API tools faq
paste
Guest User

Untitled

a guest
Oct 20th, 2017
388
0
Never
Add comment
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 7.31 KB | None | 0 0
raw download clone embed print report
  1. A(0,n) = n+1
  2. A(m,0) = A(m-1,1)
  3. A(m,n) = A(m-1,A(m,n-1))
  4.  
  5. A | n=0 1 2 3 4 5 6 7 8 9 10
  6. -----+-----------------------------------------------------------------
  7. m=0 | 1 2 3 4 5 6 7 8 9 10 11
  8. 1 | 2 3 4 5 6 7 8 9 10 11 12
  9. 2 | 3 5 7 9 11 13 15 17 19 21 23
  10. 3 | 5 13 29 61 125 253 509 1021 2045 4093 8189
  11. 4 | 13 65533 big really big...
  12.  
  13. DaGHR?atG?aGtHH1GhH
  14.  
  15. $ time pyth -c "DaGHR?atG?aGtHH1GhH ;a 3 10"
  16. 8189
  17.  
  18. real 0m0.092s
  19. user 0m0.088s
  20. sys 0m0.000s
  21.  
  22. DaGH def a(G,H):
  23. R return
  24. ? G (if G:
  25. atG (a(G-1,
  26. ? H (if H:
  27. aGtH a(G,H-1)
  28. 1 else:1)
  29. hH else:H+1)
  30.  
  31. a 0=(1+)
  32. a m=(iterate(a$m-1)1!!)
  33.  
  34. {1$1>{1){1$(A}*;}{+)}if}:A;
  35.  
  36. { # Function boilerplate
  37. 1$ # Get a copy of m: stack holds m n m
  38. 1>{ # (Optimisation): if m is greater than 1
  39. 1 # Take this as the value of A(m, -1)
  40. ){ # Repeat n+1 times:
  41. # Stack: m A(m, i-1)
  42. 1$( # Stack: m m-1 A(m, i-1)
  43. A # Stack: m A(m, i)
  44. }*
  45. ; # Lose that unwanted copy of m
  46. }{ # Else
  47. +) # A(m in {0, 1}, n) = m + n + 1
  48. }if
  49. }:A; # Function boilerplate
  50.  
  51. A=lambda m,n:m and A(m-1,n<1or A(m,n-1))or-~n
  52.  
  53. A=lambda m,n:n+(m<1or A(m-1,n<1or A(m,n-1))-n)
  54.  
  55. A(m,n){return!m?n+1:A(m-1,n?A(m,n-1):1);}
  56.  
  57.  
  58. int main()
  59. {
  60. int m,n;
  61. for(m = 0; m <= 3; m++)
  62. for(n = 0; n <= 10; n++)
  63. printf("%d %d %dn", m,n,A(m,n));
  64. return 0;
  65. }
  66.  
  67. f=(m,n)=>m?f(m-1,!n||f(m,n-1)):n+1
  68.  
  69. f(3,2) // returns 29
  70.  
  71. ($:^:(<:@[`]`1:)^:(0<[)>:)
  72.  
  73. Ack 0 n = n+1
  74. Ack m n = Iter (Ack (m-1)) n
  75. Iter f 0 = f 1
  76. Iter f n = f (Iter f (n-1))
  77.  
  78. ( >:) NB. increment n
  79. ^:(0<[) NB. if m=0, do nothing to n+1; else:
  80. ^: NB. iterate...
  81. ($: ) NB. self ($: is recursion)
  82. (<:@[ ) NB. with left arg m-1
  83. `] NB. n+1 times
  84. `1: NB. starting on 1
  85.  
  86. 3 ($:^:(<:@[`]`1:)^:(0<[)>:) 3
  87. 61
  88. ack =: ($:^:(<:@[`]`1:)^:(0<[)>:)
  89. (i.4) ack"0 table (i.11)
  90. +-----+------------------------------------------+
  91. |ack"0|0 1 2 3 4 5 6 7 8 9 10|
  92. +-----+------------------------------------------+
  93. |0 |1 2 3 4 5 6 7 8 9 10 11|
  94. |1 |2 3 4 5 6 7 8 9 10 11 12|
  95. |2 |3 5 7 9 11 13 15 17 19 21 23|
  96. |3 |5 13 29 61 125 253 509 1021 2045 4093 8189|
  97. +-----+------------------------------------------+
  98. 6!:2 '3 ($:^:(<:@[`]`1:)^:(0<[)>:) 10' NB. snugly fits in a minute
  99. 58.5831
  100.  
