302. Smallest Rectangle Enclosing Black Pixels

• Difficulty: Hard

• Topics: Binary Search

• Similar Questions:

Problem:

An image is represented by a binary matrix with 0 as a white pixel and 1 as a black pixel. The black pixels are connected, i.e., there is only one black region. Pixels are connected horizontally and vertically. Given the location (x, y) of one of the black pixels, return the area of the smallest (axis-aligned) rectangle that encloses all black pixels.

Example:

Input:
[
  "0010",
  "0110",
  "0100"
]
and x = 0, y = 2

Output: 6

Solutions:

class Solution {
public:
    int minArea(vector<vector<char>>& image, int x, int y) {
        int m = image.size();
        if (m == 0) return 0;
        int n = image[0].size();
        if (n == 0) return 0;

        int up = searchByRow(image, 0, x, m, n, true);
        int down = searchByRow(image, x, m - 1, m, n, false);
        int right = searchByColumn(image, y, n - 1, m, n, true);
        int left = searchByColumn(image, 0, y, m, n, false);

        return (down - up + 1) * (right - left + 1);

    }
private:
    int searchByRow(vector<vector<char>>& image, int up, int down, int m, int n, bool upwards) {
        while (up + 1 < down) {
            int mid = up + (down - up) / 2;
            if (pixelInRow(image, mid, m, n)) {
                if (upwards) {
                    down = mid;
                } else {
                    up = mid;
                }
            } else {
                if (upwards) {
                    up = mid;
                } else {
                    down = mid;
                }
            }
        }

        if (upwards) {
            return pixelInRow(image, up, m, n) ? up : down;
        } else {
            return pixelInRow(image, down, m, n) ? down : up;
        }
    }

    int searchByColumn(vector<vector<char>>& image, int left, int right, int m, int n, bool forwards) {
        while (left + 1 < right) {
            int mid = left + (right - left) / 2;
            if (pixelInColumn(image, mid, m, n)) {
                if (forwards) {
                    left = mid;
                } else {
                    right = mid;
                }
            } else {
                if (forwards) {
                    right = mid;
                } else {
                    left = mid;
                }
            }
        }

        if (forwards) {
            return pixelInColumn(image, right, m, n) ? right : left;
        } else {
            return pixelInColumn(image, left, m, n) ? left : right;
        }
    }

    bool pixelInRow(vector<vector<char>>& image, int row, int m, int n) {
        for (int i = 0; i < n; ++i) {
            if (image[row][i] == '1')   return true;
        }

        return false;
    }

    bool pixelInColumn(vector<vector<char>>& image, int col, int m, int n) {
        for (int i = 0; i < m; ++i) {
            if (image[i][col] == '1')   return true;
        }

        return false;
    }

};