Data update

Task/Knuths-power-tree/Python/knuths-power-tree-2.py

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+""" https://rosettacode.org/wiki/Knuth%27s_power_tree """
+
+from typing import List, Dict
+from mpmath import mp
+
+# Set decimal precision for mpmath calculations (like Go example 320 bits)
+mp.dps = 140
+
+# Global variables
+p: Dict[int, int] = {1: 0}
+lvl: List[List[int]] = [[1]]
+
+
+def path(n: int) -> List[int]:
+    """ return path to the node with id ''n'' """
+    if n == 0:
+        return []
+
+    while n not in p:
+        q: List[int] = []
+        for x in lvl[0]:
+            for y in path(x):
+                z = x + y
+                if z in p:
+                    break
+                p[z] = x
+                q.append(z)
+        lvl[0] = q
+
+    r = path(p[n]) + [n]
+    return r
+
+
+def tree_pow(x: float, n: int) -> mp.mpf:
+    """ use power tree to compute x ** n """
+    r: Dict[int, mp.mpf] = {0: mp.mpf('1'), 1: mp.mpf(str(x))}
+    prev = 0
+    for i in path(n):
+        r[i] = mp.mpf(r[i - prev] * r[prev])
+        prev = i
+    return r[n]
+
+
+def show_pow(x: float, n: int) -> None:
+    """ print the power calculation """
+    print(f"{n}: {path(n)}")
+    y = tree_pow(x, n)
+    ans = mp.nstr(y, n=100, strip_zeros=True)[
+        :-2] if mp.isint(y) else mp.nstr(y, n=10)
+    print(f"{mp.nstr(x)} ^ {n} = {ans}\n")
+
+
+if __name__ == "__main__":
+    for expo in range(18):
+        show_pow(2, expo)
+    show_pow(1.1, 81)
+    show_pow(3.0, 191)