Parse Lisp Expression

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class Solution:
    def evaluate(self, expression: str) -> int:

        tokens = deque(expression.replace('(','( ').replace(')',' )').split())

        def eva(tokens,env):

            if tokens[0] != '(':
                if tokens[0][0] in '-1234567890':
                    return int(tokens.popleft())
                else:
                    return env[tokens.popleft()]
            else:
                tokens.popleft()
                if tokens[0] in ('add', 'mult'):
                    op = tokens.popleft()
                    a, b = eva(tokens, env), eva(tokens, env)
                    val = a + b if op == 'add' else a * b
                else:
                    tokens.popleft()
                    local = env.copy()
                    while tokens[0] != '(' and tokens[1] != ')':
                        var = tokens.popleft()
                        local[var] = eva(tokens, local)
                    val = eva(tokens, local)
                tokens.popleft()
                return val

        return eva(tokens,{})

Problem Classification

The problem is in the domain of “String Manipulation” and “Interpretation of Programming Languages”. This is because we are given a string that represents a Lisp-like expression, and our task is to evaluate this string as if it were an expression in a programming language.

‘What’ Components:

  1. A string representing a Lisp-like expression is given.
  2. The expression can contain four types of components: integers, variables, “let” expressions, “add” expressions, and “mult” expressions.
  3. Each of these components needs to be evaluated to return a single integer.
  4. Expressions evaluate according to specific rules given.
  5. There is a concept of “scope” for variable evaluation.
  6. The final output is the result of the expression evaluation.

The problem can be further classified as follows:

  • Parsing and Interpreting: The input is a string that represents a programming language expression, and it must be parsed and interpreted according to specific rules to find the result.
  • Recursion: The expressions can be nested, and the problem naturally lends itself to a recursive solution. Each expression can contain subexpressions, and evaluating an expression might involve first evaluating its subexpressions.
  • Variable Scope and Assignment: The problem involves the assignment of variables and the concept of scope. A variable can have different values in different scopes, and we need to correctly handle this to interpret the expression.

These categorizations are based on the input, the desired output, and the rules and conditions given in the problem. The problem is about interpreting a programming language expression, which makes it a problem of “String Manipulation” and “Interpretation of Programming Languages”. Also, the presence of nested expressions and the need for evaluating these expressions suggest a recursive approach. Finally, the concept of variable scope and assignment is another key aspect of the problem.

Language Agnostic Coding Drills

  1. Dissection of the code:

Here are the distinct concepts in this code:

  • Python Functions: The main function evaluate and the inner function eva are key concepts used in this code.

  • Recursion: The inner function eva calls itself recursively to evaluate nested expressions. This concept is crucial for solving problems where a task is broken down into smaller subtasks of the same kind.

  • String Manipulation: The code uses replace and split to manipulate the string expressions into tokens.

  • Data Structures: Python’s deque (double-ended queue) and dictionaries are used in this code.

  • Conditionals: if-else conditionals are used extensively to handle different scenarios based on the nature of the tokens.

  • Arithmetic Operations: Basic arithmetic operations like addition and multiplication are used.

  1. Order of concepts by increasing difficulty:

    • Python Functions: This is a basic concept where one learns how to define and call functions.

    • String Manipulation: It is also a fundamental topic involving operations to process strings, which are common data types in programming.

    • Arithmetic Operations: This involves using the basic arithmetic operators like addition and multiplication. It is quite straightforward and is usually taught early in programming courses.

    • Conditionals: if-else statements are used for controlling the flow of execution based on conditions, which is a relatively easy-to-grasp concept.

    • Data Structures: Understanding and using Python’s built-in data structures like deque and dictionary requires a deeper understanding of how data is stored and accessed. Thus, it can be seen as more challenging.

    • Recursion: This is a more advanced topic that involves a function calling itself to solve smaller instances of the same problem. Understanding recursion requires a good grasp of how functions work and a solid understanding of problem-solving strategies.

  2. Problem-solving approach:

    • Start with string manipulation to convert the expression into an iterable deque of tokens. The expression is split into its individual components, each component being a separate token.

