Leetcode #2271: Maximum White Tiles Covered by a Carpet
In this guide, we solve Leetcode #2271 Maximum White Tiles Covered by a Carpet in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given a 2D integer array tiles where tiles[i] = [li, ri] represents that every tile j in the range li <= j <= ri is colored white. You are also given an integer carpetLen, the length of a single carpet that can be placed anywhere.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Binary Search, Prefix Sum, Sorting, Sliding Window
Intuition
We are looking for a contiguous region that satisfies a constraint, which is a classic sliding-window signal.
Expanding and shrinking the window lets us maintain validity without restarting the scan.
Approach
Grow the window with a right pointer, and shrink from the left only when the constraint is violated.
Track the best window as you go to keep the solution linear.
Steps:
- Expand the right end of the window.
- While invalid, move the left end to restore constraints.
- Update the best window found.
Example
Input: tiles = [[1,5],[10,11],[12,18],[20,25],[30,32]], carpetLen = 10
Output: 9
Explanation: Place the carpet starting on tile 10.
It covers 9 white tiles, so we return 9.
Note that there may be other places where the carpet covers 9 white tiles.
It can be shown that the carpet cannot cover more than 9 white tiles.
Python Solution
class Solution:
def maximumWhiteTiles(self, tiles: List[List[int]], carpetLen: int) -> int:
tiles.sort()
n = len(tiles)
s = ans = j = 0
for i, (li, ri) in enumerate(tiles):
while j < n and tiles[j][1] - li + 1 <= carpetLen:
s += tiles[j][1] - tiles[j][0] + 1
j += 1
if j < n and li + carpetLen > tiles[j][0]:
ans = max(ans, s + li + carpetLen - tiles[j][0])
else:
ans = max(ans, s)
s -= ri - li + 1
return ans
Complexity
The time complexity is O(n). The space complexity is O(1) to O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.