32 lines
1.4 KiB
APL
32 lines
1.4 KiB
APL
⍝ Determine whether given list of integers has GCD = 1
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primitive←∧/1=2∨/⊢
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⍝ Filter list given as right operand by applying predicate given as left operand
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filter←{⍵⌿⍨⍺⍺ ⍵}
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⍝ Function pytriples finds all triples given a maximum perimeter
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∇res←pytriples maxperimeter;sos;sqrt;cartprod;ascending;ab_max;c_max;a_b_pairs;sos_is_sq;add_c;perimeter_rule
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⍝ Input parameter maxperimeter is the maximum perimeter
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⍝ Sum of squares of given list of nrs
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sos←+/(×⍨⊢)
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⍝ Square root
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sqrt←(÷2)*⍨⊢
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⍝ (cartesian product) all possible pairs of integers
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⍝ from 1 to ⍵
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cartprod←{,{⍺∘.,⍵}⍨⍳⍵}
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⍝ Predicate: are values in given list ascending
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⍝ Given e.g. pair a, b, c: is a ≤ b ≤ c?
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ascending←∧/2≤/⊢
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ab_max←⌊maxperimeter÷2
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c_max←⌈maxperimeter×sqrt 2
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⍝ Selects from all a,b combinations (a<abmax, b<abmax)
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⍝ only those pairs where a ≤ b.
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a_b_pairs←ascending filter¨cartprod(ab_max)
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⍝ Predicate: is the sum of squares of a and b
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⍝ itself a square? (does it occur in the squares list)
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sos_is_sq←{{⍵≠1+c_max}(×⍨⍳c_max)⍳sos¨⍵}
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⍝ Given a pair a,b add corresponding c to form a triple
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add_c←{⍵,sqrt sos ⍵}
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⍝ Predicate: sum of items less than or equal to max
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perimeter_rule←{maxperimeter≥+/⍵}
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res←perimeter_rule¨filter add_c¨sos_is_sq filter a_b_pairs
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∇
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