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302. Smallest Rectangle Enclosing Black Pixels 👍

Approach 1: BFS

  • Time: $O(mn)$
  • Space: $O(mn)$
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class Solution {
 public:
  int minArea(vector<vector<char>>& image, int x, int y) {
    constexpr int dirs[4][2] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    const int m = image.size();
    const int n = image[0].size();
    vector<int> topLeft{x, y};
    vector<int> bottomRight{x, y};
    queue<pair<int, int>> q{{{x, y}}};
    image[x][y] = '2';  // Mark as visited.

    while (!q.empty()) {
      const auto [i, j] = q.front();
      q.pop();
      for (const auto& [dx, dy] : dirs) {
        const int r = i + dx;
        const int c = j + dy;
        if (r < 0 || r == m || c < 0 || c == n)
          continue;
        if (image[r][c] != '1')
          continue;
        topLeft[0] = min(topLeft[0], r);
        topLeft[1] = min(topLeft[1], c);
        bottomRight[0] = max(bottomRight[0], r);
        bottomRight[1] = max(bottomRight[1], c);
        q.emplace(r, c);
        image[r][c] = '2';
      }
    }

    const int width = bottomRight[1] - topLeft[1] + 1;
    const int height = bottomRight[0] - topLeft[0] + 1;
    return width * height;
  }
};

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class Solution {
  public int minArea(char[][] image, int x, int y) {
    final int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
    final int m = image.length;
    final int n = image[0].length;
    int[] topLeft = {x, y};
    int[] bottomRight = {x, y};
    Queue<Pair<Integer, Integer>> q = new ArrayDeque<>(List.of(new Pair<>(x, y)));
    image[x][y] = '2'; // Mark as visited.

    while (!q.isEmpty()) {
      final int i = q.peek().getKey();
      final int j = q.poll().getValue();
      for (int[] dir : dirs) {
        final int r = i + dir[0];
        final int c = j + dir[1];
        if (r < 0 || r == m || c < 0 || c == n)
          continue;
        if (image[r][c] != '1')
          continue;
        topLeft[0] = Math.min(topLeft[0], r);
        topLeft[1] = Math.min(topLeft[1], c);
        bottomRight[0] = Math.max(bottomRight[0], r);
        bottomRight[1] = Math.max(bottomRight[1], c);
        q.offer(new Pair<>(r, c));
        image[r][c] = '2';
      }
    }

    final int width = bottomRight[1] - topLeft[1] + 1;
    final int height = bottomRight[0] - topLeft[0] + 1;
    return width * height;
  }
}

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class Solution:
  def minArea(self, image: list[list[str]], x: int, y: int) -> int:
    dirs = ((0, 1), (1, 0), (0, -1), (-1, 0))
    m = len(image)
    n = len(image[0])
    topLeft = [x, y]
    bottomRight = [x, y]
    q = collections.deque([(x, y)])
    image[x][y] = '2'  # Mark as visited.

    while q:
      i, j = q.popleft()
      for dx, dy in dirs:
        r = i + dx
        c = j + dy
        if r < 0 or r == m or c < 0 or c == n:
          continue
        if image[r][c] != '1':
          continue
        topLeft[0] = min(topLeft[0], r)
        topLeft[1] = min(topLeft[1], c)
        bottomRight[0] = max(bottomRight[0], r)
        bottomRight[1] = max(bottomRight[1], c)
        q.append((r, c))
        image[r][c] = '2'

    width = bottomRight[1] - topLeft[1] + 1
    height = bottomRight[0] - topLeft[0] + 1
    return width * height
  • Time: $O(m\log n + n\log m)$
  • Space: $O(1)$
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class Solution {
 public:
  int minArea(vector<vector<char>>& image, int x, int y) {
    const int x1 = firstAnyOne(image, 0, x, &rowAllZeros);
    const int x2 = firstAllZeros(image, x + 1, image.size(), &rowAllZeros);
    const int y1 = firstAnyOne(image, 0, y, &colAllZeros);
    const int y2 = firstAllZeros(image, y + 1, image[0].size(), &colAllZeros);
    return (x2 - x1) * (y2 - y1);
  }

