# Path: opt_einsum/helpers.py
# @overload
# def compute_size_by_dict(indices: Iterable[int], idx_dict: List[int]) -> int:
#     ...
# 
# def flop_count(
#     idx_contraction: Collection[str],
#     inner: bool,
#     num_terms: int,
#     size_dictionary: Dict[str, int],
# ) -> int:
#     """
#     Computes the number of FLOPS in the contraction.
# 
#     Parameters
#     ----------
#     idx_contraction : iterable
#         The indices involved in the contraction
#     inner : bool
#         Does this contraction require an inner product?
#     num_terms : int
#         The number of terms in a contraction
#     size_dictionary : dict
#         The size of each of the indices in idx_contraction
# 
#     Returns
#     -------
#     flop_count : int
#         The total number of FLOPS required for the contraction.
# 
#     Examples
#     --------
# 
#     >>> flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
#     30
# 
#     >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
#     60
# 
#     """
# 
#     overall_size = compute_size_by_dict(idx_contraction, size_dictionary)
#     op_factor = max(1, num_terms - 1)
#     if inner:
#         op_factor += 1
# 
#     return overall_size * op_factor
# 
# Path: opt_einsum/typing.py



import functools
import heapq
import itertools
import operator
import random
import re
import numpy as np
from collections import Counter, OrderedDict, defaultdict
from typing import Any, Callable
from typing import Counter as CounterType
from typing import Dict, FrozenSet, Generator, List, Optional, Sequence, Set, Tuple, Union
from .helpers import compute_size_by_dict, flop_count
from .typing import ArrayIndexType, PathType
    from .path_random import random_greedy_128


class PathOptimizer:
    """Base class for different path optimizers to inherit from.

    Subclassed optimizers should define a call method with signature:

    ```python
    def __call__(self, inputs, output, size_dict, memory_limit=None):
        \"\"\"
        **Parameters:**
        ----------
        inputs : list[set[str]]
            The indices of each input array.
        outputs : set[str]
            The output indices
        size_dict : dict[str, int]
            The size of each index
        memory_limit : int, optional
            If given, the maximum allowed memory.
        \"\"\"
        # ... compute path here ...
        return path
    ```

    where `path` is a list of int-tuples specifying a contraction order.
    """

    def _check_args_against_first_call(
        self,

# Path: opt_einsum/helpers.py
# @overload
# def compute_size_by_dict(indices: Iterable[int], idx_dict: List[int]) -> int:
#     ...
# 
# def flop_count(
#     idx_contraction: Collection[str],
#     inner: bool,
#     num_terms: int,
#     size_dictionary: Dict[str, int],
# ) -> int:
#     """
#     Computes the number of FLOPS in the contraction.
# 
#     Parameters
#     ----------
#     idx_contraction : iterable
#         The indices involved in the contraction
#     inner : bool
#         Does this contraction require an inner product?
#     num_terms : int
#         The number of terms in a contraction
#     size_dictionary : dict
#         The size of each of the indices in idx_contraction
# 
#     Returns
#     -------
#     flop_count : int
#         The total number of FLOPS required for the contraction.
# 
#     Examples
#     --------
# 
#     >>> flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
#     30
# 
#     >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
#     60
# 
#     """
# 
#     overall_size = compute_size_by_dict(idx_contraction, size_dictionary)
#     op_factor = max(1, num_terms - 1)
#     if inner:
#         op_factor += 1
# 
#     return overall_size * op_factor
# 
# Path: opt_einsum/typing.py



# Path: opt_einsum/paths.py
import functools
import heapq
import itertools
import operator
import random
import re
import numpy as np
from collections import Counter, OrderedDict, defaultdict
from typing import Any, Callable
from typing import Counter as CounterType
from typing import Dict, FrozenSet, Generator, List, Optional, Sequence, Set, Tuple, Union
from .helpers import compute_size_by_dict, flop_count
from .typing import ArrayIndexType, PathType
    from .path_random import random_greedy_128



class PathOptimizer:
    """Base class for different path optimizers to inherit from.

    Subclassed optimizers should define a call method with signature:

    ```python
    def __call__(self, inputs, output, size_dict, memory_limit=None):
        \"\"\"
        **Parameters:**
        ----------
        inputs : list[set[str]]
            The indices of each input array.
        outputs : set[str]
            The output indices
        size_dict : dict[str, int]
            The size of each index
        memory_limit : int, optional
            If given, the maximum allowed memory.
        \"\"\"
        # ... compute path here ...
        return path
    ```

    where `path` is a list of int-tuples specifying a contraction order.
    """

    def _check_args_against_first_call(
        self,

        inputs: List[ArrayIndexType],