Practice/Meta/Evaluate and Simplify Mathematical Expressions

Evaluate and Simplify Mathematical Expressions

CodingMust

Problem

Build a system that can parse and evaluate mathematical expressions containing numbers, variables, operators, and parentheses. Your implementation should respect standard mathematical operator precedence rules and correctly handle nested parentheses.

You need to implement a function that takes a mathematical expression as a string and a dictionary of variable values, then returns the evaluated numeric result as a string.

The expression will contain:

• Integer and floating-point numbers
• Variables (single or multi-character identifiers like x, abc, value1)
• Binary operators: + (addition), - (subtraction), * (multiplication), / (division)
• Parentheses for grouping: ( and )

Requirements

1. Parse the expression string into a valid computational structure
2. Apply correct operator precedence (multiplication and division before addition and subtraction)
3. Evaluate parentheses from innermost to outermost
4. Substitute variables with their provided values before evaluation
5. Return the final numeric result as a string
6. Handle both integer and floating-point arithmetic correctly

Constraints

• 1 <= expression.length <= 1000
• Expression contains only valid characters: digits, operators +, -, *, /, parentheses, variables, and spaces
• All operators are binary (no unary operators like -5)
• Variable names consist of letters and digits, starting with a letter
• 0 <= variables.size <= 100
• All variable values are integers or floats in the range [-10000, 10000]
• Division by zero will not occur in test cases
• Expected time complexity: O(n) where n is the length of the expression
• Expected space complexity: O(n) for storing the parse tree or evaluation stack

Examples

Example 1:

Input: expression = "3 + 5 * 2", variables = \{\} Output: "13" Explanation: Multiplication has higher precedence than addition, so we compute 5 * 2 = 10 first, then 3 + 10 = 13.

Example 2:

Input: expression = "(3 + 5) * 2", variables = \{\} Output: "16" Explanation: Parentheses have highest precedence. We evaluate 3 + 5 = 8 first, then 8 * 2 = 16.

Example 3:

Input: expression = "x + y * 2", variables = \{"x": 10, "y": 5\} Output: "20" Explanation: Substitute variables: "10 + 5 * 2". Then evaluate: 5 * 2 = 10, then 10 + 10 = 20.

Example 4:

` Input: expression = "((a + b) * c - d) / e", variables = {"a": 2, "b": 3, "c": 4, "d": 5, "e": 3} Output: "5.0" Explanation: Work from innermost parentheses outward:

• (a + b) = (2 + 3) = 5
• 5 * c = 5 * 4 = 20
• 20 - d = 20 - 5 = 15
• 15 / e = 15 / 3 = 5.0 `