You are given an m x n binary matrix image where 0 represents a white pixel and 1 represents a black pixel.The black pixels are connected (i.e., there is only one black region). Pixels are connected horizontally and vertically.Given two integers x and y that represents the location of one of the black pixels, return the area of the smallest (axis-aligned) rectangle that encloses all black pixels.You must write an algorithm with less than O(mn) runtime complexity.
class Solution: # Time: O(m log m + n log n) — binary search for each bounding edge # Space: O(1) def min_area(self, image: list[list[str]], x: int, y: int) -> int: m, n = len(image), len(image[0]) def row_has_black(r: int) -> bool: return "1" in image[r] def col_has_black(c: int) -> bool: return any(row[c] == "1" for row in image) lo, hi = 0, x while lo < hi: mid = (lo + hi) // 2 if row_has_black(mid): hi = mid else: lo = mid + 1 top = lo lo, hi = x, m - 1 while lo < hi: mid = (lo + hi + 1) // 2 if row_has_black(mid): lo = mid else: hi = mid - 1 bottom = lo lo, hi = 0, y while lo < hi: mid = (lo + hi) // 2 if col_has_black(mid): hi = mid else: lo = mid + 1 left = lo lo, hi = y, n - 1 while lo < hi: mid = (lo + hi + 1) // 2 if col_has_black(mid): lo = mid else: hi = mid - 1 right = lo return (bottom - top + 1) * (right - left + 1)
