Foundry Transfer 12

Foundry Transfer 12 changes the context or constraint around standard algorithmic ideas. These are original Engineering Foundry instructional specifications - not employer questions and not additions to Foundry 75.

1. EF-T01

   Stable Case-Insensitive Label Groups

   Group ASCII labels by case-insensitive equality while preserving the first appearance of each group and the original spelling and order of every label.

   foundational · Separate a normalized lookup key from the original value retained in output. · Use insertion order deliberately instead of sorting groups after construction. · State the ASCII-only text contract and reject unsupported input rather than implying Unicode normalization.
2. EF-T02

   Earliest Longest Unique Event Range

   Return the earliest half-open range of maximum length whose event IDs are all distinct.

   intermediate · Maintain a variable window whose contents contain no duplicate event ID. · Use last-seen positions to move the left boundary forward without retreating. · Encode earliest-answer tie-breaking by updating only when a strictly longer range appears.
3. EF-T03

   Count Signed Target-Sum Ranges

   Count nonempty contiguous ranges whose signed integer total equals a target by matching current and earlier prefix totals.

   intermediate · Define prefix totals at boundaries so every nonempty range is a difference of two prefixes. · Use counts rather than one index because several earlier prefixes can produce different valid ranges. · Explain why negative values invalidate a positive-only sliding-window repair rule.
4. EF-T04

   Minimum Ordered Batch Capacity

   Partition positive item weights in order into at most a declared number of nonempty batches while minimizing the largest batch load.

   intermediate · Prove a greedy feasibility check for consecutive positive weights. · Prove that feasible capacities form a monotonic suffix before applying binary search. · Maintain inclusive search bounds whose upper endpoint is known feasible and account for wide totals.
5. EF-T05

   Fixed-window signal peaks

   Maintain the maximum signal value as a fixed-length observation window advances.

   intermediate · Store indices so expired candidates can be identified exactly. · Remove candidates dominated by a newer value under an explicit equal-value policy. · Explain why nested deque-removal loops are linear in aggregate.
6. EF-T06

   Earliest peak interval overlap

   Sweep half-open interval events to find peak simultaneous activity and where that peak first begins.

   intermediate · Translate half-open intervals into grouped coordinate deltas. · Apply all equal-coordinate starts and ends together so input order cannot change the answer. · Track the earliest coordinate only when a strictly larger positive peak is first reached.
7. EF-T07

   Earliest finishes in a dependency plan

   Combine topological ordering with a longest-prerequisite-chain dynamic program under unlimited parallel work.

   advanced · Normalize duplicate dependency edges before computing indegrees. · Interpret earliest start as the maximum finish time among direct prerequisites. · Detect cycles across disconnected components by comparing processed and declared task counts.
8. EF-T08

   Nearest declared grid exit

   Use breadth-first search to reach the nearest valid declared exit in a blocked rectangular grid.

   foundational · Model open grid cells and four-direction moves as an unweighted graph. · Mark cells visited when enqueued so every open cell enters the queue at most once. · Validate rectangular shape, binary cell values, start, and exits separately from unreachable-path output.
9. EF-T09

   Component count after each connection

   Maintain the number of connected components while undirected edges arrive, without decrementing for self-edges, repeats, or cycles.

   intermediate · Define representative and component-count state. · Apply path compression and union by size. · Treat an edge within one component as a no-op.
10. EF-T10

    Minimum spanning forest

    Compute the minimum total weight connecting each reachable undirected component while preserving disconnected components in the result contract.

    advanced · Define a spanning-forest objective for disconnected input. · Justify safe edge selection without accepting cycles. · Handle negative, tied, parallel, and self-loop edges.
11. EF-T11

    Minimum dictionary tokenization

    Find the fewest ASCII dictionary tokens that concatenate to the complete text, keeping choices open when a longer immediate token leads to a dead end.

    intermediate · Define a prefix DP state and unreachable sentinel. · Reject longest-token-first with a counterexample. · Deduplicate tokens without changing the result.
12. EF-T12

    Merge timestamped streams

    Merge already-sorted streams through a bounded heap frontier with deterministic timestamp, source, and within-source tie-breaking.

    intermediate · Maintain one frontier record per nonempty source. · Encode all observable tie-breakers in the heap key. · Validate the promised per-stream ordering contract.