB Output is correct
58 Correct 160 ms 18340 KB Output is correct
59 Correct 207 ms 18192 KB Output is correct
60 Correct 190 ms 18164 KB Output is correct