python---数学表达式的分析树实现

# coding = utf-8


# 使用列表实现栈的功能
class Stack:
    def __init__(self):
        self.items = []

    # 是否为空
    def is_empty(self):
        return self.items == []

    # 进栈
    def push(self, item):
        self.items.append(item)

    # 出栈
    def pop(self):
        return self.items.pop()

    # 返回栈顶值，不改变栈
    def peek(self):
        return self.items[len(self.items) - 1]

    # 返回栈长度
    def size(self):
        return len(self.items)


# 使用递归实现二叉树基本功能
class BinaryTree:
    def __init__(self, root_obj):
        self.key = root_obj
        self.left_child = None
        self.right_child = None

    def insert_left(self, new_node):
        node = BinaryTree(new_node)
        if self.left_child is None:
            self.left_child = node
        else:
            node.left_child = self.left_child
            self.left_child = node

    def insert_right(self, new_node):
        node = BinaryTree(new_node)
        if self.right_child is None:
            self.right_child = node
        else:
            node.right_child = self.right_child
            self.right_child = node

    def get_right_child(self):
        return self.right_child

    def get_left_child(self):
        return self.left_child

    def set_root_val(self, obj):
        self.key = obj

    def get_root_val(self):
        return self.key


# 建立一个算术分析树
def build_parse_tree(fp_exp):
    fp_list = fp_exp.split()
    p_stack = Stack()
    e_tree = BinaryTree(‘‘)
    p_stack.push(e_tree)
    current_tree = e_tree

    for item in fp_list:
        if item == ‘(‘:
            current_tree.insert_left(‘‘)
            p_stack.push(current_tree)
            current_tree = current_tree.get_left_child()
        elif item not in [‘+‘, ‘-‘, ‘*‘, ‘/‘, ‘)‘]:
            current_tree.set_root_val(int(item))
            parent = p_stack.pop()
            current_tree = parent
        elif item in [‘+‘, ‘-‘, ‘*‘, ‘/‘]:
            current_tree.set_root_val(item)
            current_tree.insert_right(‘‘)
            p_stack.push(current_tree)
            current_tree = current_tree.get_right_child()
        elif item == ‘)‘:
            current_tree = p_stack.pop()
        else:
            raise ValueError
    return e_tree


# 匹配加减乘除规则
class DoMatch:
    @staticmethod
    def add(op1, op2):
        return op1 + op2

    @staticmethod
    def sub(op1, op2):
        return op1 - op2

    @staticmethod
    def mul(op1, op2):
        return op1 * op2

    @staticmethod
    def true_div(op1, op2):
        return op1 / op2


# 算术分析式的求值
def evaluate(parse_tree):
    operator = DoMatch()
    opers = {‘+‘: operator.add,
             ‘-‘: operator.sub,
             ‘*‘: operator.mul,
             ‘/‘: operator.true_div
             }
    left_c = parse_tree.get_left_child()
    right_c = parse_tree.get_right_child()

    if left_c and right_c:
        fn = opers[parse_tree.get_root_val()]
        return fn(evaluate(left_c), evaluate(right_c))
    else:
        return parse_tree.get_root_val()


# 前序遍历
def pre_order(tree):
    if tree:
        print(tree.get_root_val())
        pre_order(tree.get_left_child())
        pre_order(tree.get_right_child())


# 后序遍历
def post_order(tree):
    if tree:
        print(tree.get_root_val())
        post_order(tree.get_left_child())
        post_order(tree.get_right_child())


# 中序遍历
def in_order(tree):
    if tree:
        print(tree.get_root_val())
        in_order(tree.get_left_child())
        in_order(tree.get_right_child())


# 分析树打印
def print_exp(tree):
    s_val = ‘‘
    if tree:
        s_val = ‘(‘ + str(print_exp(tree.get_left_child()))
        s_val = s_val + str(tree.get_root_val())
        s_val = s_val + str(print_exp(tree.get_right_child())) + ‘)‘
    return s_val


pt = build_parse_tree("( ( 7 + 3 ) * ( 5 - 2 ) )")
print(‘=========pre_order================‘)
pre_order(pt)
print(‘=========post_order================‘)
post_order(pt)
print(‘=========in_order================‘)
in_order(pt)
print(‘=========print_exp================‘)
print(print_exp(pt))
print(‘=========evaluate================‘)
print(evaluate(pt))

=========pre_order================
*
+
7
3
-
5
2
=========post_order================
*
+
7
3
-
5
2
=========in_order================
*
+
7
3
-
5
2
=========print_exp================
(((7)+(3))*((5)-(2)))
=========evaluate================
30