How should I practice Rectangle Point Coverage Counts?

Start by reading the full statement, solve the visible examples, then compare the pattern against related OpenAI phone screen problems in FastPrep.

Is Rectangle Point Coverage Counts associated with OpenAI?

FastPrep tags this as a OpenAI phone screen coding practice problem when the problem catalog has that company and stage context.

Rectangle Point Coverage Counts

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Problem statement

Source note: This was the coding round of an OpenAI phone screen. The report names rectangles that each have an ID, a query that counts the rectangles at a point, and a way to remove a rectangle. Reads were the heavy case, so the target was a constant-time count, and the report writes the add and remove cost as O(U+1) without saying what U is. The question had a third part that the candidate did not finish, and the report does not say what it was.

The report gives no input format, coordinate model, limits or examples. Practice choices: rectangles sit on a grid of whole cells and cover their edge cells too. You get the calls as a list of operation strings and return only the count answers. Every call is valid, IDs are case-sensitive letters and digits, and a removed ID may be added again. We read U as the number of cells a rectangle covers, and the tests check answers only, not the time each operation takes. The limits and examples are ours. The unknown third part is not part of this problem.

The judged task matches the report at about 60%.

You are given a grid of cells that is width cells wide and height cells tall. Cell (x, y) is in column x and row y, where 0 <= x < width and 0 <= y < height. At the start, the grid holds no rectangles.

Process the strings in operations in order. Each one is one of these:

"ADD id x1 y1 x2 y2": add a rectangle named id. It covers every cell (x, y) with x1 <= x <= x2 and y1 <= y <= y2, so its corner and edge cells are covered too.
"REMOVE id": remove the rectangle named id. It no longer covers any cell.
"COUNT_AT x y": count how many rectangles currently in the grid cover cell (x, y).

Rectangles may overlap, and two rectangles may cover exactly the same cells. Each one counts on its own. IDs are case-sensitive, so a and A are different IDs. Once a rectangle is removed, its id is free again, and a later ADD may use it for a new rectangle.

The problem statement continues

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Examples

Example 1

width = 5height = 4operations = ["ADD a 0 0 2 1","ADD b 1 1 4 3","COUNT_AT 1 1","COUNT_AT 2 0","COUNT_AT 4 3","COUNT_AT 0 3","REMOVE a","COUNT_AT 1 1"]return = [2,1,1,0,1]

Rectangle a covers columns 0 to 2 of rows 0 and 1. Rectangle b covers columns 1 to 4 of rows 1 to 3.

Cell (1, 1) is inside both rectangles, so the answer is 2.
Cell (2, 0) is inside a only, because b starts at row 1. The answer is 1.
Cell (4, 3) is the far corner of b. Corner cells are covered, so the answer is 1.
Cell (0, 3) is in neither rectangle, so the answer is 0.
After REMOVE a, only b covers cell (1, 1), so the answer is 1.

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