600. Smallest Rectangle Enclosing Black Pixels [LintCode]

An image is represented by a binary matrix with 0as a white pixel and 1as 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

For example, given the following image:

[
  "0010",
  "0110",
  "0100"
]

and x =0, y =2,
Return6.

往四个方向进行二分搜索，注意往不同方向搜索的时候，指针的调整规律不一样。

public class Solution {
    /*
     * @param image: a binary matrix with '0' and '1'
     * @param x: the location of one of the black pixels
     * @param y: the location of one of the black pixels
     * @return: an integer
     */
    public int minArea(char[][] image, int x, int y) {
        // write your code here
        if (image == null || image.length == 0 || image[0].length == 0) {
            return 0;
        }
        int leftBound = findLeftBound(image, 0, y);
        int rightBound = findRightBound(image, y, image[0].length - 1);
        int upperBound = findUpperBound(image, 0, x);
        int lowerBound = findLowerBound(image, x, image.length - 1);
        return (rightBound - leftBound + 1) * (lowerBound - upperBound + 1);
    }

    private int findLeftBound(char[][] image, int left, int right) {
        while (left + 1 < right) {
            int mid = left + (right - left) / 2;
            if (existBlackInCol(image, mid)) {
                right = mid;
            } else {
                left = mid;
            }
        }
        if (existBlackInCol(image, left)) {
            return left;
        }
        return right;
    }

    private int findRightBound(char[][] image, int left, int right) {
        while (left + 1 < right) {
            int mid = left + (right - left) / 2;
            if (existBlackInCol(image, mid)) {
                left = mid;
            } else {
                right = mid;
            }
        }
        if (existBlackInCol(image, right)) {
            return right;
        }
        return left;
    }

    private int findUpperBound(char[][] image, int up, int down) {
        while (up + 1 < down) {
            int mid = up + (down - up) / 2;
            if (existBlackInRow(image, mid)) {
                down = mid;
            } else {
                up = mid;
            }
        }
        if (existBlackInRow(image, up)) {
            return up;
        }
        return down;
    }

    private int findLowerBound(char[][] image, int up, int down) {
        while (up + 1 < down) {
            int mid = up + (down - up) / 2;
            if (existBlackInRow(image, mid)) {
                up = mid;
            } else {
                down = mid;
            }
        }
        if (existBlackInRow(image, down)) {
            return down;
        }
        return up;
    }

    private boolean existBlackInCol(char[][] image, int y) {
        for (int i = 0; i < image.length; i++) {
            if (image[i][y] == '1') {
                return true;
            }
        }
        return false;
    }

    private boolean existBlackInRow(char[][] image, int x) {
        for (int i = 0; i < image[0].length; i++) {
            if (image[x][i] == '1') {
                return true;
            }
        }
        return false;
    }
}