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1349. Maximum Students Taking Exam 👍

  • Time: $O(|V||E|) = O(m^2n^2)$
  • Space: $O(mn)$
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class Solution {
 public:
  int maxStudents(vector<vector<char>>& seats) {
    return accumulate(seats.begin(), seats.end(), 0,
                      [&](int subtotal, const auto& seat) {
      return subtotal + ranges::count(seat, '.');
    }) - hungarian(seats);
  }

 private:
  const vector<pair<int, int>> dirs{{-1, -1}, {0, -1}, {1, -1},
                                    {-1, 1},  {0, 1},  {1, 1}};

  int hungarian(const vector<vector<char>>& seats) {
    const int m = seats.size();
    const int n = seats[0].size();
    int count = 0;
    vector<vector<int>> seen(m, vector<int>(n));
    vector<vector<int>> match(m, vector<int>(n, -1));

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (seats[i][j] == '.' && match[i][j] == -1) {
          const int sessionId = i * n + j;
          seen[i][j] = sessionId;
          count += dfs(seats, i, j, sessionId, seen, match);
        }

    return count;
  }

  int dfs(const vector<vector<char>>& seats, int i, int j, int sessionId,
          vector<vector<int>>& seen, vector<vector<int>>& match) {
    const int m = seats.size();
    const int n = seats[0].size();

    for (const auto& [dx, dy] : dirs) {
      const int x = i + dx;
      const int y = j + dy;
      if (x < 0 || x == m || y < 0 || y == n)
        continue;
      if (seats[x][y] != '.' || seen[x][y] == sessionId)
        continue;
      seen[x][y] = sessionId;
      if (match[x][y] == -1 || dfs(seats, match[x][y] / n, match[x][y] % n,
                                   sessionId, seen, match)) {
        match[x][y] = i * n + j;
        match[i][j] = x * n + y;
        return 1;
      }
    }

    return 0;
  }
};

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class Solution {
  public int maxStudents(char[][] seats) {
    int studentsCount = 0;

    for (char[] seat : seats)
      for (final char s : seat)
        if (s == '.')
          ++studentsCount;

    return studentsCount - hungarian(seats);
  }

  private static final int[][] dirs = {{-1, -1}, {0, -1}, {1, -1}, {-1, 1}, {0, 1}, {1, 1}};

  private int hungarian(char[][] seats) {
    final int m = seats.length;
    final int n = seats[0].length;
    int count = 0;
    int[][] seen = new int[m][n];
    int[][] match = new int[m][n];
    Arrays.stream(match).forEach(A -> Arrays.fill(A, -1));

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (seats[i][j] == '.' && match[i][j] == -1) {
          final int sessionId = i * n + j;
          seen[i][j] = sessionId;
          if (dfs(seats, i, j, sessionId, seen, match))
            ++count;
        }

    return count;
  }

  private boolean dfs(char[][] seats, int i, int j, int sessionId, int[][] seen, int[][] match) {
    final int m = seats.length;
    final int n = seats[0].length;

    for (int[] dir : dirs) {
      final int x = i + dir[0];
      final int y = j + dir[1];
      if (x < 0 || x == m || y < 0 || y == n)
        continue;
      if (seats[x][y] != '.' || seen[x][y] == sessionId)
        continue;
      seen[x][y] = sessionId;
      if (match[x][y] == -1 ||
          dfs(seats, match[x][y] / n, match[x][y] % n, sessionId, seen, match)) {
        match[x][y] = i * n + j;
        match[i][j] = x * n + y;
        return true;
      }
    }

    return false;
  }
}

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class Solution:
  def maxStudents(self, seats: List[List[str]]) -> int:
    m = len(seats)
    n = len(seats[0])
    dirs = ((-1, -1), (0, -1), (1, -1), (-1, 1), (0, 1), (1, 1))
    seen = [[0] * n for _ in range(m)]
    match = [[-1] * n for _ in range(m)]

    def dfs(i: int, j: int, sessionId: int) -> int:
      for dx, dy in dirs:
        x = i + dx
        y = j + dy
        if x < 0 or x == m or y < 0 or y == n:
          continue
        if seats[x][y] != '.' or seen[x][y] == sessionId:
          continue
        seen[x][y] = sessionId
        if match[x][y] == -1 or dfs(*divmod(match[x][y], n), sessionId):
          match[x][y] = i * n + j
          match[i][j] = x * n + y
          return 1
      return 0

    def hungarian() -> int:
      count = 0
      for i in range(m):
        for j in range(n):
          if seats[i][j] == '.' and match[i][j] == -1:
            sessionId = i * n + j
            seen[i][j] = sessionId
            count += dfs(i, j, sessionId)
      return count

    return sum(seats[i][j] == '.'
               for i in range(m)
               for j in range(n)) - hungarian()