tasks a-s

Task/Non-continuous-subsequences/Python/non-continuous-subsequences-1.py

@@ -0,0 +1,9 @@
+def ncsub(seq, s=0):
+    if seq:
+        x = seq[:1]
+        xs = seq[1:]
+        p2 = s % 2
+        p1 = not p2
+        return [x + ys for ys in ncsub(xs, s + p1)] + ncsub(xs, s + p2)
+    else:
+        return [[]] if s >= 3 else []

Task/Non-continuous-subsequences/Python/non-continuous-subsequences-2.py

@@ -0,0 +1,40 @@
+from sys import argv
+import psyco
+
+def C(n, k):
+    result = 1
+    for d in xrange(1, k+1):
+        result *= n
+        n -= 1
+        result /= d
+    return result
+
+# http://oeis.org/A002662
+nsubs = lambda n: sum(C(n, k) for k in xrange(3, n+1))
+
+def ncsub(seq):
+    n = len(seq)
+    result = [None] * nsubs(n)
+    pos = 0
+
+    for i in xrange(1, 2 ** n):
+        S  = []
+        nc = False
+        for j in xrange(n + 1):
+            k = i >> j
+            if k == 0:
+                if nc:
+                    result[pos] = S
+                    pos += 1
+                break
+            elif k % 2:
+                S.append(seq[j])
+            elif S:
+                nc = True
+    return result
+
+from sys import argv
+import psyco
+psyco.full()
+n = 10 if len(argv) < 2 else int(argv[1])
+print len( ncsub(range(1, n)) )