Data commit

Task/Knuths-power-tree/Python/knuths-power-tree.py

@@ -0,0 +1,28 @@
+from __future__ import print_function
+
+# remember the tree generation state and expand on demand
+def path(n, p = {1:0}, lvl=[[1]]):
+	if not n: return []
+	while n not in p:
+		q = []
+		for x,y in ((x, x+y) for x in lvl[0] for y in path(x) if not x+y in p):
+			p[y] = x
+			q.append(y)
+		lvl[0] = q
+
+	return path(p[n]) + [n]
+
+def tree_pow(x, n):
+    r, p = {0:1, 1:x}, 0
+    for i in path(n):
+        r[i] = r[i-p] * r[p]
+        p = i
+    return r[n]
+
+def show_pow(x, n):
+    fmt = "%d: %s\n" + ["%g^%d = %f", "%d^%d = %d"][x==int(x)] + "\n"
+    print(fmt % (n, repr(path(n)), x, n, tree_pow(x, n)))
+
+for x in range(18): show_pow(2, x)
+show_pow(3, 191)
+show_pow(1.1, 81)