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import random
import sys
from contextlib import contextmanager
import sympy as sp
from sympy.core.cache import clear_cache
class TimeoutException(Exception):
pass
@contextmanager
def time_limit(seconds):
# Безопасный таймаут для Unix-подобных систем
if sys.platform != "win32":
import signal
def signal_handler(signum, frame):
raise TimeoutException("Timed out!")
old_handler = signal.signal(signal.SIGALRM, signal_handler)
signal.alarm(seconds)
try:
yield
finally:
signal.alarm(0)
signal.signal(signal.SIGALRM, old_handler)
x = sp.Symbol("x", real=True)
UNARY_OPS = {
"sin": {"symbol": sp.sin, "weight": 4},
# "cos": {"symbol": sp.cos, "weight": 4},
"exp": {"symbol": sp.exp, "weight": 4},
"ln": {"symbol": sp.log, "weight": 4},
"sqrt": {"symbol": sp.sqrt, "weight": 4},
"abs": {"symbol": sp.Abs, "weight": 4},
"tan": {"symbol": sp.tan, "weight": 4},
"pow2": {"symbol": lambda arg: sp.Pow(arg, sp.Integer(2)), "weight": 4},
"pow3": {"symbol": lambda arg: sp.Pow(arg, sp.Integer(3)), "weight": 2},
"pow4": {"symbol": lambda arg: sp.Pow(arg, sp.Integer(4)), "weight": 1},
"pow5": {"symbol": lambda arg: sp.Pow(arg, sp.Integer(5)), "weight": 1},
}
BINARY_OPS = {
"Add": {"symbol": sp.Add, "weight": 10},
"Sub": {"symbol": lambda a, b: a - b, "weight": 5},
"Mul": {"symbol": sp.Mul, "weight": 10},
"Div": {"symbol": lambda a, b: a / b, "weight": 5},
}
CONSTANTS = [-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]
class ExpressionGenerator:
def __init__(
self,
max_ops: int,
timeout: int,
unary_ops: dict = UNARY_OPS,
binary_ops: dict = BINARY_OPS,
constants: list = CONSTANTS,
) -> None:
"""
:param max_ops: Количество операторов (внутренних узлов) в выражении (n в статье).
:param unary_ops: Словарь унарных операторов.
:param binary_ops: Словарь бинарных операторов.
:param leaves: Список всех возможных листьев (переменные + константы), равномерное распределение L.
:param timeout: Таймаут для генерации и упрощения выражения.
"""
self.max_ops = max_ops
self.timeout = timeout
self.unary_ops = unary_ops
self.binary_ops = binary_ops
self.constants = constants
self.unary_ops_keys = list(unary_ops.keys())
self.unary_ops_weights = [op["weight"] for op in unary_ops.values()]
self.p1 = sum(self.unary_ops_weights)
self.binary_ops_keys = list(binary_ops.keys())
self.binary_ops_weights = [op["weight"] for op in binary_ops.values()]
self.p2 = sum(self.binary_ops_weights)
self.L = 1
self.D = [[0] * (max_ops + 1) for _ in range(max_ops + 2)]
for e in range(max_ops + 2):
self.D[e][0] = self.L**e
for n in range(1, max_ops + 1):
for e in range(1, max_ops - n + 2):
self.D[e][n] = self.L * self.D[e - 1][n] + self.p1 * self.D[e][n - 1]
if e + 1 < max_ops + 2:
self.D[e][n] += self.p2 * self.D[e + 1][n - 1]
def _sample_leaf(self):
if random.random() < 0.8:
return x
else:
return sp.Integer(random.choice(self.constants))
def _skeletonize(self, expr, c_list):
def get_c():
c = sp.Symbol(f"C_{len(c_list)}", real=True)
c_list.append(c)
return c
if expr == x:
return sp.Add(sp.Mul(get_c(), x, evaluate=False), get_c(), evaluate=False)
if expr.is_Number:
return get_c()
if expr.is_Add:
return sp.Add(
*[self._skeletonize(arg, c_list) for arg in expr.args], evaluate=False
)
if expr.is_Mul:
return sp.Mul(
*[self._skeletonize(arg, c_list) for arg in expr.args], evaluate=False
)
if expr.is_Pow:
base = self._skeletonize(expr.args[0], c_list)
if expr.args[1].has(x):
expo = self._skeletonize(expr.args[1], c_list)
else:
expo = expr.args[1]
pow_expr = sp.Pow(base, expo, evaluate=False)
return sp.Mul(get_c(), pow_expr, evaluate=False)
if expr.is_Function:
arg = self._skeletonize(expr.args[0], c_list)
return sp.Mul(get_c(), expr.func(arg), evaluate=False)
return expr
def _clean_skeleton(self, expr):
try:
expr = sp.expand(expr)
except Exception as e:
logging.warning(f"Ошибка при раскрытии скобок sp.expand: {e}")
c_counter = 0
def get_new_c() -> sp.Symbol:
nonlocal c_counter
c = sp.Symbol(f"C_{c_counter}", real=True)
c_counter += 1
return c
def _is_const(node):
return x not in getattr(node, "free_symbols", set())
def _fold(node):
if node == x:
return x
if isinstance(node, sp.Number):
return node
if _is_const(node):
return get_new_c()
if not getattr(node, "args", None):
return node
args = [_fold(arg) for arg in node.args]
