Enumerate by the hypotenuse and test finitely many shorter legs:
primitiveTriples :: [(Integer, Integer, Integer)]
primitiveTriples =
  [(a, b, c) |
     c <- [1..],
     b <- [1..c-1],
     a <- [1..b-1],
     a*a + b*b == c*c,
     gcd a (gcd b c) == 1]
The equality selects Pythagorean triples, and the greatest common divisor test makes them primitive. The bounds enforce , removing the duplicate obtained by exchanging the legs. Each fixed has a finite search, so the outer loop gives ascending hypotenuse order and reaches every qualifying triple. Infinite families supplied by Euclid's formula ensure that the stream has arbitrarily many outputs. Its first five entries are
[(3,4,5),(5,12,13),(8,15,17),(7,24,25),(20,21,29)]
Using Integer avoids overflow in the squared values. The construction prioritizes a direct correctness argument; it does not claim an optimal enumeration cost.

Ancestors (11)

  1. 4
  2. Functional programming, design and analysis of algorithms
  3. 2015
  4. Past exam of the year 1 of the computer science course of the University of Oxford
  5. Year 1 of the computer science course of the University of Oxford
  6. Computer science course of the University of Oxford
  7. Undergraduate course of the University of Oxford
  8. Course of the University of Oxford
  9. University of Oxford
  10. List of universities
  11. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version