89 lines
2.4 KiB
Plaintext
89 lines
2.4 KiB
Plaintext
# rotate 90 deg
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r ← ⍉≡⇌
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# create spiral numbers with n rows and cols
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# spiral ? n
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s ← (
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+1⇡ⁿ2 # create n^2 numbers
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⊸(
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⊸(-1×2√/↥) # t*2 - 1, where t = sqrt(max(range(n^2))) = n
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⌈÷2↙ # create [1 1 2 2 3 ...] until sum is n^2
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)
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⊜□˜▽+1°⊏ # successively take 1, 1, 2, 2, 3, ... until all n^2 numbers taken
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⇌/◇(˜⊂r)⍜⊢⍚¤ # combine all taken with rotating array to form spiral
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)
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# memoized recursive version of s
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σ ← |1 memo(
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⨬(⊂⊸(++1⇡∩/↥⊃△(⊢⊢)) r σ-1
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| ⋅(¤[1]) # base-case
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)⊸=1
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)
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# generates each diagonal of spiral array
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Σ ← +1\+ +¤[2 4 6]×8 ⇡⌊÷2
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# get numbers on diagonal
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d ← ⊜°¤ ↥⊸r⊞=. °⊏
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# is_prime(n) ? n
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p ← =1⧻°/×
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┌─╴test
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p ↚ ⊜(⊜⋕⊸≠@\s)⊸≠@\n
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⍤⤙≍ s 7 p $ 37 36 35 34 33 32 31
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$ 38 17 16 15 14 13 30
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$ 39 18 5 4 3 12 29
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$ 40 19 6 1 2 11 28
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$ 41 20 7 8 9 10 27
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$ 42 21 22 23 24 25 26
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$ 43 44 45 46 47 48 49
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└─╴
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Sol! ← +1×2⧻⍢(+2⟜(÷⊃⧻/+≡p ^0)|⋅(>0.1)) ⊙1
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# Sol!(d s) 3 # too slow
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# (σ -1×2) == s
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# Sol!(d σ -1×2) 3 # too slow (too much memory usage)
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# Sol!(⊂˜↯1÷2-1⟜(♭ Σ)) 3 # still too slow
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# okay... let's do it mathematically from scratch:
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# primes on diagonals/number of elements on diagonals
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# Chance ← ÷-1×2⟜(
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# ⊃((+5+∩×₄⊃×₂ⁿ₂)⇡
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# | (+3+⊃×₆(×4ⁿ2))⇡
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# | (+7+⊃×₁₀(×4ⁿ2))⇡
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# ) ⌊÷2
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# /+≡p⊂⊂
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# )
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#
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# ⍢(+2|>0.1 Chance) 3
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# that solved it in 4 minutes (with p memoized)... too slow!
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NewP ← (
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# get the next three prime candidates (lower right is odd square)
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⊃((+5+∩×₄⊃×₂ⁿ₂)
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| (+3+⊃×₆(×4ⁿ2))
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| (+7+⊃×₁₀(×4ⁿ2))
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)
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++∩₃p # count how many are prime (0-3)
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)
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# initial values are:
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# - 5: the amount of numbers so far; 1, 3, 5, 7, 9 (counter for diagonal)
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# - NewP.: = 3, since 3, 5, 7 are prime (counter for primes on diagonal)
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# - 0: current NewP generation. NewP 0 is 3 (see above)
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5 NewP. 0
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⍢(+4 ⊙+ ⊙⊙(⊸NewP+1) # add 4 for new corners, generate NewP(n+1)
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| >0.1 ÷ # check prime ratio
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)
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# discard number of primes and diagonal values,
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# scale generation up to side length
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# newp gen 0 -> 0*2 + 3 = side length 3
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# newp gen 1 -> 1*2 + 3 = side length 5, ...
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⋅⋅(+3×2)
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# that's a 240x speedup, from 4 minutes to 1 second. we can go faster...
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