Implement decay simulation and trailing-zero counting

Q: Implement decay simulation and trailing-zero counting

This Coding & Algorithms question for a Data Scientist role evaluates stochastic simulation and probability modeling for radioactive decay alongside combinatorics and number-theoretic reasoning for factorial trailing-zero computation, requiring implementation-level algorithmic thinking in Python.

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Question

Implement the following in Python:

Radioactive decay simulation: Half-life is 1 day. Write a simulation function that takes:
- input: integer m (number of days), integer n (number of atoms)
- process: simulate independent decay over time (you may model survival each day with probability 0.5, or equivalently sample each atom’s decay time)
- output: the final state of each particle (e.g., a boolean list/array of length n indicating survived/decayed after m days) and/or the number of survivors. Also discuss runtime and how you would validate correctness against the analytic Binomial(n, 0.5^m) result.
Factorial and trailing zeros:
- (a) Implement a factorial function in Python (mention multiple approaches).
- (b) Given an integer n , compute the number of trailing zeros in n! efficiently (better than computing n! explicitly).

Implement decay simulation and trailing-zero counting

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