Optiver·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Optiver SWE interview, got a cargo allocation problem that looked like a clean simulation at first but the constraints basically forced you to think about efficient data structures or you'd TLE on the big cases. Pretty gnarly for a single coding round.

Questions Asked (1)

You have a fixed fleet of cargo planes, each with a departure time and a capacity. Orders arrive one by one, each with a timestamp and a total cargo size. An order can only use planes that depart strictly after the order's timestamp. If the eligible planes have enough combined remaining capacity, accept the order and greedily fill planes in ascending departure order (ties broken by index); otherwise reject it with no state change. Return the allocation for each order. Aim for roughly O((n + m) log n) overall.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

My first instinct was just sort the planes once and for each order binary search for the eligible subset, then iterate through filling greedily.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases, then propose an efficient data structure solution that maintains planes sorted by departure time and supports range capacity queries and updates. Explain how to use a segment tree or Fenwick tree with binary search to achieve O((n + m) log n) time, and discuss trade-offs with simpler approaches.

Pro tip: Emphasize that the greedy allocation is optimal because filling earliest-departing planes first preserves later planes for future orders, and mention that using a segment tree with lazy propagation or a Fenwick tree with binary lifting can efficiently find the first plane with remaining capacity.

1. Clarify requirements and constraints

Ask about input sizes, whether orders are processed in timestamp order, and if planes can be partially filled. Confirm that ties in departure time are broken by index.

2. Design data structures

Propose maintaining planes in a segment tree keyed by departure time, storing remaining capacity. Support queries for total capacity after a timestamp and updates when capacity is consumed.

3. Outline algorithm for each order

For each order, query total remaining capacity of planes departing after the order's timestamp. If insufficient, reject. Otherwise, greedily allocate by repeatedly finding the earliest-departing plane with remaining capacity and filling it until the order is satisfied.

4. Analyze complexity

Explain that each order requires O(log n) for the capacity query and O(k log n) for allocations, where k is the number of planes used. Since each plane can be filled at most once per order, total allocations across all orders is O(n + m), yielding O((n + m) log n).

5. Discuss trade-offs and alternatives

Mention simpler O(nm) approaches and why they are inefficient. Compare segment tree vs. Fenwick tree with binary lifting, and note that a balanced BST with subtree sums could also work.

Key Points to Mention

Greedy allocation is optimal because using earliest-departing planes first leaves later planes available for future orders.
Segment tree or Fenwick tree can efficiently maintain remaining capacities and support range sum queries and point updates.
Binary search on the segment tree (or binary lifting on Fenwick) finds the first plane with remaining capacity in O(log n).
Total number of plane fill operations across all orders is bounded by O(n + m) because each plane is filled at most once per order, and once full it is never used again.
Edge cases: orders with no eligible planes, orders that exactly match capacity, and ties in departure times.
The overall time complexity is O((n + m) log n) and space complexity is O(n + m) for storing planes and allocations.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.