Data commit

Task/Hofstadter-Q-sequence/Jq/hofstadter-q-sequence-1.jq

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+# For n>=2, Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2))
+def Q:
+  def Q(n):
+    n as $n
+    | (if . == null then [1,1,1] else . end) as $q
+    | if $q[$n] != null then $q
+      else
+        $q | Q($n-1) as $q1
+        | $q1 | Q($n-2) as $q2
+        | $q2 | Q($n - $q2[$n - 1]) as $q3   # Q(n - Q(n-1))
+        | $q3 | Q($n - $q3[$n - 2]) as $q4   # Q(n - Q(n-2))
+        | ($q4[$n - $q4[$n-1]] + $q4[$n - $q4[$n -2]]) as $ans
+        | $q4 | setpath( [$n]; $ans)
+      end ;
+
+  . as $n | null | Q($n) | .[$n];
+
+# count the number of times Q(i) > Q(i+1) for 0 < i < n
+def flips(n):
+  (reduce range(3; n) as $n
+    ([1,1,1]; . + [ .[$n - .[$n-1]] + .[$n - .[$n - 2 ]] ] )) as $q
+  | reduce range(0; n) as $i
+      (0; . + (if $q[$i] > $q[$i + 1] then 1 else 0 end)) ;
+
+# The three tasks:
+((range(0;11), 1000) | "Q(\(.)) = \( . | Q)"),
+
+(100000 | "flips(\(.)) = \(flips(.))")

Task/Hofstadter-Q-sequence/Jq/hofstadter-q-sequence-2.jq

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+$ uname -a
+Darwin Mac-mini 13.3.0 Darwin Kernel Version 13.3.0: Tue Jun  3 21:27:35 PDT 2014; root:xnu-2422.110.17~1/RELEASE_X86_64 x86_64
+$ time jq -r -n -f hofstadter.jq
+Q(0) = 1
+Q(1) = 1
+Q(2) = 1
+Q(3) = 2
+Q(4) = 3
+Q(5) = 3
+Q(6) = 4
+Q(7) = 5
+Q(8) = 5
+Q(9) = 6
+Q(10) = 6
+Q(1000) = 502
+flips(100000) = 49798
+
+real	0m0.562s
+user	0m0.541s
+sys	0m0.011s