We use a stack. Read the expression token by token and follow two rules:
def build_expression_tree(postfix_expr):
stack = []
operators = {'+', '-', '*', '/'}
for token in postfix_expr:
if token in operators:
# Create node, pop right then left,
# attach children, and push parent back.
else:
# Create a node and push to stack.
return stack[0]