# 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, let expression, add expression, 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 one 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 the result is 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 the result is the multiplication of the evaluation of e1 and the evaluation of e2.

For 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", and "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 the scope.

Example 1:

Input: expression = "(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.

Example 2:

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

Example 3:

Input: expression = "(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.

# Solution

Approach 1: remember the scope with (values, tokens) where they get to put on a stack when seeing an inner parenthesis. Inner parenthesis gets evaluated first under the outer scope (values). When seeing a ), pop a stack item to evaluate the outer expression.

# Code (Python)

Approach 1:

class Solution:
    def evaluate(self, expression: str) -> int:
        return self.evaluate_tokens(self.tokenize(expression))
    def tokenize(self, expression):
        return expression.replace('(', '( ').replace(')', ' )').split(' ')

    def evaluate_tokens(self, tokenized):
        stack = [] # stores list of (values, tokens) for the current scope
        values = {}
        tokens = [] # no brackets in there

        def get_value(var):
            # if var has corresponding mapping (is a variable), return the mapped value; 
            # else it's just a stringed number so return itself
            return values.get(var, var)
        def evaluate(tokens):
            if tokens[0] in ('add', 'mult'):
                return str({
                    'add': lambda a, b: a + b,
                    'mult': lambda a, b: a * b,
                }[tokens[0]](int(get_value(tokens[1])), int(get_value(tokens[2]))))
            else: # let
                i = 1
                for i in range(1, len(tokens) - 1, 2): # all except for the last expression
                    if tokens[i + 1]:
                        values[tokens[i]] = get_value(tokens[i + 1])
                # if there's an expression to return
                if i + 2 == len(tokens) - 1:
                    return get_value(tokens[-1])
                # otherwise the return value needs to be calculated later
        for token in tokenized:
            if token == '(':
                # save current values and token to stack, start a new scope
                if tokens and tokens[0] == 'let':
                # remember the old tokens and values
                stack.append((tokens, dict(values))) # dict() copies the values so it won't be modified later
                tokens = [] # tokens get refreshed, values need to keep when going 1 level deeper for evaluation
            elif token == ')':
                val = evaluate(tokens)
                # restore outer scope
                tokens, values = stack.pop()
        return int(tokens[0])

# Code (C++)

Approach 1:

Approach 2: