How to Think Like a Computer Scientist - Learning with Python, 2008a

20.2 Traversing trees 209
20.2 Traversing trees
Any time you see a new data structure, your first question should be, “How do I
traverse it?” The most natural way to traverse a tree is recursively. For example,
if the tree contains integers as cargo, this function returns their sum:
def total(tree):
if tree == None: return 0
return total(tree.left) + total(tree.right) + tree.cargo
The base case is the empty tree, which contains no cargo, so the sum is 0. The
recursive step makes two recursive calls to find the sum of the child trees. When
the recursive calls complete, we add the cargo of the parent and return the total.
20.3 Expression trees
A tree is a natural way to represent the structure of an expression. Unlike other
notations, it can represent the computation unambiguously. For example, the
infix expression 1 + 2 * 3 is ambiguous unless we know that the multiplication
happens before the addition.
This expression tree represents the same computation:
tree
cargo +
left
right
cargo 1
left
right
cargo
left
*
right
cargo 2
cargo 3
left right left right
The nodes of an expression tree can be operands like 1 and 2 or operators like
+ and *. Operands are leaf nodes; operator nodes contain references to their
operands. (All of these operators are binary, meaning they have exactly two
operands.)
We can build this tree like this:
>>> tree = Tree(’+’, Tree(1), Tree(’*’, Tree(2), Tree(3)))