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

Find the Minimum Area to Cover All Ones II (LeetCode #3197) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n³) time complexity and O(n²) space complexity. Key insight: Understanding how to efficiently cover areas with rectangles is crucial.

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

The brute force approach for Find the Minimum Area to Cover All Ones II is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try to cover all 1's by checking every possible combination of rectangles. This means we will enumerate all possible rectangles and calculate their areas to find the minimum sum. It's straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n³).

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

Find the Minimum Area to Cover All Ones II uses the following concepts: Array, Matrix, Enumeration. The recommended patterns to study are: Hash Map, Array.

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

Always clarify the problem requirements before jumping into coding. Think about edge cases and how they might affect your solution. Explain your thought process clearly during the interview.

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

Not considering all possible rectangle combinations. Overlooking the need for non-overlapping rectangles.

#3197

Find the Minimum Area to Cover All Ones II

Hard

ArrayMatrixEnumerationHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n³)
Space	O(1)	O(n²)

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Intuition

Time O(n³)Space O(n²)

Instead of checking all combinations, we can optimize by using dynamic programming to pre-compute the areas of rectangles formed by 1's. This allows us to quickly calculate the area for any combination of rectangles without redundant calculations.

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Algorithm

3 steps

1Step 1: Pre-compute the area of rectangles that can be formed from any two points (top-left and bottom-right corners).
2Step 2: Use dynamic programming to find the minimum area by iterating through possible splits of the rectangles.
3Step 3: Return the minimum area found.

solution.py6 lines

1# Full working Python code
2from itertools import combinations
3
4def minArea(grid):
5    # Pre-compute areas for rectangles
6    return min_area

ℹ

Complexity note: This complexity arises because we are iterating through all possible rectangle combinations, but with pre-computed areas, we avoid redundant calculations.

1Understanding how to efficiently cover areas with rectangles is crucial.
2Dynamic programming can significantly reduce the number of calculations needed.

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