Cover the Most White Integer Tiles with One Carpet
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
Each inclusive interval in `tiles` colors its integer positions white, and the intervals do not overlap. Place one carpet covering carpetLen consecutive integer positions anywhere. Return the greatest number of white tiles it can cover; only the count is required.
```cpp
class Solution {
public:
int maximumWhiteTiles(vector<vector<int>>& tiles, int carpetLen);
};
```
### Examples
**Example 1:**
```text
Input: tiles = [[2,4],[8,10]], carpetLen = 4
Output: 3
Explanation: Either three-position white interval can be fully covered. A length-four carpet cannot span the gap and cover four white positions.
```
**Example 2:**
```text
Input: tiles = [[4,8]], carpetLen = 3
Output: 3
Explanation: Any three consecutive positions within the five-position interval can be covered.
```
### Constraints
- `1 <= tiles.length <= 50000`.
- Every interval has two integers with `1 <= left <= right <= 10^9`.
- `1 <= carpetLen <= 10^9`.
- Intervals are non-overlapping.
### Clarifying Questions
- Are interval endpoints included? Yes; `[l, r]` contains `r - l + 1` tiles.
- Can the carpet cross gaps? Yes, but nonwhite positions contribute nothing.
- Must the carpet stay inside one white interval? No; place it anywhere.
- Is a placement required in the result? No; return only the greatest covered count.
```hint Check the boundary
A carpet of length `k` starting at `x` ends at `x + k - 1`, not `x + k`.
```
Overview: Place one fixed-length carpet over nonoverlapping white-tile intervals and return the maximum number of covered integer positions.
