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What’s a good way to keep track of intervals that you have already painted?
Create an array of all 1’s, and when you have painted an interval, set the values in that interval to 0.
Using this array, how can you quickly calculate the amount of new area that you paint on a given day?
Calculate the sum of the new array in the interval that you paint.
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Yes, interval management and range query problems similar to this one are common in FAANG-style interviews. They test knowledge of data structures like segment trees, ordered sets, and techniques for handling overlapping intervals.
Commonly used data structures include ordered sets, maps for interval merging, and segment trees for range queries and updates. These structures allow efficient detection of overlaps and quick updates when new intervals are painted.
The optimal approach typically uses an ordered set or interval map to track previously painted segments. By skipping already painted portions and merging intervals, the algorithm only counts newly painted areas efficiently. This avoids scanning each unit in the range.
The difficulty comes from handling overlapping intervals efficiently while avoiding repeated counting of painted areas. Large coordinate ranges make brute-force approaches impractical, so advanced data structures and interval management techniques are required.