Random Distinct Numbers Function | Dataford Interview Questions

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Ford Pro telemetry services need batches of distinct numeric identifiers for simulated vehicle events. Implement a function that returns count uniformly random, distinct integers from the inclusive range [start, end] without materializing the entire range.

The function must support an optional seed so tests and replayable simulations produce deterministic results. The output order should be random, and every valid subset of size count must have equal probability. Do not use random.sample or construct a list containing every value in the input range.

Formal Specification

Implement generate_distinct_numbers(start, end, count, seed=None).

Inputs are integers start, end, and count, plus an optional integer seed.
start <= end, and 0 <= count <= end - start + 1 are guaranteed for valid inputs.
Return a Python list containing exactly count distinct integers from [start, end].
Raise ValueError when the range is invalid or too small for count.
With the same inputs and seed, return the same sequence.

Constraints

-10^12 <= start <= end <= 10^12
0 <= count <= 10^5
count <= end - start + 1
The full numeric range may be too large to store in memory

Function Signature

def generate_distinct_numbers(start, end, count, seed=None):