"""
 an example of a tree data structure
 and a recursive program to count
 the nodes in the tree.

 Jim Mahoney cs.marlboro.edu | GPL | Nov 2011
"""

print """The tree looks like this:
      a
     / \\
    b   c
       /|\\
      d e f
"""

# Quick quiz 1: W
# Why are there \\ rather than \ characters in the print statement above?

# Define each node as a dictionary, starting at the bottom.
# (The nodes beneath a 'parent' are called 'children'.)
f = {'name':'f', 'kids':[]}
e = {'name':'e', 'kids':[]}
d = {'name':'d', 'kids':[]}
c = {'name':'c', 'kids':[d, e, f]}
b = {'name':'b', 'kids':[]}
a = {'name':'a', 'kids':[b, c]}

# Here's what it looks like as a single python data structure.
import pprint
pp = pprint.PrettyPrinter()
print "Here's how it looks as a data structure:"
pp.pprint(a)

# Now the recursive function.
# Quick quiz 2 : why this doesn't recur forever?
def count_tree_nodes(node):
    """Return number of nodes at and below this one"""
    count = 1
    for child in node['kids']:
        count = count + count_nodes(child)
    return count

print "The number of nodes in the tree is %i." % count_tree_nodes(a)

# Quick quiz 3:
# What would happen if we tried to use this on a graph?
#
# (Graphs can have loops, in which the 'lower' ones
# connect back to 'higer' ones.)
#
# Not-as-quick quiz 4:
# How could you define a graph in a python structure?
#
# Even-longer quiz 5:
# Could the count_tree_nodes function be
# adopted to work on graphs?