  101. (0&<~(<:@#~$:/@,1:^:)>:)
  102.  
  103. nat_rec _ S(fun _ b n=>nat_iter(S n)b 1)
  104.  
  105. Welcome to Coq 8.4pl6 (November 2015)
  106.  
  107. Coq < Compute nat_rec _ S(fun _ b n=>nat_iter(S n)b 1) 3 10.
  108. = 8189
  109. : nat
  110.  
  111. 00000000: 1607 2d88 072f 68 ..-../h
  112.  
  113. 000101100000011100101101100010000000011100101111011010
  114.  
  115. (define(a m n)(if(= m 0)(+ n 1)(a(- m 1)(if(= n 0)1(a m(- n 1))))))
  116.  
  117. 0~a~n_:=n+1
  118. m_~a~n_:=a[m-1,If[n<1,1,a[m,n-1]]]
  119.  
  120. $RecursionLimit = Infinity
  121.  
  122. A=(m,n)=>m?A(m-1,n?A(m,n-1):1):n+1
  123.  
  124. (d A
  125. (q( (m n)
  126. (i m
  127. (i n
  128. (A (s m 1)
  129. (A m
  130. (s n 1)
  131. )
  132. )
  133. (A (s m 1)
  134. 1
  135. )
  136. )
  137. (s n
  138. (s 0 1)
  139. )
  140. )
  141. ) )
  142. )
  143.  
  144. func (m,n int)int{r:=0
  145. switch{case m==0&&n!=0:r=n+1
  146. case m!=0&&n==0:r=a(m-1,1)
  147. case m!=0&&n!=0:r=a(m-1,a(m,n-1))}
  148. return r}
  149.  
  150. $ time go run ack
  151. 16381
  152. real 0m1.434s
  153. user 0m1.432s
  154. sys 0m0.004s
  155.  
  156. a::Int->Int->Int
  157. a 0 n=n+1
  158. a m 0=a (m-1) 1
  159. a m n=a (m-1) a m (n-1)
  160.  
  161. a=function(m,n){"if"(m,a(m-1,"if"(n,a(m,n-1),1)),n+1)}
  162.  
  163. > a(3,8)
  164. [1] 2045
  165.  
  166. DECLARE @m INT=4,@n INT=1;WITH R AS(SELECT 2 C, 1 X UNION ALL SELECT POWER(2,C),X+1FROM R)SELECT IIF(@m=0,@n+1,IIF(@m=1,@n+2,IIF(@m=2,2*@n+3,IIF(@m=3,POWER(2,@n+3)-3,IIF(@m=4,(SELECT TOP(1)C FROM R WHERE x= @n+3)-3,-1)))))
  167.  
  168. M?GgtG?HgGtH1hH
  169.  
  170. iiRuldr%l%lR$d%rd:u%d:%+uRu:ro
  171.  
  172. >:@]`(1$:~<:@[)`(<:@[$:[$:_1+])@.(0>.[:<:@#.,&*)M.
  173.  
  174. A=:>:@]`(1$:~<:@[)`(<:@[$:[$:_1+])@.(0>.[:<:@#.,&*)M.
  175. timespacex 'res=:(i.4) A"0 table (i.11)'
  176. 0.0336829 3.54035e6
  177. res
  178. ┌───┬──────────────────────────────────────────┐
  179. │A"0│0 1 2 3 4 5 6 7 8 9 10│
  180. ├───┼──────────────────────────────────────────┤
  181. │0 │1 2 3 4 5 6 7 8 9 10 11│
  182. │1 │2 3 4 5 6 7 8 9 10 11 12│
  183. │2 │3 5 7 9 11 13 15 17 19 21 23│
  184. │3 │5 13 29 61 125 253 509 1021 2045 4093 8189│
  185. └───┴──────────────────────────────────────────┘
  186.  
