Maximum White Tiles Covered by a Carpet LeetCode solution in Python

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class Solution:
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    def maximumWhiteTiles(self, tiles: List[List[int]], carpetLen: int) -> int:
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        tiles.sort()
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        # j: window index
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        j = cover = res = 0
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        for i in range(len(tiles)):
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            # slide the window as far as we can to cover fully the intervals with the carpet
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            while j < len(tiles) and tiles[j][1] - tiles[i][0] + 1 <= carpetLen:
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                cover += tiles[j][1] - tiles[j][0] + 1
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                j += 1
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            # process the remnant, that is, when the tiles[j] is covered by the carpet partially(not fully)
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            if j < len(tiles) and tiles[j][0] - tiles[i][0] + 1 <= carpetLen:
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                res = max(res, cover + carpetLen - (tiles[j][0] - tiles[i][0]))
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            else:
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                res = max(res, cover)
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            # when the tiles[j] is covered partially, the interval is not added to the variable cover
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            if i != j:
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                cover -= tiles[i][1] - tiles[i][0] + 1
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            j = max(j, i + 1)
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        return res