py-14-regex-engine
0.000
Challenge Ā· difficulty 5/5
# Backtracking regex matcher
Implement a file **`solution.py`** containing a function `fullmatch` that decides
whether a regular expression matches a string. You must implement the matching
yourself with a **backtracking** algorithm ā **do not** call Python's `re` module.
```python
def fullmatch(pattern: str, text: str) -> bool:
"""Return True iff `pattern` matches the ENTIRE `text`."""
```
`fullmatch` is **anchored**: the pattern must consume the entire `text`, as if it
were wrapped in an implicit `^...$`. Matching only a prefix of `text` is **not**
a match.
## Supported syntax
An *element* is the smallest matchable unit. It is one of:
- A **literal character** ā matches exactly itself (e.g. `a` matches `"a"`).
- `.` ā matches **any single character**.
- An **escaped character** `\x` ā the backslash strips any special meaning from
the next character, which then matches **literally**. So `\.` matches a literal
`.`, `\*` a literal `*`, `\\` a literal backslash, `\[` a literal `[`. Escaping
an ordinary character (e.g. `\a`) just matches that character.
- A **character class** `[...]`:
- `[abc]` matches any **one** of the listed characters.
- `[^abc]` matches any one character **not** listed (a *negated* class). The `^`
is special only as the **first** character inside the brackets.
- **Ranges** like `[a-z]`, `[0-9]`, `[A-Za-z0-9]` match any character whose code
point falls in the (inclusive) range.
- A `-` that appears **first or last** inside the class (right after `[` or
`[^`, or right before `]`) is a **literal** `-`, not a range.
- A class always matches **exactly one** character of `text` (so a class can
never match against the empty string at a position).
## Quantifiers
A quantifier applies to the **single preceding element**:
- `*` ā **zero or more** of the preceding element.
- `+` ā **one or more** of the preceding element.
- `?` ā **zero or one** of the preceding element.
Quantifiers are **greedy**: they consume as many repetitions as possible, but they
**must backtrack** ā giving repetitions back one at a time ā so that the rest of
the pattern can still match and the **whole** text can be consumed.
A quantifier always binds to the whole element immediately to its left, where an
element is a literal char, an escaped char `\x`, `.`, or an entire `[...]` class.
For example, in `a[0-9]*b` the `*` applies to the class `[0-9]`, and in `\.*` the
`*` applies to the escaped literal dot.
## Not supported
There are **no** groups `(...)` and **no** alternation `|`. You do not need to
handle them.
## Semantics / edge cases
- The **empty pattern** matches **only** the empty string.
- `a*` matches `""` (zero repetitions). `a+` does **not** match `""`.
- Greedy backtracking: `a*a` matches `"aaa"` ā the `*` first grabs all three
`a`s, then gives one back so the trailing `a` can match.
- `.*` matches **anything** (including `""`); `.+` matches any non-empty string.
- Anchoring: `a` does **not** match `"ab"` (trailing `b` unconsumed), and `b` does
not match `"ab"` (leading `a` unconsumed).
## Worked example
```python
assert fullmatch("a*a", "aaa") is True # '*' backtracks, gives back one 'a'
assert fullmatch("a+", "") is False # '+' needs at least one
assert fullmatch("a?b", "b") is True # '?' matches zero
assert fullmatch("[a-z]+[0-9]*", "abc12") is True
assert fullmatch("[^0-9]+", "abc") is True # negated class
assert fullmatch("h\\.t", "h.t") is True # escaped dot is literal
assert fullmatch("h.t", "hat") is True # '.' matches any char
assert fullmatch("a.c", "ac") is False # '.' needs one char
assert fullmatch("colou?r", "color") is True
assert fullmatch("", "") is True
assert fullmatch("", "x") is False
```
tests/test_regex_engine.py
from solution import fullmatch
def test_empty_pattern_matches_only_empty():
assert fullmatch("", "") is True
assert fullmatch("", "x") is False
assert fullmatch("", "abc") is False
def test_plain_literals():
assert fullmatch("abc", "abc") is True
assert fullmatch("abc", "abd") is False
assert fullmatch("a", "a") is True
assert fullmatch("a", "") is False
def test_anchoring_requires_full_consume():
# leading and trailing extra chars must cause failure
assert fullmatch("a", "ab") is False
assert fullmatch("b", "ab") is False
assert fullmatch("ab", "abc") is False
assert fullmatch("bc", "abc") is False
assert fullmatch("abc", "ab") is False
def test_dot_matches_any_single_char():
assert fullmatch("h.t", "hat") is True
assert fullmatch("h.t", "h9t") is True
assert fullmatch(".", "x") is True
assert fullmatch(".", "") is False # needs exactly one char
assert fullmatch("a.c", "ac") is False # dot must consume one
assert fullmatch("...", "abc") is True
assert fullmatch("...", "ab") is False
def test_star_zero_or_more():
assert fullmatch("a*", "") is True
assert fullmatch("a*", "a") is True
assert fullmatch("a*", "aaaa") is True
assert fullmatch("a*", "aaab") is False
assert fullmatch("ba*", "b") is True
