# python - Creating formula based on binary tree leaves

I have list of points with length n (in below example n = 6) after that I have made some other points based on these default point for example point 7 are made by "anding" point 5 and point 4 and so on now my question is based on the data structure I have, how can I retrieve the chain of formula? for example for the point 10 (recursive or non recursive) how can I say from where this point is coming?.

If I want to know how point 10 is made it must return something like this:

``(((5 & 4) | 3) | 2) & (5 & 4)`` You need a representation of what you've got before you start. I suggest sth like this:

``````points = [ None,  # dummy value to fill index 0 (we want to start at 1)
None, None, None, None, None, None,  # for the first six atoms
(5, 4, '&'),  # for point 7
(7, 3, '|'),  # for point 8
(8, 2, '|'),  # for point 9
(9, 7, '&') ]  # for point 10
``````

Then creating a formula as a string is just recursive:

``````def formula(points, n):
if points[n] is None:
return str(n)
a, b, operator = points[n]
return '(%s %s %s)' % (formula(points, a), operator, formula(points, b))

print formula(points, 10)
``````

This will print

``````((((5 & 4) | 3) | 2) & (5 & 4))
``````

To get all points used in a formula as a set, just use this:

``````def used(points, n):
if points[n] is None:
return { n }
a, b, operator = points[n]
return used(points, a) | used(points, b)

print used(points, 10)
``````

will print:

``````set([2, 3, 4, 5])
``````