    • A copy of the tokens and an empty environment dictionary is passed to the eva function. The environment dictionary is used to keep track of variable values in the current scope.

    • In the eva function, if the first token is not an opening parenthesis, it’s either a number or a variable. If it’s a number, convert it to integer and return. If it’s a variable, return its value from the environment dictionary.

    • If the first token is an opening parenthesis, then we are dealing with an expression. The code further distinguishes between “add”, “mult”, and “let” expressions, evaluating each accordingly.

    • For “add” and “mult” expressions, the code recursively evaluates the next two tokens (which can be either numbers, variables, or other expressions) and performs the corresponding arithmetic operation.

    • For “let” expressions, a new scope is created (by copying the current environment), and variable-value pairs are processed sequentially until an expression is encountered. The expression is then evaluated in the context of the updated environment.

    • The recursion allows the code to handle nested expressions, as each expression can be treated as a sub-problem similar to the original one. This is a powerful strategy in programming and problem-solving, allowing complex problems to be broken down into simpler, manageable sub-problems.

Targeted Drills in Python

  1. Python Coding Drills:

    • Python Functions

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      def greet(name):
    print(f"Hello, {name}!")

greet("Python Learner")

      This simple function takes in a name and prints a greeting. Functions are fundamental building blocks in Python.

    • String Manipulation

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      expression = "(add 1 2)"
tokens = expression.replace('(','( ').replace(')',' )').split()
print(tokens)

      This code takes a string expression, adds spaces around parentheses and splits the string into a list of tokens. String manipulations are often used to preprocess and format data.

    • Arithmetic Operations

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      a, b = 5, 2
print("Addition:", a + b)
print("Multiplication:", a * b)

      This drill shows how to perform basic arithmetic operations in Python.

    • Conditionals

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      number = 7
if number % 2 == 0:
    print(f"{number} is even")
else:
    print(f"{number} is odd")

      The above code determines if a number is even or odd using if-else statements.

    • Data Structures

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      # Deque
from collections import deque
d = deque([1, 2, 3])
d.appendleft(0)
d.append(4)
print(d)

# Dictionary
env = {"x": 1, "y": 2}
print(env['x'])

      These drills show how to use deque and dictionary in Python.

    • Recursion

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      def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
print(factorial(5))

      This code computes the factorial of a number using recursion.

  2. Problem-Specific Concepts:

    • Handling Lisp-like expressions: Our main problem is evaluating Lisp-like expressions which include numbers, operations (add, mult), variable assignments (let), and scopes. It’s essential to understand how to parse and evaluate such expressions.

    Drills for these concepts could include:

    • Parsing and evaluating simple mathematical expressions:

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      expression = "(add 1 2)"
tokens = expression.replace('(','( ').replace(')',' )').split()
result = 0
if tokens[1] == "add":
    result = int(tokens[2]) + int(tokens[3])
print(result)

    • Handling variable assignment and scoping:

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      env = {}
env["x"] = 1
print(env["x"])

    This drill shows how to store variable values in a dictionary which acts as an environment for variable scoping.

  3. Integrating the pieces:

    Once all drills are complete, they can be integrated to solve the problem:

    • Begin by defining the main function evaluate which accepts a string expression as input.
    • Inside this function, perform string manipulation to split the expression into tokens.
    • Create an environment dictionary to keep track of variable values.
    • Define an inner recursive function eva that accepts tokens and the environment as inputs. This function will evaluate an expression based on its first token:
      • If it’s a number, convert it to integer and return.
      • If it’s a variable, return its value from the environment.
      • If it’s an opening parenthesis, it means we’re dealing with

an operation. Further parse it into “add”, “mult”, or “let” expressions, and process each case accordingly, making use of recursion to evaluate nested expressions. - Finally, return the result of calling eva with the tokens and the environment as arguments.

Each drill enhances the complexity of the function, starting from simple string manipulations, understanding arithmetic operations, using conditionals to handle different cases, using data structures to store values, and employing recursion to solve the problem in a divide-and-conquer manner. All these concepts are brought together to create a function that can evaluate complex Lisp-like expressions.