assert fullmatch("ba*c", "bc") is True
assert fullmatch("ba*c", "baaac") is True
def test_plus_one_or_more():
assert fullmatch("a+", "") is False
assert fullmatch("a+", "a") is True
assert fullmatch("a+", "aaa") is True
assert fullmatch("a+", "aaab") is False
assert fullmatch("ba+c", "bac") is True
assert fullmatch("ba+c", "bc") is False
def test_question_zero_or_one():
assert fullmatch("a?", "") is True
assert fullmatch("a?", "a") is True
assert fullmatch("a?", "aa") is False
assert fullmatch("colou?r", "color") is True
assert fullmatch("colou?r", "colour") is True
assert fullmatch("colou?r", "colouur") is False
assert fullmatch("a?b", "b") is True
assert fullmatch("a?b", "ab") is True
def test_greedy_backtracking_star():
# '*' must give characters back so the trailing 'a' can match
assert fullmatch("a*a", "aaa") is True
assert fullmatch("a*a", "a") is True
assert fullmatch("a*a", "") is False # need at least one 'a'
assert fullmatch("a*ab", "aaab") is True
assert fullmatch("a*ab", "ab") is True
def test_dotstar_matches_anything():
assert fullmatch(".*", "") is True
assert fullmatch(".*", "anything at all 123 !@#") is True
assert fullmatch(".+", "") is False
assert fullmatch(".+", "x") is True
# backtracking through dot-star
assert fullmatch(".*b", "aaabxb") is True
assert fullmatch(".*b", "aaabx") is False
def test_dotstar_backtracking_with_suffix():
assert fullmatch("a.*z", "az") is True
assert fullmatch("a.*z", "abcz") is True
assert fullmatch("a.*z", "abc") is False
assert fullmatch("x.*y.*z", "xyz") is True
assert fullmatch("x.*y.*z", "x111y222z") is True
def test_char_class_basic():
assert fullmatch("[abc]", "a") is True
assert fullmatch("[abc]", "b") is True
assert fullmatch("[abc]", "c") is True
assert fullmatch("[abc]", "d") is False
assert fullmatch("[abc]", "") is False
assert fullmatch("[abc]", "ab") is False # class matches exactly one
def test_char_class_ranges():
assert fullmatch("[a-z]", "m") is True
assert fullmatch("[a-z]", "M") is False
assert fullmatch("[0-9]", "7") is True
assert fullmatch("[0-9]", "a") is False
assert fullmatch("[A-Za-z0-9]", "Q") is True
assert fullmatch("[A-Za-z0-9]", "q") is True
assert fullmatch("[A-Za-z0-9]", "5") is True
assert fullmatch("[A-Za-z0-9]", "_") is False
def test_char_class_with_quantifiers():
assert fullmatch("[a-z]+", "hello") is True
assert fullmatch("[a-z]+", "Hello") is False
assert fullmatch("[a-z]+[0-9]*", "abc12") is True
assert fullmatch("[a-z]+[0-9]*", "abc") is True
assert fullmatch("[a-z]+[0-9]*", "123") is False
assert fullmatch("[0-9]*", "") is True
def test_negated_char_class():
assert fullmatch("[^0-9]", "a") is True
assert fullmatch("[^0-9]", "5") is False
assert fullmatch("[^0-9]+", "abc") is True
assert fullmatch("[^0-9]+", "ab3c") is False
assert fullmatch("[^abc]", "d") is True
assert fullmatch("[^abc]", "a") is False
def test_literal_dash_in_class():
# '-' first or last in the class is a literal dash
assert fullmatch("[-a]", "-") is True
assert fullmatch("[-a]", "a") is True
assert fullmatch("[a-]", "-") is True
assert fullmatch("[a-]", "a") is True
assert fullmatch("[a-]", "b") is False
# literal dash in a negated class
assert fullmatch("[^-]", "-") is False
assert fullmatch("[^-]", "x") is True
def test_escaped_metacharacters():
assert fullmatch("h\\.t", "h.t") is True
assert fullmatch("h\\.t", "hat") is False # escaped dot is literal
assert fullmatch("a\\*b", "a*b") is True
assert fullmatch("a\\*b", "aab") is False
assert fullmatch("a\\\\b", "a\\b") is True # \\ -> literal backslash
assert fullmatch("\\[x\\]", "[x]") is True
assert fullmatch("a\\+", "a+") is True
assert fullmatch("a\\?", "a?") is True
def test_escaped_element_with_quantifier():
# quantifier applies to the escaped element
assert fullmatch("\\.*", "") is True
assert fullmatch("\\.*", "...") is True
assert fullmatch("\\.*", ".a.") is False
assert fullmatch("\\*+", "***") is True
assert fullmatch("\\*+", "") is False
def test_combined_realistic_patterns():
# identifier-ish: letter then letters/digits/underscore-via-class
assert fullmatch("[a-z][a-z0-9]*", "x") is True
assert fullmatch("[a-z][a-z0-9]*", "var123") is True
assert fullmatch("[a-z][a-z0-9]*", "1var") is False
# crude decimal: digits . digits
assert fullmatch("[0-9]+\\.[0-9]+", "3.14") is True
assert fullmatch("[0-9]+\\.[0-9]+", "3.") is False
assert fullmatch("[0-9]+\\.[0-9]+", ".14") is False
assert fullmatch("[0-9]+\\.[0-9]+", "10.005") is True
def test_clear_non_matches():
assert fullmatch("abc", "") is False
assert fullmatch("a+b+", "aaa") is False
assert fullmatch("[xyz]+", "xya") is False
assert fullmatch("a.c.e", "abcd") is False
assert fullmatch("a*b*c*", "cba") is False
System prompt
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.Errors (stderr)
no code extracted from responseReasoning (chain-of-thought)
The user wants a Python function `fullmatch(pattern: str, text: str) -> bool` that implements a backtracking regex matcher.
