Evaluate arithmetic expression with variables

Implement an expression evaluator for a string expr containing non-negative integers, variables (alphabetic names), operators +, -, *, /, parentheses '()' and spaces. Given a dictionary mapping variable names to integer values, compute the signed 64-bit result using standard operator precedence (*/ before +-), left-to-right associativity, and support unary +/-. Division truncates toward zero. The evaluator must run in O(L) time where L is the length of expr and use O(L) extra space. Return an error for invalid tokens or mismatched parentheses. Follow-ups: extend to exponentiation '^' (right-associative) and a function max(a,b).