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传递闭包问题

(a->b&&b->c)--->(a->c)

图的表示最好用邻接链表的方式。

floyd

这样做是超时的。

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;
const int MAXSIZE = 1005;
bool road[MAXSIZE][MAXSIZE];
int n, m;

int main() {
    memset(road, 0, sizeof(road));
    cin >> n >> m;
    int a, b;
    for (int i = 0; i < m; ++i) {
        cin >> a >> b;
        a--, b--;
        road[a][b] = true;
    }
    for (int i = 0; i < n; ++i) {
        road[i][i] = true;
    }
    // 求传递闭包
    for (int k = 0; k < n; ++k) {
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i == j || i == k || j == k) continue;
                if (road[i][k] && road[k][j]) {
                    road[i][j] = true;
                }
            }
        }
    }
    int ans = 0;
    for (int i = 0; i < n; ++i) {
        int sum = 0;
        for (int j = 0; j < n; ++j) {
            if (road[i][j] || road[j][i])
                sum++;
        }
        if (sum == n)
            ans++;
    }
    cout << ans << endl;
}

正反BFS仍然超时

#include 
#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;
const int MAXSIZE = 1010;
bool road[MAXSIZE][MAXSIZE];
bool fakeroad[MAXSIZE][MAXSIZE];
bool visit[MAXSIZE];
bool connect[MAXSIZE][MAXSIZE];
int n, m;
int main() {
//    freopen("../in.txt", "r", stdin);
    cin >> n >> m;
    int a, b;
    for (int i = 0; i < m; ++i) {
        cin >> a >> b;
        a--, b--;
        road[a][b] = true;
        fakeroad[b][a] = true;
    }
    queue<int> Q;
    for (int i = 0; i < n; ++i) {
        memset(visit, 0, sizeof(visit));
        visit[i] = true;
        Q.push(i);
        while (!Q.empty()){
            int temp = Q.front();
            Q.pop();
            for (int j = 0; j < n; ++j) {
                if (!visit[j]&&road[temp][j]){
                    visit[j] = true;
                    Q.push(j);
                    connect[i][j] = true;
                }
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        memset(visit, 0, sizeof(visit));
        visit[i] = true;
        Q.push(i);
        while (!Q.empty()){
            int temp = Q.front();
            Q.pop();
            for (int j = 0; j < n; ++j) {
                if (!visit[j]&&fakeroad[temp][j]){
                    visit[j] = true;
                    Q.push(j);
                    connect[i][j] = true;
                }
            }
        }
    }
    int ans = 0;
    for (int i = 0; i < n; ++i) {
        bool flag = true;
        for (int j = 0; j < n; ++j) {
            if (i == j) continue;
            if (!connect[i][j])
                flag = false;
        }
        if (flag)
            ans++;
    }
    cout << ans << endl;
}

邻接链表表示

#include 
#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;
const int MAXSIZE = 1010;
vector<int > road[MAXSIZE];
vector<int > fakeroad[MAXSIZE];
bool visit[MAXSIZE];
bool connect[MAXSIZE][MAXSIZE];
int n, m;
int main() {
//    freopen("../in.txt", "r", stdin);
    cin >> n >> m;
    int a, b;
    for (int i = 0; i < m; ++i) {
        cin >> a >> b;
        a--, b--;
        road[a].push_back(b);
        fakeroad[b].push_back(a);
    }
    queue<int> Q;
    for (int i = 0; i < n; ++i) {
        memset(visit, 0, sizeof(visit));
        visit[i] = true;
        Q.push(i);
        while (!Q.empty()){
            int temp = Q.front();
            Q.pop();
            for (int j = 0; j < road[temp].size(); ++j) {
                int k = road[temp][j];
                if (!visit[k]){
                    visit[k] = true;
                    Q.push(k);
                    connect[i][k] = true;
                }
            }
        }
    }
    for (int i = 0; i < n; ++i) {
        memset(visit, 0, sizeof(visit));
        visit[i] = true;
        Q.push(i);
        while (!Q.empty()){
            int temp = Q.front();
            Q.pop();
            for (int j = 0; j < fakeroad[temp].size(); ++j) {
                int k = fakeroad[temp][j];
                if (!visit[k]){
                    visit[k] = true;
                    Q.push(k);
                    connect[i][k] = true;
                }
            }
        }
    }
    int ans = 0;
    for (int i = 0; i < n; ++i) {
        bool flag = true;
        for (int j = 0; j < n; ++j) {
            if (i == j) continue;
            if (!connect[i][j])
                flag = false;
        }
        if (flag)
            ans++;
    }
    cout << ans << endl;
}