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-- Perl Weekly Challenge 159
CREATE SCHEMA IF NOT EXISTS pwc159;
CREATE OR REPLACE FUNCTION
pwc159.farey_not_unique( n int )
RETURNS TABLE( f text, v numeric )
AS $CODE$
DECLARE
numerator int;
denominator int;
dd int;
nn int;
BEGIN
-- bootstrap term
SELECT '0/1', 0
INTO f, v;
RETURN NEXT;
FOR denominator IN 2 .. n LOOP
FOR numerator IN 1 .. denominator LOOP
nn := numerator;
dd := denominator;
IF dd % nn = 0 THEN
dd := dd / nn;
nn := 1;
END IF;
IF nn % dd = 0 THEN
nn := nn / dd;
dd := 1;
END IF;
IF nn / dd = 1 THEN
CONTINUE;
END IF;
SELECT nn || '/' || dd, nn/dd::numeric
INTO f, v;
RETURN NEXT;
END LOOP;
END LOOP;
-- end term
SELECT '1/1', 1
INTO f, v;
RETURN NEXT;
RETURN;
END
$CODE$
LANGUAGE plpgsql;
WITH farey AS (
SELECT distinct( f ), v
FROM pwc159.farey_not_unique( 5 )
ORDER BY v
)
SELECT f
FROM farey;
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