The pattern must match the entire text.
Supported features:
- Literal characters
- `.` matches any single character
- Escaped characters `\x`
- Character classes `[...]`, `[^...]`, ranges `[a-z]`, literal `-` at start/end
- Quantifiers `*`, `+`, `?` (greedy with backtracking)
- No groups `(...)` or alternation `|`
- Anchored match (entire text must be consumed)
Let's design a recursive backtracking matcher.
We can parse the pattern into a list of tokens, or process it directly with indices.
Given the simplicity, processing with indices or a token list is fine.
Let's tokenize the pattern first to make it easier.
Tokens could be:
- `Literal(char)`
- `Dot`
- `Class(chars, negated)`
- `Star`, `Plus`, `Question` (quantifiers)
Actually, it's easier to keep quantifiers attached to their preceding element, or handle them in the matcher.
Let's define a token structure:
`Element` can be `Literal`, `Dot`, `Class`.
`Pattern` is a list of `(Element, Quantifier?)` where Quantifier is `None`, `*`, `+`, `?`.
Wait, parsing character classes correctly is important.
Rules for `[...]`:
- Starts with `[`
- If next is `^`, negated.
- Ends with `]`
- Inside, `-` is a range operator unless it's first or last.
- `\` escapes characters inside classes too? The problem says "An escaped character `\x` ... matches literally". It doesn't explicitly say escaping works inside classes, but usually it does. I'll assume `\` works inside classes too, or just treat `\` as escaping the next char generally. Actually, the problem says "An escaped character `\x` ... the backslash strips any special meaning from the next character". It's safer to handle `\` inside classes as well. But standard regex usually handles it. I'll stick to simple parsing: inside `[...]`, if we see `\`, consume next char as literal. If we see `-` at start or end, it's literal. Otherwise, it's a range.
Let's write a parser.
Pattern string `p`.
Index `i`.
Function `parse()` returns list of tokens.
Each token is a tuple: `(type, value, quantifier)`
Types: `LIT`, `DOT`, `CLASS`
Quantifiers: `None`, `*`, `+`, `?`
Parsing logic:
```python
def parse(pattern):
tokens = []
i = 0
n = len(pattern)
while i < n:
c = pattern[i]
if c == '\\':
i += 1
if i < n:
tokens.append(('LIT', pattern[i], None))
i += 1
else:
# trailing backslash? treat as literal or ignore? Usually literal.
tokens.append(('LIT', '\\', None))
elif c == '.':
tokens.append(('DOT', None, None))
i += 1
elif c == '[':
i += 1
negated = False
if i < n and pattern[i] == '^':
negated = True
i += 1
chars = set()
# handle first char specially for '-'
if i < n and pattern[i] == '-':
chars.add('-')
i += 1
while i < n and pattern[i] != ']':
if pattern[i] == '\\':
i += 1
if i < n:
chars.add(pattern[i])
i += 1
continue
if i + 2 < n and pattern[i+1] == '-' and pattern[i+2] != ']':
start = pattern[i]
end = pattern[i+2]
for code in range(ord(start), ord(end) + 1):
chars.add(chr(code))
i += 3
else:
chars.add(pattern[i])
i += 1
# handle last char if it's '-'
if i < n and pattern[i] == ']':
# check if the char before ']' was '-'
# Actually, the loop above handles ranges. If we just added a single char, it's fine.
# But what if the class is `[-a]` or `[a-]`?
# My logic: if i < n and pattern[i] == '-', add it.
# Then loop until ']'.
# If the last char before ']' is '-', it will be added as a single char in the loop.
# Wait, range logic: `pattern[i+1] == '-' and pattern[i+2] != ']'`
# If it's `[a-]`, i points to 'a'. i+1 is '-', i+2 is ']'. Condition fails. Adds 'a'. i becomes i+1.
# Next iter: i points to '-'. i+1 is ']'. Condition fails. Adds '-'. i becomes i+1.
# Next iter: i points to ']'. Loop ends. Correct.
pass
if i < n and pattern[i] == ']':
i += 1
tokens.append(('CLASS', (chars, negated), None))
elif c in '*+?':
# Quantifier applies to previous token
if tokens:
tokens[-1] = (tokens[-1][0], tokens[-1][1], c)
i += 1
else:
tokens.append(('LIT', c, None))
i += 1
return tokens
```
Wait, the quantifier handling in parsing: `elif c in '*+?':` should be handled after adding a token, or we can just check during parsing. But what if the pattern starts with `*`? The problem says quantifier applies to preceding element. We can assume valid patterns or handle gracefully. I'll assume valid patterns as per typical coding challenges, but I'll make it robust.
Actually, it's simpler to parse into a list of `(element, quantifier)` where element is a function or tuple.
Let's refine parsing.
I'll represent elements as:
- `('LIT', char)`
- `('DOT',)`
- `('CLASS', chars_set, negated)`
And quantifiers as `None`, `*`, `+`, `?`.