  187. {⍺=0:⍵+1⋄⍵=0:1∇⍨⍺-1⋄(⍺-1)∇⍺∇⍵-1}
  188.  
  189. $Y1%j:j.0=m:2%k:k.0=n:m.n.>[k.1+!|m.n.<[#Y,j.1-,1;|m.n.*0=[#Y,j.1-,#Y,j.,k.1+;;]]]@
  190.  
  191. import java.math.*;class a{BigInteger A(BigInteger b,BigInteger B){if(b.equals(BigInteger.ZERO))return B.add(BigInteger.ONE);if(B.equals(BigInteger.ZERO))return A(b.subtract(BigInteger.ONE),BigInteger.ONE);return A(b.subtract(BigInteger.ONE),A(b,B.subtract(BigInteger.ONE)));}}
  192.  
  193. proc A m n {expr {$m?[A [expr $m-1] [expr {$n?[A $m [expr $n-1]]:1}]]:$n+1}}
  194.  
  195. m=0, n=0, A=1, time=3.5e-5 seconds
  196. m=0, n=1, A=2, time=2e-6 seconds
  197. m=0, n=2, A=3, time=8e-6 seconds
  198. m=0, n=3, A=4, time=1e-6 seconds
  199. m=0, n=4, A=5, time=2e-6 seconds
  200. m=0, n=5, A=6, time=1e-6 seconds
  201. m=0, n=6, A=7, time=1e-6 seconds
  202. m=0, n=7, A=8, time=1e-6 seconds
  203. m=0, n=8, A=9, time=1e-6 seconds
  204. m=0, n=9, A=10, time=0.0 seconds
  205. m=0, n=10, A=11, time=1e-6 seconds
  206. m=1, n=0, A=2, time=4e-6 seconds
  207. m=1, n=1, A=3, time=6e-6 seconds
  208. m=1, n=2, A=4, time=1e-5 seconds
  209. m=1, n=3, A=5, time=1.2e-5 seconds
  210. m=1, n=4, A=6, time=1.5e-5 seconds
  211. m=1, n=5, A=7, time=2e-5 seconds
  212. m=1, n=6, A=8, time=2e-5 seconds
  213. m=1, n=7, A=9, time=2.6e-5 seconds
  214. m=1, n=8, A=10, time=3e-5 seconds
  215. m=1, n=9, A=11, time=3e-5 seconds
  216. m=1, n=10, A=12, time=3.3e-5 seconds
  217. m=2, n=0, A=3, time=8e-6 seconds
  218. m=2, n=1, A=5, time=2.2e-5 seconds
  219. m=2, n=2, A=7, time=3.9e-5 seconds
  220. m=2, n=3, A=9, time=6.3e-5 seconds
  221. m=2, n=4, A=11, time=9.1e-5 seconds
  222. m=2, n=5, A=13, time=0.000124 seconds
  223. m=2, n=6, A=15, time=0.000163 seconds
  224. m=2, n=7, A=17, time=0.000213 seconds
  225. m=2, n=8, A=19, time=0.000262 seconds
  226. m=2, n=9, A=21, time=0.000316 seconds
  227. m=2, n=10, A=23, time=0.000377 seconds
  228. m=3, n=0, A=5, time=2.2e-5 seconds
  229. m=3, n=1, A=13, time=0.000145 seconds
  230. m=3, n=2, A=29, time=0.000745 seconds
  231. m=3, n=3, A=61, time=0.003345 seconds
  232. m=3, n=4, A=125, time=0.015048 seconds
  233. m=3, n=5, A=253, time=0.059836 seconds
  234. m=3, n=6, A=509, time=0.241431 seconds
  235. m=3, n=7, A=1021, time=0.971836 seconds
  236. m=3, n=8, A=2045, time=3.908884 seconds
  237. m=3, n=9, A=4093, time=15.926341 seconds
  238. m=3, n=10, A=8189, time=63.734713 seconds
Add Comment
Please, Sign In to add comment
Public Pastes
We use cookies for various purposes including analytics. By continuing to use Pastebin, you agree to our use of cookies as described in the Cookies Policy.  OK, I Understand
Not a member of Pastebin yet?
Sign Up, it unlocks many cool features!