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Prime Tables

  • How to run the test suite

    • ruby -Itest tests/all_tests.rb

  • How to run the service from irb

    • require './primes.rb'
    • require './print_grid.rb'
    • Primes.new.process(50) 
      => [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
    • puts PrintGrid.new.process(4) 
      |       |     2 |     3 |     5 |     7 |
|     2 |     4 |     6 |    10 |    14 |
|     3 |     6 |     9 |    15 |    21 |
|     5 |    10 |    15 |    25 |    35 |
|     7 |    14 |    21 |    35 |    49 |

  • What I'm pleased with

    • The modular approach the code was built

  • What would I do if I had more time?

    • Implement memoization/caching for prime calculation and grid building

  • Overall thought process

    • (0) Find optimal algorithm

      • Sqrt method T(n) = O(√ n) S(n) = S(n)
      • Recursion T(n) = O(n) S(n) = S(n)
      • Fermat's Theorem T(n) = O(n) S(n) = S(n) Interesting case here. If the problem was to strictly find the the prime number, then we could find the solution in O(1) using this algorithm, but since we are concerned with the grid of numbers up to n, this doesn't help us much.
      • Sieve of Eratosthenes T(n) = O(n*log(log(n))) S(n) = O(n) https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

      Sieves

    • (1) Implement algorithm

    • (2) Print (n+1)X(n+1) grid of numbers

    • (3) Memoize values, so that we don't redo the work when multiple calls are made ❌