Let's rewrite parser carefully.
```python
def parse(pattern):
tokens = []
i = 0
n = len(pattern)
while i < n:
c = pattern[i]
if c == '\\':
i += 1
if i < n:
tokens.append(('LIT', pattern[i], None))
i += 1
else:
tokens.append(('LIT', '\\', None))
elif c == '.':
tokens.append(('DOT', None, None))
i += 1
elif c == '[':
i += 1
ā¦[19519 chars elided]ā¦
negated = True
i += 1
chars = set()
if i < n and p[i] == '-':
chars.add('-')
i += 1
while i < n and p[i] != ']':
if p[i] == '\\':
i += 1
if i < n:
chars.add(p[i])
i += 1
continue
if i + 2 < n and p[i+1] == '-' and p[i+2] != ']':
start = p[i]
end = p[i+2]
for code in range(ord(start), ord(end) + 1):
chars.add(chr(code))
i += 3
else:
chars.add(p[i])
i += 1
if i < n and p[i] == ']':
i += 1
tokens.append(('CLASS', (chars, negated), None))
elif c in '*+?':
if tokens:
t = tokens[-1]
tokens[-1] = (t[0], t[1], c)
i += 1
else:
tokens.append(('LIT', c, None))
i += 1
return tokens
tokens = parse(pattern)
def matches(ti, si):
if ti == len(tokens):
return si == len(text)
t_type, t_val, quant = tokens[ti]
def elem_match(char):
if t_type == 'LIT':
return char == t_val
elif t_type == 'DOT':
return True
elif t_type == 'CLASS':
chars, negated = t_val
in_c = char in chars
return not in_c if negated else in_c
return False
if quant is None:
if si < len(text) and elem_match(text[si]):
return matches(ti + 1, si + 1)
return False
elif quant == '?':
if si < len(text) and elem_match(text[si]):
if matches(ti + 1,Self-repair attempts
[
{
"total": 1,
"answer": "",
"passed": 0,
"reasoning": "The user wants a Python function `fullmatch(pattern: str, text: str) -> bool` that implements a backtracking regex matcher.\nThe pattern must match the entire text.\nSupported features:\n- Literal characters\n- `.` matches any single character\n- Escaped characters `\\x`\n- Character classes `[...]`, `[^...]`, ranges `[a-z]`, literal `-` at start/end\n- Quantifiers `*`, `+`, `?` (greedy with backtracking)\n- No groups `(...)` or alternation `|`\n- Anchored match (entire text must be consumed)\n\nLet's design a recursive backtracking matcher.\nWe can parse the pattern into a list of tokens, or process it directly with indices.\nGiven the simplicity, processing with indices or a token list is fine.\nLet's tokenize the pattern first to make it easier.\nTokens could be:\n- `Literal(char)`\n- `Dot`\n- `Class(chars, negated)`\n- `Star`, `Plus`, `Question` (quantifiers)\n\nActually, it's easier to keep quantifiers attached to their preceding element, or handle them in the matcher.\nLet's define a token structure:\n`Element` can be `Literal`, `Dot`, `Class`.\n`Pattern` is a list of `(Element, Quantifier?)` where Quantifier is `None`, `*`, `+`, `?`.\n\nWait, parsing character classes correctly is important.\nRules for `[...]`:\n- Starts with `[`\n- If next is `^`, negated.\n- Ends with `]`\n- Inside, `-` is a range operator unless it's first or last.\n- `\\` escapes characters inside classes too? The problem says \"An escaped character `\\x` ... matches literally\". It doesn't explicitly say escaping works inside classes, but usually it does. I'll assume `\\` works inside classes too, or just treat `\\` as escaping the next char generally. Actually, the problem says \"An escaped character `\\x` ... the backslash strips any special meaning from the next character\". It's safer to handle `\\` inside classes as well. But standard regex usually handles it. I'll stick to simple parsing: inside `[...]`, if we see `\\`, consume next char as literal. If we see `-` at start or end, it's literal. Otherwise, it's a range.\n\nLet's write a parser.\nPattern string `p`.\nIndex `i`.\nFunction `parse()` returns list of tokens.\nEach token is a tuple: `(type, value, quantifier)`\nTypes: `LIT`, `DOT`, `CLASS`\nQuantifiers: `None`, `*`, `+`, `?`\n\nParsing logic:\n```python\ndef parse(pattern):\n tokens = []\n i = 0\n n = len(pattern)\n while i < n:\n c = pattern[i]\n if c == '\\\\':\n i += 1\n if i < n:\n tokens.append(('LIT', pattern[i], None))\n i += 1\n else:\n # trailing backslash? treat as literal or ignore? Usually literal.\n tokens.append(('LIT', '\\\\', None))\n elif c == '.':\n tokens.append(('DOT', None, None))\n i += 1\n elif c == '[':\n i += 1\n negated = False\n if i < n and pattern[i] == '^':\n negated = True\n i += 1\n chars = set()\n # handle first char specially for '-'\n if i < n and pattern[i] == '-':\n chars.add('-')\n i += 1\n while i < n and pattern[i] != ']':\n if pattern[i] == '\\\\':\n i += 1\n if i < n:\n chars.add(pattern[i])\n i += 1\n continue\n if i + 2 < n and pattern[i+1] == '-' and pattern[i+2] != ']':\n start = pattern[i]\n end = pattern[i+2]\n for code in range(ord(start), ord(end) + 1):\n chars.add(chr(code))\n i += 3\n else:\n chars.add(pattern[i])\n i += 1\n # handle last char if it's '-'\n if i < n and pattern[i] == ']':\n # check if the char before ']' was '-'\n # Actually, the loop above handles ranges. If we just added a single char, it's fine.