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 e1and 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.

因为input的结构比较固定，mult 和 add后面永远是接两个数或者表达式，或者一样一个，所以我们可以把input不断递归，使得最后input是一个数。这样就把问题解决了。

对于let，永远是多个pair+表达式，处理也是一样。

class Solution {
    public int evaluate(String expression) {
        return helper(expression, new HashMap<>());
    }
    
    private int helper(String expression, Map<String, Integer> map) {
        if (isNumber(expression)) {
            return Integer.parseInt(expression);
        }
        
        if (isVariable(expression)) {
            return map.get(expression);
        }
        List<String> tokens = parse(expression);
        
        if (tokens.get(0).equals("add")) {
            return helper(tokens.get(1), map) + helper(tokens.get(2), map);
        } else if (tokens.get(0).equals("mult")) {
            return helper(tokens.get(1), map) * helper(tokens.get(2), map);
        } else {
            Map<String, Integer> newMap = new HashMap<>(map);
            for (int i = 1; i < tokens.size() - 1; i += 2) {
                newMap.put(tokens.get(i), helper(tokens.get(i + 1), newMap));
            }
            return helper(tokens.get(tokens.size() - 1), newMap);
        }
    }
    
    private boolean isNumber(String expression) {
        char firstLetter = expression.charAt(0);
        return firstLetter == '-' || firstLetter == '+' || firstLetter <= '9' && firstLetter >= '0';
    }
    
    private boolean isVariable(String expression) {
        char firstLetter = expression.charAt(0);
        return firstLetter <= 'z' && firstLetter >= 'a';
    }
    
    private List<String> parse(String exp) {
        List<String> parts = new ArrayList<>();
        exp = exp.substring(1, exp.length() - 1);
        int startIndex = 0;
        while (startIndex < exp.length()) {
            int endIndex = next(exp, startIndex);
            parts.add(exp.substring(startIndex, endIndex));
            startIndex = endIndex + 1;
        }
        return parts;
    }
    
    private int next(String expression, int startIndex) {
        if (expression.charAt(startIndex) == '(') {
            int count = 1;
            startIndex++;
            while (startIndex < expression.length() && count > 0) {
                if (expression.charAt(startIndex) == '(') {
                    count++;
                } else if (expression.charAt(startIndex) == ')') {
                    count--;
                }
                startIndex++;
            }
        } else {
            while (startIndex < expression.length() && expression.charAt(startIndex) != ' ') {
                startIndex++;
            }
        }
        return startIndex;
    }
}

如果问题里面没有let，代码可以简化为：

class Solution {
    public int evaluate(String expression) {
        if (isNumber(expression)) {
            return Integer.parseInt(expression);
        }
        
        List<String> tokens = parse(expression);
        
        if (tokens.get(0).equals("add")) {
            return evaluate(tokens.get(1)) + evaluate(tokens.get(2));
        } else {
            return evaluate(tokens.get(1)) * evaluate(tokens.get(2));
        }
    }
    
    private boolean isNumber(String expression) {
        char firstLetter = expression.charAt(0);
        return firstLetter == '-' || firstLetter == '+' || firstLetter <= '9' && firstLetter >= '0';
    }
    
    private List<String> parse(String exp) {
        List<String> parts = new ArrayList<>();
        exp = exp.substring(1, exp.length() - 1);
        int startIndex = 0;
        while (startIndex < exp.length()) {
            int endIndex = next(exp, startIndex);
            parts.add(exp.substring(startIndex, endIndex));
            startIndex = endIndex + 1;
        }
        return parts;
    }
    
    private int next(String expression, int index) {
        if (expression.charAt(index) == '(') {
            int count = 1;
            index++;
            while (index < expression.length() && count > 0) {
                if (expression.charAt(index) == '(') {
                    count++;
                } else if (expression.charAt(index) == ')') {
                    count--;
                }
                index++;
            }
        } else {
            while (index < expression.length() && expression.charAt(index) != ' ') {
                index++;
            }
        }
        return index;
    }
}