Fix solution edge cases and recursion failures

[Achal13jain]

Summary

• fix the prime sieve for n < 2 and add boundary handling across core solutions
• replace recursion-limit-prone graph and tree implementations with iterative traversals
• prevent accidental caller-input mutation in sorting and histogram solutions
• repair the standalone Sum of Beauty API and remove import-time demo output
• add regression coverage for deep inputs, empty inputs, cycles, and mutation

Verification

• 31 unit tests pass
• all solution scripts execute successfully
• more than 78,000 randomized/exhaustive reference comparisons completed during the audit