\n # But what if the class is `[-a]` or `[a-]`?\n # My logic: if i < n and pattern[i] == '-', add it.\n # Then loop until ']'.\n # If the last char before ']' is '-', it will be added as a single char in the loop.\n # Wait, range logic: `pattern[i+1] == '-' and pattern[i+2] != ']'`\n # If it's `[a-]`, i points to 'a'. i+1 is '-', i+2 is ']'. Condition fails. Adds 'a'. i becomes i+1.\n # Next iter: i points to '-'. i+1 is ']'. Condition fails. Adds '-'. i becomes i+1.\n # Next iter: i points to ']'. Loop ends. Correct.\n pass\n if i < n and pattern[i] == ']':\n i += 1\n tokens.append(('CLASS', (chars, negated), None))\n elif c in '*+?':\n # Quantifier applies to previous token\n if tokens:\n tokens[-1] = (tokens[-1][0], tokens[-1][1], c)\n i += 1\n else:\n tokens.append(('LIT', c, None))\n i += 1\n return tokens\n```\nWait, the quantifier handling in parsing: `elif c in '*+?':` should be handled after adding a token, or we can just check during parsing. But what if the pattern starts with `*`? The problem says quantifier applies to preceding element. We can assume valid patterns or handle gracefully. I'll assume valid patterns as per typical coding challenges, but I'll make it robust.\n\nActually, it's simpler to parse into a list of `(element, quantifier)` where element is a function or tuple.\nLet's refine parsing.\nI'll represent elements as:\n- `('LIT', char)`\n- `('DOT',)`\n- `('CLASS', chars_set, negated)`\n\nAnd quantifiers as `None`, `*`, `+`, `?`.\n\nLet's rewrite parser carefully.\n```python\ndef parse(pattern):\n tokens = []\n i = 0\n n = len(pattern)\n while i < n:\n c = pattern[i]\n if c == '\\\\':\n i += 1\n if i < n:\n tokens.append(('LIT', pattern[i], None))\n i += 1\n else:\n tokens.append(('LIT', '\\\\', None))\n elif c == '.':\n tokens.append(('DOT', None, None))\n i += 1\n elif c == '[':\n i += 1\n \nā¦[19519 chars elided]ā¦\n negated = True\n i += 1\n chars = set()\n if i < n and p[i] == '-':\n chars.add('-')\n i += 1\n while i < n and p[i] != ']':\n if p[i] == '\\\\':\n i += 1\n if i < n:\n chars.add(p[i])\n i += 1\n continue\n if i + 2 < n and p[i+1] == '-' and p[i+2] != ']':\n start = p[i]\n end = p[i+2]\n for code in range(ord(start), ord(end) + 1):\n chars.add(chr(code))\n i += 3\n else:\n chars.add(p[i])\n i += 1\n if i < n and p[i] == ']':\n i += 1\n tokens.append(('CLASS', (chars, negated), None))\n elif c in '*+?':\n if tokens:\n t = tokens[-1]\n tokens[-1] = (t[0], t[1], c)\n i += 1\n else:\n tokens.append(('LIT', c, None))\n i += 1\n return tokens\n\n tokens = parse(pattern)\n \n def matches(ti, si):\n if ti == len(tokens):\n return si == len(text)\n \n t_type, t_val, quant = tokens[ti]\n \n def elem_match(char):\n if t_type == 'LIT':\n return char == t_val\n elif t_type == 'DOT':\n return True\n elif t_type == 'CLASS':\n chars, negated = t_val\n in_c = char in chars\n return not in_c if negated else in_c\n return False\n\n if quant is None:\n if si < len(text) and elem_match(text[si]):\n return matches(ti + 1, si + 1)\n return False\n elif quant == '?':\n if si < len(text) and elem_match(text[si]):\n if matches(ti + 1,",
"test_error": "no code extracted from response"
},
{
"total": 1,
"answer": "",
"passed": 0,
"reasoning": "The user wants a Python function `fullmatch(pattern: str, text: str) -> bool` that implements a backtracking regex matcher.\nIt needs to support:\n- Literal characters\n- `.` (any single character)\n- Escaped characters `\\x`\n- Character classes `[...]`, `[^...]`, ranges `[a-z]`, literal `-` at start/end\n- Quantifiers `*`, `+`, `?` (greedy, backtracking)\n- No groups or alternation\n- Anchored match (entire text must be consumed)\n\nI need to implement this from scratch without using `re`.\n\nLet's design a recursive backtracking matcher.\nThe pattern can be parsed into a list of tokens, or we can process it on the fly.\nGiven the simplicity, processing on the fly or parsing into a list of nodes is fine.\nLet's parse the pattern into a list of elements, where each element is either a literal, a dot, a class, or a quantified element.