new_expr = node.func(*args)
if new_expr.is_Mul:
has_x = []
no_x = []
for a in new_expr.args:
if _is_const(a):
no_x.append(a)
else:
has_x.append(a)
if no_x:
return sp.Mul(get_new_c(), *has_x)
return new_expr
if new_expr.is_Add:
has_x = []
no_x = []
for a in new_expr.args:
if _is_const(a):
no_x.append(a)
else:
has_x.append(a)
x_terms = set()
res_terms = []
if no_x:
res_terms.append(get_new_c())
for term in has_x:
if term.is_Mul:
x_parts = [a for a in term.args if not _is_const(a)]
x_key = sp.Mul(*x_parts)
else:
x_key = term
if x_key not in x_terms:
x_terms.add(x_key)
res_terms.append(sp.Mul(get_new_c(), x_key))
if not res_terms:
return sp.Integer(0)
if len(res_terms) == 1:
return res_terms[0]
return sp.Add(*res_terms)
return new_expr
clean_expr = _fold(expr)
final_free_syms = getattr(clean_expr, "free_symbols", set())
used_c = sorted(
[s for s in final_free_syms if str(s).startswith("C_")],
key=lambda s: int(str(s).split("_")[1]),
)
new_c_list = []
reindex_map = {}
for i, old_c in enumerate(used_c):
new_c = sp.Symbol(f"C_{i}", real=True)
new_c_list.append(new_c)
reindex_map[old_c] = new_c
clean_expr = clean_expr.xreplace(reindex_map)
return clean_expr, new_c_list
def _generate_raw(self, fixed_n: int):
"""
Генерирует AST дерево в префиксной нотации (Алгоритм 2 из статьи),
и собирает из него SymPy выражение.
"""
e = 1
n = fixed_n
tree_nodes = []
while n > 0:
probs = []
choices = []
for k in range(e):
if self.p1 > 0:
w1 = (self.L**k) * self.p1 * self.D[e - k][n - 1]
if w1 > 0:
probs.append(w1)
choices.append((k, 1))
if self.p2 > 0 and (e - k + 1) < len(self.D):
w2 = (self.L**k) * self.p2 * self.D[e - k + 1][n - 1]
if w2 > 0:
probs.append(w2)
choices.append((k, 2))
if sum(probs) == 0:
return None
k, arity = random.choices(choices, weights=probs, k=1)[0]
for _ in range(k):
tree_nodes.append(("leaf", None))
if arity == 1:
op_name = random.choices(
self.unary_ops_keys, weights=self.unary_ops_weights, k=1
)[0]
tree_nodes.append(("unary", op_name))
e = e - k
else:
op_name = random.choices(
self.binary_ops_keys, weights=self.binary_ops_weights, k=1
)[0]
tree_nodes.append(("binary", op_name))
e = e - k + 1
n -= 1
for _ in range(e):
tree_nodes.append(("leaf", None))
iterator = iter(tree_nodes)
def build_ast():
try:
token_type, value = next(iterator)
except StopIteration:
return None
if token_type == "leaf":
return self._sample_leaf()
elif token_type == "unary":
arg = build_ast()
if arg is None:
return None
func = self.unary_ops[value]["symbol"]
return func(arg)
elif token_type == "binary":
arg1 = build_ast()
arg2 = build_ast()
if arg1 is None or arg2 is None:
return None
func = self.binary_ops[value]["symbol"]
return func(arg1, arg2)
return build_ast()
def generate_expr(self):
attempts = 0
n = random.randint(1, self.max_ops)
while True:
attempts += 1
if attempts % 100000 == 0:
clear_cache()
stage = "INIT"
expr = None
try:
with time_limit(self.timeout):
stage = "GENERATE"
expr = self._generate_raw(n)
if expr is None:
continue
stage = "SIMPLIFY"
expr = sp.simplify(expr)
if expr.has(sp.I, sp.nan, sp.zoo, sp.oo, -sp.oo) or not expr.has(x):
continue
stage = "SKELETONIZE"
c_list = []
raw_skeleton = self._skeletonize(expr, c_list)
extra_c = sp.Symbol(f"C_{len(c_list)}", real=True)
c_list.append(extra_c)
raw_skeleton = sp.Add(raw_skeleton, extra_c, evaluate=False)
stage = "CLEAN_SKELETON"
skeleton, c_list = self._clean_skeleton(raw_skeleton)
if not skeleton.has(x):
continue
max_c = min(3, len(c_list))
num_random_c = random.randint(0, max_c)
chosen_cs = set(random.sample(c_list, num_random_c))
inactive_c_values = {
c: sp.Integer(1) for c in c_list if c not in chosen_cs
}
expr_instantiated = skeleton.subs(inactive_c_values)
c_values = {}
for c in chosen_cs:
val = random.uniform(0.5, 5.0)
if random.random() < 0.5:
val = -val
c_values[c] = val
expr_instantiated = expr_instantiated.subs(c_values)
return skeleton, expr, expr_instantiated
except TimeoutException:
try:
bad_expr = str(expr) if expr is not None else "None"
except Exception:
bad_expr = "Неизвестное выражение (стадия генерации)"
logging.error(
f"Timeout[{stage}] {self.timeout} секунд. Пропущено выражение: {bad_expr}"
)
continue
except Exception:
logging.exception("Ошибка при генерации выражения.")
continue
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