Data commit

Task/Hofstadter-Figure-Figure-sequences/Python/hofstadter-figure-figure-sequences-1.py

@@ -0,0 +1,46 @@
+def ffr(n):
+    if n < 1 or type(n) != int: raise ValueError("n must be an int >= 1")
+    try:
+        return ffr.r[n]
+    except IndexError:
+        r, s = ffr.r, ffs.s
+        ffr_n_1 = ffr(n-1)
+        lastr = r[-1]
+        # extend s up to, and one past, last r
+        s += list(range(s[-1] + 1, lastr))
+        if s[-1] < lastr: s += [lastr + 1]
+        # access s[n-1] temporarily extending s if necessary
+        len_s = len(s)
+        ffs_n_1 = s[n-1] if len_s > n else (n - len_s) + s[-1]
+        ans = ffr_n_1 + ffs_n_1
+        r.append(ans)
+        return ans
+ffr.r = [None, 1]
+
+def ffs(n):
+    if n < 1 or type(n) != int: raise ValueError("n must be an int >= 1")
+    try:
+        return ffs.s[n]
+    except IndexError:
+        r, s = ffr.r, ffs.s
+        for i in range(len(r), n+2):
+            ffr(i)
+            if len(s) > n:
+                return s[n]
+        raise Exception("Whoops!")
+ffs.s = [None, 2]
+
+if __name__ == '__main__':
+    first10 = [ffr(i) for i in range(1,11)]
+    assert first10 == [1, 3, 7, 12, 18, 26, 35, 45, 56, 69], "ffr() value error(s)"
+    print("ffr(n) for n = [1..10] is", first10)
+    #
+    bin = [None] + [0]*1000
+    for i in range(40, 0, -1):
+        bin[ffr(i)] += 1
+    for i in range(960, 0, -1):
+        bin[ffs(i)] += 1
+    if all(b == 1 for b in bin[1:1000]):
+        print("All Integers 1..1000 found OK")
+    else:
+        print("All Integers 1..1000 NOT found only once: ERROR")

Task/Hofstadter-Figure-Figure-sequences/Python/hofstadter-figure-figure-sequences-2.py

@@ -0,0 +1,29 @@
+cR = [1]
+cS = [2]
+
+def extend_RS():
+	x = cR[len(cR) - 1] + cS[len(cR) - 1]
+	cR.append(x)
+	cS += range(cS[-1] + 1, x)
+	cS.append(x + 1)
+
+def ff_R(n):
+	assert(n > 0)
+	while n > len(cR): extend_RS()
+	return cR[n - 1]
+
+def ff_S(n):
+	assert(n > 0)
+	while n > len(cS): extend_RS()
+	return cS[n - 1]
+
+# tests
+print([ ff_R(i) for i in range(1, 11) ])
+
+s = {}
+for i in range(1, 1001): s[i] = 0
+for i in range(1, 41):  del s[ff_R(i)]
+for i in range(1, 961): del s[ff_S(i)]
+
+# the fact that we got here without a key error
+print("Ok")

Task/Hofstadter-Figure-Figure-sequences/Python/hofstadter-figure-figure-sequences-3.py

@@ -0,0 +1,2 @@
+[1, 3, 7, 12, 18, 26, 35, 45, 56, 69]
+Ok

Task/Hofstadter-Figure-Figure-sequences/Python/hofstadter-figure-figure-sequences-4.py

@@ -0,0 +1,26 @@
+from itertools import islice
+
+def R():
+	n = 1
+	yield n
+	for s in S():
+		n += s
+		yield n;
+
+def S():
+	yield 2
+	yield 4
+	u = 5
+	for r in R():
+		if r <= u: continue;
+		for x in range(u, r): yield x
+		u = r + 1
+
+def lst(s, n): return list(islice(s(), n))
+
+print "R:", lst(R, 10)
+print "S:", lst(S, 10)
+print sorted(lst(R, 40) + lst(S, 960)) == list(range(1,1001))
+
+# perf test case
+# print sum(lst(R, 10000000))