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1970. Last Day Where You Can Still Cross 👍

  • Time: $O(\texttt{row} \cdot \texttt{col} \cdot \log (\texttt{row} \cdot \texttt{col}))$
  • Space: $O(\texttt{row} \cdot \texttt{col})$
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class Solution {
 public:
  int latestDayToCross(int row, int col, vector<vector<int>>& cells) {
    int ans = 0;
    int l = 1;
    int r = cells.size() - 1;

    while (l <= r) {
      const int m = (l + r) / 2;
      if (canWalk(m, row, col, cells)) {
        ans = m;
        l = m + 1;
      } else {
        r = m - 1;
      }
    }

    return ans;
  }

 private:
  static constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

  bool canWalk(int day, int row, int col, const vector<vector<int>>& cells) {
    vector<vector<int>> matrix(row, vector<int>(col));
    for (int i = 0; i < day; ++i) {
      const int x = cells[i][0] - 1;
      const int y = cells[i][1] - 1;
      matrix[x][y] = 1;
    }

    queue<pair<int, int>> q;

    for (int j = 0; j < col; ++j)
      if (matrix[0][j] == 0) {
        q.emplace(0, j);
        matrix[0][j] = 1;
      }

    while (!q.empty()) {
      const auto [i, j] = q.front();
      q.pop();
      for (const auto& [dx, dy] : dirs) {
        const int x = i + dx;
        const int y = j + dy;
        if (x < 0 || x == row || y < 0 || y == col)
          continue;
        if (matrix[x][y] == 1)
          continue;
        if (x == row - 1)
          return true;
        q.emplace(x, y);
        matrix[x][y] = 1;
      }
    }

    return false;
  }
};

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class Solution {
  public int latestDayToCross(int row, int col, int[][] cells) {
    int ans = 0;
    int l = 1;
    int r = cells.length - 1;

    while (l <= r) {
      final int m = (l + r) / 2;
      if (canWalk(m, row, col, cells)) {
        ans = m;
        l = m + 1;
      } else {
        r = m - 1;
      }
    }

    return ans;
  }

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

  private boolean canWalk(int day, int row, int col, int[][] cells) {
    int[][] matrix = new int[row][col];
    for (int i = 0; i < day; ++i) {
      final int x = cells[i][0] - 1;
      final int y = cells[i][1] - 1;
      matrix[x][y] = 1;
    }

    Queue<Pair<Integer, Integer>> q = new ArrayDeque<>();

    for (int j = 0; j < col; ++j)
      if (matrix[0][j] == 0) {
        q.offer(new Pair<>(0, j));
        matrix[0][j] = 1;
      }

    while (!q.isEmpty()) {
      final int i = q.peek().getKey();
      final int j = q.poll().getValue();
      for (int[] dir : dirs) {
        final int x = i + dir[0];
        final int y = j + dir[1];
        if (x < 0 || x == row || y < 0 || y == col)
          continue;
        if (matrix[x][y] == 1)
          continue;
        if (x == row - 1)
          return true;
        q.offer(new Pair<>(x, y));
        matrix[x][y] = 1;
      }
    }

    return false;
  }
}

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class Solution:
  def latestDayToCross(self, row: int, col: int, cells: list[list[int]]) -> int:
    dirs = ((0, 1), (1, 0), (0, -1), (-1, 0))

    def canWalk(day: int) -> bool:
      matrix = [[0] * col for _ in range(row)]
      for i in range(day):
        x, y = cells[i]
        matrix[x - 1][y - 1] = 1

      q = collections.deque()

      for j in range(col):
        if matrix[0][j] == 0:
          q.append((0, j))
          matrix[0][j] = 1

      while q:
        i, j = q.popleft()
        for dx, dy in dirs:
          x = i + dx
          y = j + dy
          if x < 0 or x == row or y < 0 or y == col:
            continue
          if matrix[x][y] == 1:
            continue
          if x == row - 1:
            return True
          q.append((x, y))
          matrix[x][y] = 1

      return False

    ans = 0
    l = 1
    r = len(cells) - 1

    while l <= r:
      m = (l + r) // 2
      if canWalk(m):
        ans = m
        l = m + 1
      else:
        r = m - 1

    return ans