Smallest Rectangle Enclosing Black Pixels

Statement

You are given an $m \times n$ binary matrix image, where $0$ represents a white pixel and $1$ represents a black pixel.

All black pixels in the matrix form a single connected region, where connectivity is defined by horizontal or vertical adjacency.

Given two integers x and y that represent the coordinates of one of the black pixels, write an algorithm to find the area of the smallest axis-aligned rectangle that encloses all the black pixels.

Note: Your solution must have a runtime complexity less than $O(m \times n)$.

Constraints:

• $m$ $==$ image.length

• $n$ == image[i].length

• $1 \leq m, n \leq 100$

• image[i][j] is either $0$ or $1$

• $0 \leq$ x $< m$

• $0 \leq$ y $< n$

• image[x][y] $== 1$

• The black pixels in the image only form one component.

Examples