How do you solve Maximum White Tiles Covered by a Carpet on LeetCode?

Maximum White Tiles Covered by a Carpet (LeetCode #2271) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: The placement of the carpet can be optimized by considering the starting position of each tile.

What is the time complexity of Maximum White Tiles Covered by a Carpet?

The optimal solution for Maximum White Tiles Covered by a Carpet runs in O(n log n) time and uses O(n) space. The sorting step takes O(n log n), and the sliding window approach runs in O(n), making this overall efficient.

What is the brute force solution for Maximum White Tiles Covered by a Carpet?

The brute force approach for Maximum White Tiles Covered by a Carpet is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible starting position for the carpet and counting how many white tiles it covers. This is straightforward but inefficient, especially as the number of tiles increases. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for Maximum White Tiles Covered by a Carpet?

Always consider edge cases, such as when the carpet length is longer than the distance between tiles. Explain your thought process clearly while coding; it helps the interviewer understand your approach. Practice explaining your code as you write it to simulate the interview environment.

What are common mistakes when solving Maximum White Tiles Covered by a Carpet?

Not sorting the tiles before processing, leading to incorrect calculations. Failing to account for the overlap of the carpet with the end of the tiles.

#2271

Maximum White Tiles Covered by a Carpet

Medium

ArrayBinary SearchGreedySliding WindowSortingPrefix SumSliding WindowPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(n)

The optimal approach uses a sliding window technique combined with prefix sums to efficiently calculate the maximum number of white tiles that can be covered by the carpet. This significantly reduces the time complexity by avoiding redundant calculations.

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Algorithm

3 steps

1Step 1: Sort the tiles based on their starting position.
2Step 2: Create a prefix sum array to store the cumulative number of white tiles covered up to each tile.
3Step 3: Use a sliding window to determine the maximum number of tiles covered by placing the carpet starting from each tile's position.

solution.py18 lines

1# Full working Python code
2
3def maxWhiteTiles(tiles, carpetLen):
4    tiles.sort()
5    prefix_sum = [0] * (len(tiles) + 1)
6    for i in range(len(tiles)):
7        prefix_sum[i + 1] = prefix_sum[i] + (tiles[i][1] - tiles[i][0] + 1)
8    max_covered = 0
9    j = 0
10    for i in range(len(tiles)):
11        while j < len(tiles) and tiles[j][0] <= tiles[i][0] + carpetLen:
12            j += 1
13        covered = prefix_sum[j] - prefix_sum[i]
14        if j > 0 and tiles[j - 1][1] > tiles[i][0] + carpetLen:
15            covered -= tiles[j - 1][1] - (tiles[i][0] + carpetLen)
16        max_covered = max(max_covered, covered)
17    return max_covered
18

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Complexity note: The sorting step takes O(n log n), and the sliding window approach runs in O(n), making this overall efficient.

1The placement of the carpet can be optimized by considering the starting position of each tile.
2Using prefix sums allows for quick calculations of the total number of covered tiles.

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