Data commit

Task/Hofstadter-Q-sequence/Python/hofstadter-q-sequence-1.py

@@ -0,0 +1,16 @@
+def q(n):
+    if n < 1 or type(n) != int: raise ValueError("n must be an int >= 1")
+    try:
+        return q.seq[n]
+    except IndexError:
+        ans = q(n - q(n - 1)) + q(n - q(n - 2))
+        q.seq.append(ans)
+        return ans
+q.seq = [None, 1, 1]
+
+if __name__ == '__main__':
+    first10 = [q(i) for i in range(1,11)]
+    assert first10 == [1, 1, 2, 3, 3, 4, 5, 5, 6, 6], "Q() value error(s)"
+    print("Q(n) for n = [1..10] is:", ', '.join(str(i) for i in first10))
+    assert q(1000) == 502, "Q(1000) value error"
+    print("Q(1000) =", q(1000))

Task/Hofstadter-Q-sequence/Python/hofstadter-q-sequence-2.py

@@ -0,0 +1,19 @@
+from sys import getrecursionlimit
+
+def q1(n):
+    if n < 1 or type(n) != int: raise ValueError("n must be an int >= 1")
+    try:
+        return q.seq[n]
+    except IndexError:
+        len_q, rlimit = len(q.seq), getrecursionlimit()
+        if (n - len_q) > (rlimit // 5):
+            for i in range(len_q, n, rlimit // 5):
+                q(i)
+        ans = q(n - q(n - 1)) + q(n - q(n - 2))
+        q.seq.append(ans)
+        return ans
+
+if __name__ == '__main__':
+    tmp = q1(100000)
+    print("Q(i+1) < Q(i) for i [1..100000] is true %i times." %
+          sum(k1 < k0 for k0, k1 in zip(q.seq[1:], q.seq[2:])))

Task/Hofstadter-Q-sequence/Python/hofstadter-q-sequence-3.py

@@ -0,0 +1,13 @@
+def q(n):
+    l = len(q.seq)
+    while l <= n:
+        q.seq.append(q.seq[l - q.seq[l - 1]] + q.seq[l - q.seq[l - 2]])
+	l += 1
+    return q.seq[n]
+q.seq = [None, 1, 1]
+
+print("Q(n) for n = [1..10] is:", [q(i) for i in range(1, 11)])
+print("Q(1000) =", q(1000))
+q(100000)
+print("Q(i+1) < Q(i) for i [1..100000] is true %i times." %
+      sum([q.seq[i] > q.seq[i + 1] for i in range(1, 100000)]))