\nActually, it's easier to keep the pattern as a list of \"atoms\" followed by optional quantifiers.\nAn atom is: literal char, `.`, escaped char, or `[...]`.\nA quantifier modifies the preceding atom.\n\nLet's define a recursive function `match(pattern_idx, text_idx)` that returns True if `pattern[pattern_idx:]` matches `text[text_idx:]`.\nBase cases:\n- If `pattern_idx == len(pattern)`: return `text_idx == len(text)`\n- If `text_idx == len(text)`: check if remaining pattern can match empty string (only if all remaining atoms have `*` or `?` quantifiers, or are optional). Actually, the recursive structure handles this naturally if we handle quantifiers correctly.\n\nWait, handling quantifiers in a recursive descent matcher:\nIf the next pattern element has a quantifier `*`, `+`, or `?`:\nWe try to match the atom as many times as possible (greedy), then recursively call `match` for the rest of the pattern. If it fails, we backtrack by reducing the number of matches for the atom and try again.\n\nLet's formalize the pattern parsing.\nWe can convert the pattern string into a list of tuples: `(atom, quantifier)`.\n`atom` can be:\n- `'L'` (literal char)\n- `'.'` (dot)\n- `'C'` (character class, stores a set or a function to check membership)\n`quantifier` can be:\n- `None` (exactly one)\n- `'*'` (zero or more)\n- `'+'` (one or more)\n- `'?'` (zero or one)\n\nParsing logic:\nIterate through `pattern` string.\nIf we see `[`, parse until `]`. Handle `^` for negation, `-` for ranges.\nIf we see `\\`, next char is literal.\nOtherwise, char is literal or `.`.\nAfter parsing an atom, check if next char is `*`, `+`, `?`. If so, attach as quantifier.\n\nLet's write a parser function `parse(pattern)`:\n```python\ndef parse(pattern):\n tokens = []\n i = 0\n n = len(pattern)\n while i < n:\n if pattern[i] == '[':\n # parse character class\n j = i + 1\n if j < n and pattern[j] == '^':\n neg = True\n j += 1\n else:\n neg = False\n \n chars = set()\n while j < n and pattern[j] != ']':\n if j + 2 < n and pattern[j+1] == '-' and pattern[j+2] != ']':\n # range\n start = pattern[j]\n end = pattern[j+2]\n for c in range(ord(start), ord(end) + 1):\n chars.add(chr(c))\n j += 3\n else:\n chars.add(pattern[j])\n j += 1\n # j is at ']'\n tokens.append(('C', chars, neg))\n i = j + 1\n elif pattern[i] == '\\\\':\n i += 1\n if i < n:\n tokens.append(('L', pattern[i]))\n i += 1\n else:\n # trailing backslash? treat as literal or ignore? Usually literal.\n tokens.append(('L', '\\\\'))\n elif pattern[i] == '.':\n tokens.append(('D',)) # Dot\n i += 1\n else:\n tokens.append(('L', pattern[i]))\n i += 1\n \n # check quantifier\n if i < n and pattern[i] in '*+?':\n q = pattern[i]\n tokens[-1] = tokens[-1] + (q,)\n i += 1\n \n return tokens\n```\nWait, the tuple structure varies. Let's standardize:\nEach token is a dict or a fixed-length tuple.\nLet's use a list of objects or tuples: `(type, value, quantifier)`\n`type`: 'L', 'D', 'C'\n`value`: char for L, set for C, None for D\n`quantifier`: None, '*', '+', '?'\n\nRefined parser:\n```python\ndef parse(pattern):\n tokens = []\n i = 0\n n = len(pattern)\n while i < n:\n if pattern[i] == '[':\n j = i + 1\n neg = False\n if j < n and pattern[j] == '^':\n neg = True\n j += 1\n \n chars = set()\n while j < n and pattern[j] != ']':\n if j + 2 < n and pattern[j+1] == '-' and pattern[j+2] != ']':\n start = pattern[j]\n end = pattern[j+2]\n for c in range(ord(start), ord(end) + 1):\n chars.add(chr(c))\n j += 3\n else:\n chars.add(pattern[j])\n j += 1\n tokens.append(('C', chars, neg, None))\n i = j + 1\n elif pattern[i] == '\\\\':\n i += 1\n val = pattern[i] if i < n else '\\\\'\n tokens.append(('L', val, None))\n i += 1\n elif pattern[i] == '.':\n tokens.append(('D', None, None))\n i += 1\n else:\n tokens.append(('L', pattern[i], None))\n i += 1\n \n if i < n and pattern[i] in '*+?':\n q = pattern[i]\n tokens[-1] = tokens[-1][:-1] + (q,) # replace None with q\n i += 1\n return tokens\n```\nWait, `tokens[-1] = tokens[-1][:-1] + (q,)` works if the tuple is `(type, value, neg?, quantifier)`.\nFor 'C', it's `('C', chars, neg, None)`. So `tokens[-1][:-1] + (q,)` becomes `('C', chars, neg, q)`. Correct.\nFor 'L', it's `('L', val, None)`. Becomes `('L', val, q)`. Correct.\nFor 'D', it's `('D', None, None)`. Becomes `('D', None, q)`. Correct.\n\nNow the matcher:\n```python\ndef match(tokens, t_idx, p_idx):\n if p_idx == len(tokens):\n \nā¦[18930 chars elided]ā¦\n \n return solve(0, 0)\n```\n\nWait, `tokens[-1] = tokens[-1][:-1] + (q,)` might fail if `tokens` is empty? But `tokens` is never empty when this line runs because we just appended. So it's safe.