Port forward tree iterator from python to rust.

python_experiments/flip_exponent_for_tests/flip.py

@@ -0,0 +1,39 @@
+#!/usr/bin/env python
+#
+from math import log10
+
+
+def main():
+    for x, y, z, num_nodes in sorted(list(get_matches(90, 90)), key=lambda val: val[3]):
+        if num_nodes < 1000000:
+            print(f"{x}**{y} == {y}**{z} == {num_nodes}")
+
+
+def get_matches(max_x: int, max_y: int):
+    for x in range(2, max_x):
+        for y in range(2, max_y):
+            diff, y_exp = check(x, y)
+            if diff == 0:
+                yield (x, y, y_exp, x**y)
+
+
+def check(x: int, y: int):
+    num_nodes = x**y
+    # y**z = x**y
+    # zlogy = ylogx
+    # z = ylogx/logy
+
+    # flipped:
+    exp_for_y = y * log10(x) / log10(y)
+    # Round the exp for y to be a plain integer
+    exp_for_y = round(exp_for_y)
+    flipped_num_nodes = y**exp_for_y
+
+    # compare the num nodes after rounding to find a good fit with integers.
+    diff = abs(num_nodes - flipped_num_nodes)
+
+    return diff, exp_for_y
+
+
+if __name__ == "__main__":
+    main()