LC 1349. Maximum Students Taking Exam (Hungarian / Max Flow)

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 Solution 1 Hungarian:

class Solution {
public:
    int m,n;
    vector<vector<int>> g;
    vector<vector<int>> dir={{0,-1},{-1,-1},{1,-1},{0,1},{-1,1},{1,1}};
    int maxStudents(vector<vector<char>>& seats) {
        m=seats.size();
        n=seats[0].size();
        g=vector<vector<int>>(m*n,vector<int>(m*n,0));
        int seatcnt=0;
        for(int i=0;i<m;++i){
            for(int j=0;j<n;++j){
                if(seats[i][j]=='#') continue;
                seatcnt++;
                if(j%2==0){
                    for(int d=0;d<6;++d){
                        int ni=i+dir[d][0];
                        int nj=j+dir[d][1];
                        if(ni<0 || ni>=m || nj<0 || nj>=n || seats[ni][nj]=='#') continue;
                        g[i*n+j][ni*n+nj]=1;
                    }
                }
            }
        }
        vector<int> mat(m*n,-1);
        int cnt=0;
        for(int i=0;i<m;++i){
            for(int j=0;j<n;++j){
                if(j%2==0 && seats[i][j]=='.'){
                    vector<int> visited(m*n,0);
                    if(dfs(i*n+j,mat,visited)){
                        cnt++;
                    }
                }
            }
        }
        return seatcnt-cnt;
    }
    
    bool dfs(int u, vector<int> &mat, vector<int> &visited){
        for(int i=0;i<m*n;++i){
            if(g[u][i]==1){
                if(visited[i]==1) continue;
                visited[i]=1;
                if(mat[i]==-1 || dfs(mat[i],mat,visited)){
                    mat[i]=u;
                    return true;
                }
            }
        }
        return false;
    }
    
};

Solution 2 Max Flow:

class Solution {
public:
    int m,n;
    vector<vector<int>> g;
    vector<vector<int>> dir={{0,-1},{-1,-1},{1,-1},{0,1},{-1,1},{1,1}};
    int S,T;
    int flow;
    int maxStudents(vector<vector<char>>& seats) {
        m=seats.size();
        n=seats[0].size();
        S=m*n;
        T=m*n+1;
        g=vector<vector<int>>(m*n+2,vector<int>(m*n+2,0));  // residual capacity 
        int seatcnt=0;
        for(int i=0;i<m;++i){
            for(int j=0;j<n;++j){
                if(seats[i][j]=='#') continue;
                seatcnt++;
                if(j%2==0){
                    g[S][i*n+j]=1;
                    for(int d=0;d<6;++d){
                        int ni=i+dir[d][0];
                        int nj=j+dir[d][1];
                        if(ni<0 || ni>=m || nj<0 || nj>=n || seats[ni][nj]=='#') continue;
                        g[i*n+j][ni*n+nj]=1;
                    }
                }else{
                    g[i*n+j][T]=1;
                }
            }
        }
        flow=0;
        EK();
        return seatcnt-flow;
    }
    
    void EK(){
        while(true){
            vector<int> pre(m*n+2,-1);
            bfs(pre);
            if(pre[T]==-1) break;
            int v=T;
            while(true){
                int u=pre[v];
                g[u][v]--;
                g[v][u]++;
                v=u;
                if(v==S) break;
            }
            flow++;
        }
    }
    
    void bfs(vector<int> &pre){
        queue<int> q;
        q.push(S);
        vector<int> visited(m*n+2,0);
        visited[S]=1;
        while(!q.empty()){
            int cur=q.front();
            q.pop();
            for(int i=0;i<m*n+2;++i){
                if(visited[i]==0 && g[cur][i]==1){
                    visited[i]=1;
                    q.push(i);
                    pre[i]=cur;
                }
            }
        }
    }
    
};