\n\nOne minor improvement: `matches_atom` is redefined on every call to `solve`. It's fine, but I can move it out or keep it. It's cheap.\n\nLet's test `fullmatch(\"a*b\", \"b\")` again.\n`tokens = [('L', 'a', '*'), ('L', 'b', None)]`\n`solve(0, 0)`: `quant='*'`. `count=0`. `range(0, -1, -1)` -> `[0]`.\n`c=0`: `solve(1, 0)` -> `quant=None`. `text[0]='b'`. `matches_atom('b')` for `a` is False. Returns False.\nWait! `a*` should match zero `a`s, then `b` should match `b`.\nMy code: `solve(1, 0)` checks `token[1]` which is `('L', 'b', None)`.\n`matches_atom` for `b` checks `char == 'b'`. `text[0]` is `'b'`. So it returns True!\nAh, I misread my own trace. `solve(1, 0)` will match `b` correctly. So it returns True. Correct.\n\nWhat about `fullmatch(\"a*b\", \"ab\")`?\n`solve(0, 0)`: `count=1`. `range(1, -1, -1)` -> `[1, 0]`.\n`c=1`: `solve(1, 1)` -> matches `b` at `text[1]`. True.\nCorrect.\n\nOne thing: `fullmatch(\"a*b\", \"aab\")`?\n`count=2`. `range(2, -1, -1)` -> `[2, 1, 0]`.\n`c=2`: `solve(1, 2)` -> matches `b` at `text[2]`. True.\nCorrect.\n\nAll good.\n\nI will produce the final solution.\nI'll add `import sys` and `sys.setrecursionlimit(2000)` just in case, though probably not needed. Actually, I'll skip it to keep it clean. The recursion depth is proportional to pattern length, not text length.\n\nFinal check of the prompt: \"Implement a file `solution.py` containing a function `fullmatch`...\"\nI will output exactly that.\n\nOne detail: `tokens[-1] = tokens[-1][:-1] + (q,)` works, but `tokens[-1]` is a tuple. Tuples are immutable, so this creates a new tuple and assigns it to the list. That's correct.\n\nWait, `('C', chars, neg, None)` has length 4. `[:-1]` gives length 3. `+ (q,)` gives length 4. Correct.\n`('L', val, None)` has length 3. `[:-1]` gives length 2. `+ (q,)` gives length 3. Correct.\n`('D', None, None)` has length 3. `[:-1]` gives length 2. `+ (q,)`",
"test_error": "no code extracted from response"
},
{
"total": 1,
"answer": "",
"passed": 0,
"reasoning": "The user wants a Python function `fullmatch(pattern: str, text: str) -> bool` that implements a backtracking regex matcher.\nIt needs to support:\n- Literal characters\n- `.` (any single character)\n- Escaped characters `\\x`\n- Character classes `[...]`, `[^...]`, ranges `[a-z]`, literal `-` at start/end\n- Quantifiers `*`, `+`, `?` (greedy with backtracking)\n- Full match (anchored)\n- No groups or alternation.\n\nLet's design the solution.\nWe can parse the pattern into a list of tokens. Each token will be a tuple or object representing an element and an optional quantifier.\nActually, since we need backtracking, a recursive approach or an explicit stack approach works. Given Python's recursion limit, an explicit stack or iterative approach might be safer, but recursion is usually fine for typical regex lengths. I'll stick to recursion for simplicity, or implement a simple backtracking engine.\n\nLet's define the structure of a parsed pattern:\nA list of `(element, quantifier)` pairs.\n`element` can be:\n- `'literal'`: char\n- `'dot'`: matches any char\n- `'class'`: list of chars or ranges, negated flag\n`quantifier` can be:\n- `None` (exactly one)\n- `'*'` (zero or more)\n- `'+'` (one or more)\n- `'?'` (zero or one)\n\nParsing the pattern:\nIterate through the pattern string.\nIf we see `[`, parse until `]`. Handle `^` for negation. Handle ranges. Handle `-` at start/end.\nIf we see `\\`, next char is literal.\nOtherwise, it's a literal or `.`.\nAfter parsing an element, check if the next char is a quantifier (`*`, `+`, `?`). If so, attach it to the element and advance.\n\nLet's write a parser function.\n```python\ndef parse_pattern(pattern):\n tokens = []\n i = 0\n n = len(pattern)\n while i < n:\n if pattern[i] == '[':\n # Parse character class\n j = i + 1\n negated = False\n if j < n and pattern[j] == '^':\n negated = True\n j += 1\n \n chars = set()\n # Handle first char being '-'\n if j < n and pattern[j] == '-':\n chars.add('-')\n j += 1\n \n while j < n and pattern[j] != ']':\n if j + 2 < n and pattern[j+1] == '-' and pattern[j+2] != ']':\n # Range\n start_char = pattern[j]\n end_char = pattern[j+2]\n for c in range(ord(start_char), ord(end_char) + 1):\n chars.add(chr(c))\n j += 3\n else:\n chars.add(pattern[j])\n j += 1\n \n # Handle last char being '-'\n if j > i + 1 + negated and pattern[j-1] == '-':\n # Actually, the spec says: \"A `-` that appears first or last inside the class ... is a literal `-`\"\n # My loop above handles ranges. If `-` is last, it won't form a range because pattern[j+2] would be `]` or out of bounds.