Obstacle Placement Queries
Reported by candidates from Hudson River Trading's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
The detail that matters in this Hudson River Trading OA, reported September 2026, is the block that ends at x - 1 and covers x - size through x - 1. Obstacles get added over time, and queries ask whether a range is clear. It looks like a range-check problem, and it is. If you're taking it in the next day or two, the job is picking a structure that handles inserts and range queries fast. Brute force will bite you on large inputs. StealthCoder sits invisibly on your screen as a safety net if you blank on the structure mid-assessment.
The problem
You are given an infinite integer number line and an array operations. Process the operations in order while maintaining the coordinates that contain obstacles. [1, x]: Place an obstacle at coordinate x. Coordinate x is guaranteed to contain no obstacle when this operation is performed. [2, x, size]: Check whether a block of length size can end immediately before coordinate x. The block would occupy every integer coordinate from x - size through x - 1. Append '1' to the answer if none of those coordinates contains an obstacle; otherwise append '0'. This operation only checks feasibility and does not place the block. Return the binary string formed by the results of all type-2 operations in their original order. Function solution(operations: int[][]) → String Examples Example 1 operations = [[1,2],[1,5],[2,5,2],[2,6,3],[2,2,1],[2,3,2]] return = "1010" Place obstacles at coordinates 2 and 5. The block before 5 covers 3 and 4, so append 1. The block before 6 covers 3, 4, and 5; coordinate 5 is blocked, so append 0. The block before 2 covers only coordinate 1, so append 1. The block before 3 covers coordinates 1 and 2; coordinate 2 is blocked, so append 0.
Reported by candidates. Source: FastPrep
Pattern and pitfall
The trick: a query is 1 exactly when no obstacle lies in [x - size, x - 1]. So you only need the largest obstacle strictly less than x. If that obstacle is below x - size, answer 1, else 0. That's a predecessor query on a dynamic set. Use a sorted set with binary search for the floor lookup, or a segment tree or Fenwick tree over coordinates if you compress them offline. Since the operations are all known upfront, offline coordinate compression works fine. Common pitfalls: off-by-one on the range (the end is x - 1, not x), and treating an obstacle at x itself as blocking. It doesn't. Also don't scan the range per query, that's O(size) each. If the sorted-set idea slips away under pressure, StealthCoder is the hedge for the live OA, reading the problem and handing you the structure.
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Obstacle Placement Queries FAQ
What's the trick in Obstacle Placement Queries?+
Reduce each check to one predecessor lookup. Find the largest obstacle strictly less than x. If it's less than x - size, the block fits and you append 1. Otherwise append 0. No range scanning needed.
Does an obstacle at x itself block the placement?+
No. The block covers x - size through x - 1 only. In the example, the block before 5 with size 2 covers 3 and 4, so the obstacle at 5 doesn't matter and the answer is 1.
What data structure should I use?+
A sorted set with floor lookup is the cleanest. In Python, use bisect on a sorted list, though insertion is linear. For guaranteed speed, compress coordinates offline and use a segment tree or Fenwick tree storing the max obstacle position.
How hard is this one really?+
Medium. The idea is short once you see the predecessor framing. The difficulty is spotting it quickly and avoiding off-by-one errors. A brute-force range scan passes small cases and fails big ones.
How do I prepare in 48 hours for a Hudson River Trading OA?+
Practice dynamic set problems: predecessor and successor queries, binary search on sorted lists, and basic segment trees. Write the solution once by hand and test it against the example string 1010. Edge cases matter: empty set, size larger than x, and negative coordinates.