3195. Find the Minimum Area to Cover All Ones I

Problem Link

Description

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You are given a 2D binary array grid. Find a rectangle with horizontal and vertical sides with the smallest area, such that all the 1's in grid lie inside this rectangle.

Return the minimum possible area of the rectangle.

 

Example 1:

Input: grid = [[0,1,0],[1,0,1]]

Output: 6

Explanation:

The smallest rectangle has a height of 2 and a width of 3, so it has an area of 2 * 3 = 6.

Example 2:

Input: grid = [[1,0],[0,0]]

Output: 1

Explanation:

The smallest rectangle has both height and width 1, so its area is 1 * 1 = 1.

 

Constraints:

• 1 <= grid.length, grid[i].length <= 1000
• grid[i][j] is either 0 or 1.
• The input is generated such that there is at least one 1 in grid.

Solution

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Python3

class Solution:
    def minimumArea(self, grid: List[List[int]]) -> int:
        rows, cols = len(grid), len(grid[0])
        minR, maxR = inf, -inf
        minC, maxC = inf, -inf
        
        for i in range(rows):
            for j in range(cols):
                if grid[i][j] == 1:
                    minR = min(minR, i)
                    maxR = max(maxR, i)
                    minC = min(minC, j)
                    maxC = max(maxC, j)
        
        return (maxR - minR + 1) * (maxC - minC + 1)