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Task/Hofstadter-Q-sequence/ERRE/hofstadter-q-sequence.erre

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+PROGRAM HOFSTADER_Q
+
+!
+! for rosettacode.org
+!
+
+DIM Q%[10000]
+
+PROCEDURE QSEQUENCE(Q,FLAG%->SEQ$)
+! if FLAG% is true accumulate sequence in SEQ$
+! (attention to string var lenght=255)
+! otherwise calculate values in Q%[] only
+
+  LOCAL N
+  Q%[1]=1
+  Q%[2]=1
+  SEQ$="1 1"
+  IF NOT FLAG% THEN Q=NUM END IF
+  FOR N=3 TO Q DO
+    Q%[N]=Q%[N-Q%[N-1]]+Q%[N-Q%[N-2]]
+    IF FLAG% THEN SEQ$=SEQ$+STR$(Q%[N]) END IF
+  END FOR
+END PROCEDURE
+
+BEGIN
+  NUM=10000
+  QSEQUENCE(10,TRUE->SEQ$)
+  PRINT("Q-sequence(1..10) : ";SEQ$)
+  QSEQUENCE(1000,FALSE->SEQ$)
+  PRINT("1000th number of Q sequence : ";Q%[1000])
+  FOR N=2 TO NUM DO
+    IF Q%[N]<Q%[N-1] THEN NN+=1 END IF
+  END FOR
+  PRINT("Number of Q(n)<Q(n+1) for n<=10000 : ";NN)
+END PROGRAM

Task/Hofstadter-Q-sequence/EchoLisp/hofstadter-q-sequence.echolisp

@@ -0,0 +1,23 @@
+(define RECURSE_BUMP 500) ;; minimum of chrome:500 safari:1000 firefox:2000
+
+;; count flips
+(define (flips N)
+	(for/sum ((n (in-range 2 (1+ N))))
+	#:when (< (Q n) (Q (1- n)))  1))
+		
+(cache-size 120000)
+(define (Q n)
+	;; prevent browser stack overflow at low-cost
+	(when (zero? (modulo n RECURSE_BUMP)) (for ((i (in-range 0 n RECURSE_BUMP ))) (Q i)))
+	(+ (Q (- n (Q (1- n)))) (Q (- n (Q (- n 2))))))
+(remember 'Q #(1 1 1)) ;; memoize and init
+
+
+;; first call : check stack OK
+(Q 100000) → 48157
+
+(for ((i 11)) (write (Q i)))
+1 1 1 2 3 3 4 5 5 6 6
+
+(Q 1000)  → 502
+(flips 100000) → 49798

Task/Hofstadter-Q-sequence/Nim/hofstadter-q-sequence.nim

@@ -0,0 +1,14 @@
+var q = @[1, 1]
+for n in 2 .. <100_000: q.add q[n-q[n-1]] + q[n-q[n-2]]
+
+echo q[0..9]
+assert q[0..9] == @[1, 1, 2, 3, 3, 4, 5, 5, 6, 6]
+
+echo q[999]
+assert q[999] == 502
+
+var lessCount = 0
+for n in 1 .. <100_000:
+  if q[n] < q[n-1]:
+    inc lessCount
+echo lessCount

Task/Hofstadter-Q-sequence/Oforth/hofstadter-q-sequence.oforth

@@ -0,0 +1,8 @@
+: QSeqTask
+| q i |
+   ListBuffer newSize(100000) dup add(1) dup add(1) ->q
+   0 3 100000 for: i [
+      q add(q at(i q at(i 1-) -) q at(i q at(i 2 -) -) +)
+      q at(i) q at(i 1-) < ifTrue: [ 1+ ]
+      ]
+   q left(10) println q at(1000) println println ;

Task/Hofstadter-Q-sequence/Ring/hofstadter-q-sequence.ring

@@ -0,0 +1,8 @@
+n = 20
+aList = list(n)
+aList[1] = 1
+aList[2] = 1
+for i = 1 to n
+    if i >= 3 aList[i] = ( aList[i - aList[i-1]] + aList[i - aList[i-2]] ) ok
+    if i <= 20 see "n = " + string(i) + " : "+ aList[i] + nl ok
+next

Task/Hofstadter-Q-sequence/Sidef/hofstadter-q-sequence-1.sidef

@@ -0,0 +1,8 @@
+func Q(n) is cached {
+    n <= 2 ? 1
+           : Q(n - Q(n-1))+Q(n-Q(n-2))
+}
+
+say "First 10 terms: #{10.of {|n| Q(n) }.dump }"
+say "Term 1000: #{Q(1000)}"
+say "Terms less than preceding in first 100k: #{2..100000->count{|i|Q(i)<Q(i-1)}}"

Task/Hofstadter-Q-sequence/Sidef/hofstadter-q-sequence-2.sidef

@@ -0,0 +1,8 @@
+var Q = [0, 1, 1];
+100_000.times {
+    Q << (Q[-Q[-1]] + Q[-Q[-2]])
+}
+
+say "First 10 terms: #{Q.ft(1, 10).dump}"
+say "Term 1000: #{Q[1000]}"
+say "Terms less than preceding in first 100k: #{2..100000->count{|i|Q[i]<Q[i-1]}}"

Task/Hofstadter-Q-sequence/Visual-FoxPro/hofstadter-q-sequence.visual

@@ -0,0 +1,28 @@
+LOCAL p As Integer, i As Integer
+CLEAR
+p = 0
+? "Hofstadter Q Sequence"
+? "First 10 terms:"
+FOR i = 1 TO 10
+	?? Q(i, @p)
+ENDFOR	
+? "1000th term:", Q(1000, @p)
+? "100000th term:", q(100000, @p)
+? "Number of terms less than the preceding term:", p
+
+FUNCTION Q(n As Integer, k As Integer) As Integer
+LOCAL i As Integer
+LOCAL ARRAY aq[n]
+aq[1] = 1
+IF n > 1
+    aq[2] = 1
+ENDIF	
+k = 0
+FOR i = 3 TO n
+    aq[i] = aq[i - aq[i-1]] + aq[i-aq[i-2]]
+    IF aq(i) < aq(i-1)
+    	k = k + 1
+    ENDIF	
+ENDFOR
+RETURN aq[n]
+ENDFUNC

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

@@ -0,0 +1,28 @@
+# 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

@@ -0,0 +1,20 @@
+$ 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