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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Hailstone-sequence/Pure/hailstone-sequence.pure Normal file
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// 1. Create a routine to generate the hailstone sequence for a number.
type odd x::int = x mod 2;
type even x::int = ~odd x;
odd x = typep odd x;
even x = typep even x;
hailstone 1 = [1];
hailstone n::even = n:hailstone (n div 2);
hailstone n::odd = n:hailstone (3*n + 1);
// 2. Use the routine to show that the hailstone sequence for the number 27
// has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1
n = 27;
hs = hailstone n;
l = # hs;
using system;
printf
("the hailstone sequence for the number %d has %d elements " +
"starting with %s and ending with %s\n")
(n, l, __str__ (hs!!(0..3)), __str__ ( hs!!((l-4)..l)));
// 3. Show the number less than 100,000 which has the longest hailstone
// sequence together with that sequences length.
printf ("the number under 100,000 with the longest sequence is %d " +
"with a sequence length of %d\n")
(foldr (\ (a,b) (c,d) -> if (b > d) then (a,b) else (c,d))
(0,0)
(map (\ x -> (x, # hailstone x)) (1..100000)));