 private:
  int firstAnyOne(const vector<vector<char>>& image, int l, int r,
                  function<bool(const vector<vector<char>>&, int)> allZeros) {
    while (l < r) {
      const int m = (l + r) / 2;
      if (allZeros(image, m))
        l = m + 1;
      else
        r = m;
    }
    return l;
  }

  int firstAllZeros(const vector<vector<char>>& image, int l, int r,
                    function<bool(const vector<vector<char>>&, int)> allZeros) {
    while (l < r) {
      const int m = (l + r) / 2;
      if (allZeros(image, m))
        r = m;
      else
        l = m + 1;
    }
    return l;
  }

  static bool rowAllZeros(const vector<vector<char>>& image, int rowIndex) {
    return all_of(image[rowIndex].cbegin(), image[rowIndex].cend(),
                  [](int pixel) { return pixel == '0'; });
  }

  static bool colAllZeros(const vector<vector<char>>& image, int colIndex) {
    for (int i = 0; i < image.size(); ++i)
      if (image[i][colIndex] == '1')
        return false;
    return true;
  }
};

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class Solution {
  public int minArea(char[][] image, int x, int y) {
    this.image = image;
    final int x1 = firstAnyOne(0, x, rowAllZeros);
    final int x2 = firstAllZeros(x + 1, image.length, rowAllZeros);
    final int y1 = firstAnyOne(0, y, colAllZeros);
    final int y2 = firstAllZeros(y + 1, image[0].length, colAllZeros);
    return (x2 - x1) * (y2 - y1);
  }

  private char[][] image;

  private int firstAnyOne(int l, int r, Function<Integer, Boolean> allZeros) {
    while (l < r) {
      final int m = (l + r) / 2;
      if (allZeros.apply(m))
        l = m + 1;
      else
        r = m;
    }
    return l;
  }

  private int firstAllZeros(int l, int r, Function<Integer, Boolean> allZeros) {
    while (l < r) {
      final int m = (l + r) / 2;
      if (allZeros.apply(m))
        r = m;
      else
        l = m + 1;
    }
    return l;
  }

  Function<Integer, Boolean> rowAllZeros = new Function<>() {
    public Boolean apply(Integer rowIndex) {
      return new String(image[rowIndex]).chars().allMatch(pixel -> pixel == '0');
    }
  };

  Function<Integer, Boolean> colAllZeros = new Function<>() {
    public Boolean apply(Integer colIndex) {
      for (int i = 0; i < image.length; ++i)
        if (image[i][colIndex] == '1')
          return false;
      return true;
    }
  };
}

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class Solution:
  def minArea(self, image: list[list[str]], x: int, y: int) -> int:
    def firstAnyOne(l: int, r: int, allZeros: Callable[[int], bool]) -> int:
      while l < r:
        m = (l + r) // 2
        if allZeros(m):
          l = m + 1
        else:
          r = m
      return l

    def firstAllZeros(l: int, r: int, allZeros: Callable[[int], bool]) -> int:
      while l < r:
        m = (l + r) // 2
        if allZeros(m):
          r = m
        else:
          l = m + 1
      return l

    def colAllZeros(colIndex: int) -> bool:
      return all(pixel == '0' for pixel in list(zip(*image))[colIndex])

    def rowAllZeros(rowIndex: int) -> bool:
      return all(pixel == '0' for pixel in image[rowIndex])

    x1 = firstAnyOne(0, x, rowAllZeros)
    x2 = firstAllZeros(x + 1, len(image), rowAllZeros)
    y1 = firstAnyOne(0, y, colAllZeros)
    y2 = firstAllZeros(y + 1, len(image[0]), colAllZeros)
    return (x2 - x1) * (y2 - y1)