How do you solve Find the Minimum Area to Cover All Ones I on LeetCode?

Find the Minimum Area to Cover All Ones I (LeetCode #3195) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Finding the bounding box of all 1's is crucial for minimizing the area.

What is the brute force solution for Find the Minimum Area to Cover All Ones I?

The brute force approach for Find the Minimum Area to Cover All Ones I is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible rectangle in the grid that could encompass all the 1's. This is straightforward but inefficient, as it requires examining many rectangles. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Minimum Area to Cover All Ones I?

Find the Minimum Area to Cover All Ones I uses the following concepts: Array, Matrix. The recommended patterns to study are: Bounding Box, Grid Traversal.

What are the interview tips for Find the Minimum Area to Cover All Ones I?

Always consider edge cases, like a grid filled with only 1's. Explain your thought process clearly while coding. Practice dry-running your solution with different inputs.

What are common mistakes when solving Find the Minimum Area to Cover All Ones I?

Failing to account for all 1's when calculating the area. Not initializing min and max variables correctly.

#3195

Find the Minimum Area to Cover All Ones I

Medium

ArrayMatrixBounding BoxGrid Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution involves finding the minimum and maximum coordinates of all the 1's in the grid. This allows us to define a single rectangle that covers all the 1's without needing to check every possible rectangle.

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Algorithm

3 steps

1Step 1: Initialize variables to track the minimum and maximum row and column indices of 1's.
2Step 2: Iterate through the grid to find the coordinates of all 1's, updating the min and max indices as needed.
3Step 3: Calculate the area of the rectangle defined by these min and max indices.

solution.py13 lines

1# Full working Python code
2
3def minArea(grid):
4    rows, cols = len(grid), len(grid[0])
5    min_row, max_row, min_col, max_col = rows, -1, cols, -1
6    for r in range(rows):
7        for c in range(cols):
8            if grid[r][c] == 1:
9                min_row = min(min_row, r)
10                max_row = max(max_row, r)
11                min_col = min(min_col, c)
12                max_col = max(max_col, c)
13    return (max_row - min_row + 1) * (max_col - min_col + 1)

ℹ

Complexity note: The time complexity is O(n) because we only need to traverse the grid once to find the coordinates of all 1's. The space complexity is O(1) since we are using a constant amount of extra space.

1Finding the bounding box of all 1's is crucial for minimizing the area.
2Iterating through the grid to find min and max coordinates is efficient.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.