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Task/Paraffins/Python/paraffins.py

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+try:
+    import psyco
+    psyco.full()
+except ImportError:
+    pass
+
+MAX_N = 300
+BRANCH = 4
+
+ra = [0] * MAX_N
+unrooted = [0] * MAX_N
+
+def tree(br, n, l, sum = 1, cnt = 1):
+    global ra, unrooted, MAX_N, BRANCH
+    for b in xrange(br + 1, BRANCH + 1):
+        sum += n
+        if sum >= MAX_N:
+            return
+
+        # prevent unneeded long math
+        if l * 2 >= sum and b >= BRANCH:
+            return
+
+        if b == br + 1:
+            c = ra[n] * cnt
+        else:
+            c = c * (ra[n] + (b - br - 1)) / (b - br)
+
+        if l * 2 < sum:
+            unrooted[sum] += c
+
+        if b < BRANCH:
+            ra[sum] += c;
+            for m in range(1, n):
+                tree(b, m, l, sum, c)
+
+def bicenter(s):
+    global ra, unrooted
+    if not (s & 1):
+        aux = ra[s / 2]
+        unrooted[s] += aux * (aux + 1) / 2
+
+
+def main():
+    global ra, unrooted, MAX_N
+    ra[0] = ra[1] = unrooted[0] = unrooted[1] = 1
+
+    for n in xrange(1, MAX_N):
+        tree(0, n, n)
+        bicenter(n)
+        print "%d: %d" % (n, unrooted[n])
+
+main()