题目描述：

LeetCode 736. Parse Lisp Expression

You are given a string expression representing a Lisp-like expression to return the integer value of.

The syntax for these expressions is given as follows.

• An expression is either an integer, a let-expression, an add-expression, a mult-expression, or an assigned variable. Expressions always evaluate to a single integer.

• (An integer could be positive or negative.)

• A let-expression takes the form (let v1 e1 v2 e2 ... vn en expr), where let is always the string "let", then there are 1 or more pairs of alternating variables and expressions, meaning that the first variable v1 is assigned the value of the expression e1, the second variable v2 is assigned the value of the expression e2, and so on sequentially; and then the value of this let-expression is the value of the expression expr.

• An add-expression takes the form (add e1 e2) where add is always the string "add", there are always two expressions e1, e2, and this expression evaluates to the addition of the evaluation of e1 and the evaluation of e2.

• A mult-expression takes the form (mult e1 e2) where mult is always the string "mult", there are always two expressions e1, e2, and this expression evaluates to the multiplication of the evaluation of e1 and the evaluation of e2.

• For the purposes of this question, we will use a smaller subset of variable names. A variable starts with a lowercase letter, then zero or more lowercase letters or digits. Additionally for your convenience, the names "add", "let", or "mult" are protected and will never be used as variable names.

• Finally, there is the concept of scope. When an expression of a variable name is evaluated, within the context of that evaluation, the innermost scope (in terms of parentheses) is checked first for the value of that variable, and then outer scopes are checked sequentially. It is guaranteed that every expression is legal. Please see the examples for more details on scope.

Evaluation Examples:

Input: (add 1 2)
Output: 3

Input: (mult 3 (add 2 3))
Output: 15

Input: (let x 2 (mult x 5))
Output: 10

Input: (let x 2 (mult x (let x 3 y 4 (add x y))))
Output: 14
Explanation: In the expression (add x y), when checking for the value of the variable x,
we check from the innermost scope to the outermost in the context of the variable we are trying to evaluate.
Since x = 3 is found first, the value of x is 3.

Input: (let x 3 x 2 x)
Output: 2
Explanation: Assignment in let statements is processed sequentially.

Input: (let x 1 y 2 x (add x y) (add x y))
Output: 5
Explanation: The first (add x y) evaluates as 3, and is assigned to x.
The second (add x y) evaluates as 3+2 = 5.

Input: (let x 2 (add (let x 3 (let x 4 x)) x))
Output: 6
Explanation: Even though (let x 4 x) has a deeper scope, it is outside the context
of the final x in the add-expression.  That final x will equal 2.

Input: (let a1 3 b2 (add a1 1) b2) 
Output 4
Explanation: Variable names can contain digits after the first character.

Note:

• The given string expression is well formatted: There are no leading or trailing spaces, there is only a single space separating different components of the string, and no space between adjacent parentheses. The expression is guaranteed to be legal and evaluate to an integer.
• The length of expression is at most 2000. (It is also non-empty, as that would not be a legal expression.)
• The answer and all intermediate calculations of that answer are guaranteed to fit in a 32-bit integer.

题目大意：

计算Lisp表达式，实现三种操作let（赋值），add（加法）和 mult（乘法）

解题思路：

递归 + 字符串处理

编写辅助函数findGroup（从左括号处提取括号表达式），findExpr（提取数字、变量或者运算符）

将当前表达式expression利用辅助函数拆分成若干个部分，记为tokens

对于add操作，返回expr(token1) + expr(token2) + ... + expr(tokenN)

对于mult操作，返回expr(token1) * expr(token2) * ... * expr(tokenN)

对于let操作，对于token1 ... tokenN-1执行赋值，最后返回expr(tokenN)，赋值可以利用变量字典dmap实现

需要注意的是变量的作用域（scope），每一层括号维护一个作用域，内层作用域的变量可以覆盖外层作用域的同名变量。

作用域可以通过传递变量字典的副本实现。

Python代码：

class Solution(object):
    def __init__(self):
        self.exprchars = 'abcdefghijklmnopqrstuvwxyz0123456789+-'

    def findGroup(self, expression):
        cnt = 1
        for x in range(1, len(expression)):
            if expression[x] == '(': cnt += 1
            elif expression[x] == ')': cnt -= 1
            if cnt == 0: return expression[:x+1], expression[x+1:]
    
    def findExpr(self, expression):
        for x in range(len(expression)):
            if not expression[x] in self.exprchars:
                return expression[:x], expression[x:]
        return expression, ''

    def solve(self, expression, dmap):
        if expression[0] in '+-' or expression.isdigit(): return int(expression)
        elif expression in dmap: return dmap[expression]
        es = expression[1:-1]
        tokens = []
        while es:
            if es[0] == ' ':
                es = es[1:]
                continue
            elif es[0] in self.exprchars:
                token, es = self.findExpr(es)
            elif es[0] == '(':
                token, es = self.findGroup(es)
            tokens.append(token)
        if tokens[0] == 'add':
            return sum(self.solve(token, dict(dmap)) for token in tokens[1:])
        elif tokens[0] == 'mult':
            return reduce(operator.mul, (self.solve(token,  dict(dmap)) for token in tokens[1:]))
        elif tokens[0] == 'let':
            for x in range(1, len(tokens) - 1, 2):
                dmap[tokens[x]] = self.solve(tokens[x + 1],  dict(dmap))
            return self.solve(tokens[-1],  dict(dmap))

    def evaluate(self, expression):
        """
        :type expression: str
        :rtype: int
        """
        return self.solve(expression, {})

 

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