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Longest Contiguous Subarray Problem

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Problem

Coalition's risk-processing pipeline receives an array of integer event scores. Find the length of the longest contiguous subarray in which every value is a qualifying prime.

A value qualifies when it is non-negative, prime, and either even or happy. A happy number eventually reaches 1 when repeatedly replaced by the sum of the squares of its decimal digits. Values that enter the cycle 4, 16, 37, 58, 89, 145, 42, 20 are not happy.

Because a qualifying run must contain only valid values, scan the array and track the current run length, resetting it whenever a value fails the predicate. The input values can be as large as unsigned 64-bit integers, so use deterministic Miller-Rabin primality testing rather than trial division through the square root.

Formal Specification

Implement longest_happy_prime_run(nums), where nums is a list of integers. Return an integer representing the maximum length of a contiguous subarray whose values all qualify. Return 0 when no value qualifies.

Constraints

  • 0 <= len(nums) <= 10^5
  • -10^18 <= nums[i] < 2^64
  • A number qualifies if it is prime and either even or happy
  • Return 0 when no value qualifies

Function Signature

def longest_happy_prime_run(nums):
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