\n # Wait, if pattern is `[a-]`, j starts at `a`. `pattern[j+1]` is `-`, `pattern[j+2]` is `]`. So it won't match range condition. It adds `a`, then `-`. Correct.\n # But what if `[a-z-]`? `j` at `a`, range `a-z`, adds chars. `j` becomes index of `-`. Next iter: `pattern[j]` is `-`. `j+2` is `]` or out. Adds `-`. Correct.\n pass\n \n if j < n and pattern[j] == ']':\n j += 1 # consume `]`\n else:\n # Malformed, but assume valid per spec\n pass\n \n tokens.append(('class', chars, negated))\n i = j\n elif pattern[i] == '\\\\':\n i += 1\n if i < n:\n tokens.append(('literal', pattern[i]))\n i += 1\n else:\n # Trailing backslash, treat as literal? Spec says \\x matches x. Assume valid.\n tokens.append(('literal', '\\\\'))\n elif pattern[i] == '.':\n tokens.append(('dot',))\n i += 1\n else:\n tokens.append(('literal', pattern[i]))\n i += 1\n \n # Check for quantifier\n if i < n and pattern[i] in '*+?':\n quant = pattern[i]\n tokens[-1] = tokens[-1] + (quant,)\n i += 1\n \n return tokens\n```\n\nWait, the character class parsing needs to be robust.\nLet's refine the class parsing logic.\nThe spec says:\n- `[abc]` matches any one of listed.\n- `[^abc]` negated.\n- Ranges `[a-z]`.\n- `-` first or last is literal.\nMy logic:\n```python\n j = i + 1\n negated = False\n if j < n and pattern[j] == '^':\n negated = True\n j += 1\n \n chars = set()\n # We need to carefully handle '-'\n # Let's collect items inside brackets first\n items = []\n while j < n and pattern[j] != ']':\n if j + 2 < n and pattern[j+1] == '-' and pattern[j+2] != ']':\n items.append(('range', pattern[j], pattern[j+2]))\n j += 3\n else:\n items.append(('char', pattern[j]))\n j += 1\n \n # Now process items into chars set\n for item in items:\n if item[0] == 'range':\n start, end = item[1], item[2]\n for c in range(ord(start), ord(end) + 1):\n chars.add(chr(c))\n else:\n chars.add(item[1])\n \n # Wait, what if `-` is first or last?\n # If `[a-]`, items will be `[('char', 'a'), ('char', '-')]`. Correct.\n # If `[-a]`, items will be `[('char', '-'), ('char', 'a')]`. Correct.\n # If `[a-z]`, items will be `[('range', 'a', 'z')]`. Correct.\n # This handles the spec correctly.\n```\nActually, the spec says: \"A `-` that appears first or last inside the class (right after `[` or `[^`, or right before `]`) is a literal `-`, not a range.\"\nMy logic `pattern[j+2] != ']'` correctly prevents treating `-` before `]` as a range separator.\n\nā¦[21626 chars elided]ā¦\nde exactly that.\nI'll also add `import sys` and `sys.setrecursionlimit(10000)` at the top just to be robust, though not strictly required. Actually, I'll skip imports to keep it minimal unless necessary. The recursion depth is bounded by number of tokens, which is small. So it's fine.\n\nFinal check of the prompt: \"Implement a file solution.py containing a function fullmatch...\"\nI will output the code block.\n\nOne potential issue: `pattern` like `a*` on `\"\"`.\n`tokens`: `[('literal', 'a', '*')]`\n`match(0, 0)`: `quant='*'`, `max_k=0`. Loop `range(0, -1, -1)` -> `k=0`. `match(1, 0)`. `ti=1` == len. `si=0` == len. Returns True. Correct.\n\n`pattern` like `a+` on `\"\"`.\n`max_k=0`. `if max_k == 0: return False`. Correct.\n\n`pattern` like `a?` on `\"\"`.\n`quant='?'`. `si < len` is False. Skips if. Returns `match(1, 0)`. `ti=1` == len. `si=0` == len. Returns True. Correct.\n\nAll edge cases covered.\nI'll produce the solution. \nOne minor adjustment: I'll make sure indentation and formatting are perfect.\nThe code is ready.\nI will wrap it in the requested format.\nNo extra text.\nProceed. \nOutput matches the solution.\nOne thing: `sys.setrecursionlimit` is sometimes needed for backtracking regex on long strings with many quantifiers, but here depth is proportional to pattern length. I'll add it just in case, it doesn't hurt. Actually, I'll skip it to keep it clean. The problem statement doesn't mention huge inputs.\n\nFinal code:\n```python\ndef fullmatch(pattern: str, text: str) -> bool:\n \"\"\"Return True iff `pattern` matches the ENTIRE `text`.\"\"\"\n def parse_pattern(pat):\n tokens = []\n i = 0\n n = len(pat)\n while i < n:\n if pat[i] == '[':\n j = i + 1\n negated = False\n if j < n and pat[j] == '^':\n negated = True\n j += 1\n \n chars = set()\n while j < n and pat[j] != ']':\n if j + 2 < n and pat[j+1] == '-' and pat[j+2] != ']':\n start_char",
"test_error": ""
}
]