2271. Maximum White Tiles Covered by a Carpet LeetCode Solution

In this guide, you will get 2271. Maximum White Tiles Covered by a Carpet LeetCode Solution with the best time and space complexity. The solution to Maximum White Tiles Covered by a Carpet problem is provided in various programming languages like C++, Java, and Python. This will be helpful for you if you are preparing for placements, hackathons, interviews, or practice purposes. The solutions provided here are very easy to follow and include detailed explanations.

Table of Contents

1. Problem Statement
2. Complexity Analysis
3. Maximum White Tiles Covered by a Carpet solution in C++
4. Maximum White Tiles Covered by a Carpet solution in Java
5. Maximum White Tiles Covered by a Carpet solution in Python
6. Additional Resources

Problem Statement of Maximum White Tiles Covered by a Carpet

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.
Return the maximum number of white tiles that can be covered by the carpet.

Example 1:

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.

Example 2:

Input: tiles = [[10,11],[1,1]], carpetLen = 2
Output: 2
Explanation: Place the carpet starting on tile 10.
It covers 2 white tiles, so we return 2.

Constraints:

1 <= tiles.length <= 5 * 104
tiles[i].length == 2
1 <= li <= ri <= 109
1 <= carpetLen <= 109
The tiles are non-overlapping.

Complexity Analysis

• Time Complexity: O(\texttt{sort})
• Space Complexity: O(n)

2271. Maximum White Tiles Covered by a Carpet LeetCode Solution in C++

class Solution {
 public:
  int maximumWhiteTiles(vector<vector<int>>& tiles, int carpetLen) {
    if (ranges::any_of(tiles, [&](const auto& tile) {
      return tile[1] - tile[0] + 1 >= carpetLen;
    }))
      return carpetLen;

    int ans = 0;
    vector<int> starts;
    vector<int> prefix(tiles.size() + 1);

    ranges::sort(tiles);

    for (const vector<int>& tile : tiles)
      starts.push_back(tile[0]);

    for (int i = 0; i < tiles.size(); ++i) {
      const int length = tiles[i][1] - tiles[i][0] + 1;
      prefix[i + 1] = prefix[i] + length;
    }

    for (int i = 0; i < tiles.size(); ++i) {
      const int s = tiles[i][0];
      const int carpetEnd = s + carpetLen - 1;
      const int endIndex =
          ranges::upper_bound(starts, carpetEnd) - starts.begin() - 1;
      const int notCover = max(0, tiles[endIndex][1] - carpetEnd);
      ans = max(ans, prefix[endIndex + 1] - prefix[i] - notCover);
    }

    return ans;
  }
};
/* code provided by PROGIEZ */

2271. Maximum White Tiles Covered by a Carpet LeetCode Solution in Java

class Solution {
  public int maximumWhiteTiles(int[][] tiles, int carpetLen) {
    if (Arrays.stream(tiles).anyMatch(tile -> tile[1] - tile[0] + 1 >= carpetLen))
      return carpetLen;

    int ans = 0;
    List<Integer> starts = new ArrayList<>();
    int[] prefix = new int[tiles.length + 1];

    Arrays.sort(tiles, (a, b) -> Integer.compare(a[0], b[0]));

    for (int[] tile : tiles)
      starts.add(tile[0]);

    for (int i = 0; i < tiles.length; ++i) {
      final int length = tiles[i][1] - tiles[i][0] + 1;
      prefix[i + 1] = prefix[i] + length;
    }

    for (int i = 0; i < tiles.length; ++i) {
      final int s = tiles[i][0];
      final int carpetEnd = s + carpetLen - 1;
      final int endIndex = firstGreater(starts, carpetEnd) - 1;
      final int notCover = Math.max(0, tiles[endIndex][1] - carpetEnd);
      ans = Math.max(ans, prefix[endIndex + 1] - prefix[i] - notCover);
    }

    return ans;
  }

  private int firstGreater(List<Integer> A, int target) {
    final int i = Collections.binarySearch(A, target + 1);
    return i < 0 ? -i - 1 : i;
  }
}
// code provided by PROGIEZ

2271. Maximum White Tiles Covered by a Carpet LeetCode Solution in Python

class Solution:
  def maximumWhiteTiles(self, tiles: list[list[int]], carpetLen: int) -> int:
    if any(tile[1] - tile[0] + 1 >= carpetLen for tile in tiles):
      return carpetLen

    ans = 0
    prefix = [0] * (len(tiles) + 1)

    tiles.sort()
    starts = [tile[0] for tile in tiles]

    for i, tile in enumerate(tiles):
      length = tile[1] - tile[0] + 1
      prefix[i + 1] = prefix[i] + length

    for i, (s, _) in enumerate(tiles):
      carpetEnd = s + carpetLen - 1
      endIndex = bisect_right(starts, carpetEnd) - 1
      notCover = max(0, tiles[endIndex][1] - carpetEnd)
      ans = max(ans, prefix[endIndex + 1] - prefix[i] - notCover)

    return ans
 # code by PROGIEZ

Additional Resources

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