# 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


DEFAULT_COMBO_FACTOR = 64


def _dp_compare_combo(
    cost1: int,
    cost2: int,
    i1_union_i2: Set[int],
    size_dict: List[int],
    cost_cap: int,
    s1: int,
    s2: int,
    xn: Dict[int, Any],
    g: int,
    all_tensors: int,
    inputs: List[FrozenSet[int]],
    i1_cut_i2_wo_output: Set[int],
    memory_limit: Optional[int],
    contract1: Union[int, Tuple[int]],
    contract2: Union[int, Tuple[int]],
    factor: Union[int, float] = DEFAULT_COMBO_FACTOR,
    combine: Callable = sum,
) -> None:
    """Like ``_dp_compare_flops`` but sieves the potential contraction based
    on some combination of both the flops and size,
    """
    s = s1 | s2
    i = _dp_calc_legs(g, all_tensors, s, inputs, i1_cut_i2_wo_output, i1_union_i2)
    mem = compute_size_by_dict(i, size_dict)

# 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



DEFAULT_COMBO_FACTOR = 64


def _dp_compare_combo(
    cost1: int,
    cost2: int,
    i1_union_i2: Set[int],
    size_dict: List[int],
    cost_cap: int,
    s1: int,
    s2: int,
    xn: Dict[int, Any],
    g: int,
    all_tensors: int,
    inputs: List[FrozenSet[int]],
    i1_cut_i2_wo_output: Set[int],
    memory_limit: Optional[int],
    contract1: Union[int, Tuple[int]],
    contract2: Union[int, Tuple[int]],
    factor: Union[int, float] = DEFAULT_COMBO_FACTOR,
    combine: Callable = sum,
) -> None:
    """Like ``_dp_compare_flops`` but sieves the potential contraction based
    on some combination of both the flops and size,
    """
    s = s1 | s2
    i = _dp_calc_legs(g, all_tensors, s, inputs, i1_cut_i2_wo_output, i1_union_i2)
    mem = compute_size_by_dict(i, size_dict)

    f = compute_size_by_dict(i1_union_i2, size_dict)