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Submission #588756

# Submission time Handle Problem Language Result Execution time Memory
588756 2022-07-04T02:50:05 Z 79brue Star Trek (CEOI20_startrek) C++17
100 / 100
 260 ms 31692 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);
    }

    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 2 ms 4948 KB Output is correct
2 Correct 4 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 4 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 3 ms 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 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 3 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 4 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 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 3 ms 5076 KB Output is correct
4 Correct 3 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 4 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 5076 KB Output is correct
12 Correct 260 ms 24124 KB Output is correct
13 Correct 212 ms 31676 KB Output is correct
14 Correct 173 ms 18036 KB Output is correct
15 Correct 213 ms 17928 KB Output is correct
16 Correct 165 ms 17808 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 3 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 4 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 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 3 ms 4948 KB Output is correct
15 Correct 3 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 3 ms 4948 KB Output is correct
20 Correct 3 ms 4948 KB Output is correct
21 Correct 4 ms 5204 KB Output is correct
22 Correct 3 ms 5204 KB Output is correct
23 Correct 4 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 5076 KB Output is correct
29 Correct 3 ms 5204 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 4948 KB Output is correct
3 Correct 3 ms 5076 KB Output is correct
4 Correct 3 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 4 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 5076 KB Output is correct
12 Correct 260 ms 24124 KB Output is correct
13 Correct 212 ms 31676 KB Output is correct
14 Correct 173 ms 18036 KB Output is correct
15 Correct 213 ms 17928 KB Output is correct
16 Correct 165 ms 17808 KB Output is correct
17 Correct 2 ms 4948 KB Output is correct
18 Correct 3 ms 5076 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 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 3 ms 4948 KB Output is correct
25 Correct 3 ms 4948 KB Output is correct
26 Correct 4 ms 5204 KB Output is correct
27 Correct 3 ms 5204 KB Output is correct
28 Correct 4 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 5076 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 3 ms 5076 KB Output is correct
36 Correct 221 ms 24156 KB Output is correct
37 Correct 209 ms 31692 KB Output is correct
38 Correct 149 ms 18096 KB Output is correct
39 Correct 181 ms 17740 KB Output is correct
40 Correct 194 ms 17792 KB Output is correct
41 Correct 202 ms 28108 KB Output is correct
42 Correct 197 ms 29384 KB Output is correct
43 Correct 141 ms 16552 KB Output is correct
44 Correct 173 ms 17720 KB Output is correct
45 Correct 193 ms 17840 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 4 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 4 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 3 ms 4948 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 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 4 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 5076 KB Output is correct
19 Correct 260 ms 24124 KB Output is correct
20 Correct 212 ms 31676 KB Output is correct
21 Correct 173 ms 18036 KB Output is correct
22 Correct 213 ms 17928 KB Output is correct
23 Correct 165 ms 17808 KB Output is correct
24 Correct 2 ms 4948 KB Output is correct
25 Correct 3 ms 5076 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 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 3 ms 4948 KB Output is correct
32 Correct 3 ms 4948 KB Output is correct
33 Correct 4 ms 5204 KB Output is correct
34 Correct 3 ms 5204 KB Output is correct
35 Correct 4 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 5076 KB Output is correct
41 Correct 3 ms 5204 KB Output is correct
42 Correct 3 ms 5076 KB Output is correct
43 Correct 221 ms 24156 KB Output is correct
44 Correct 209 ms 31692 KB Output is correct
45 Correct 149 ms 18096 KB Output is correct
46 Correct 181 ms 17740 KB Output is correct
47 Correct 194 ms 17792 KB Output is correct
48 Correct 202 ms 28108 KB Output is correct
49 Correct 197 ms 29384 KB Output is correct
50 Correct 141 ms 16552 KB Output is correct
51 Correct 173 ms 17720 KB Output is correct
52 Correct 193 ms 17840 KB Output is correct
53 Correct 217 ms 31672 KB Output is correct
54 Correct 215 ms 28896 KB Output is correct
55 Correct 131 ms 15404 KB Output is correct
56 Correct 205 ms 24140 KB Output is correct
57 Correct 166 ms 17864 KB Output is correct
58 Correct 169 ms 18028 KB Output is correct
59 Correct 184 ms 17908 KB Output is correct
60 Correct 167 ms 17844 KB Output is correct