# 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

    def __call__(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
        memory_limit: Optional[int] = None,
    ) -> PathType:
        raise NotImplementedError


def ssa_to_linear(ssa_path: PathType) -> PathType:
    """
    Convert a path with static single assignment ids to a path with recycled
    linear ids. For example:

    ```python
    ssa_to_linear([(0, 3), (2, 4), (1, 5)])
    #> [(0, 3), (1, 2), (0, 1)]
    ```
    """
    ids = np.arange(1 + max(map(max, ssa_path)), dtype=np.int32)  # type: ignore
    path = []
    for ssa_ids in ssa_path:
        path.append(tuple(int(ids[ssa_id]) for ssa_id in ssa_ids))
        for ssa_id in ssa_ids:
            ids[ssa_id:] -= 1
    return path



# 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


    def __call__(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
        memory_limit: Optional[int] = None,
    ) -> PathType:
        raise NotImplementedError


def ssa_to_linear(ssa_path: PathType) -> PathType:
    """
    Convert a path with static single assignment ids to a path with recycled
    linear ids. For example:

    ```python
    ssa_to_linear([(0, 3), (2, 4), (1, 5)])
    #> [(0, 3), (1, 2), (0, 1)]
    ```
    """
    ids = np.arange(1 + max(map(max, ssa_path)), dtype=np.int32)  # type: ignore
    path = []
    for ssa_ids in ssa_path:
        path.append(tuple(int(ids[ssa_id]) for ssa_id in ssa_ids))
        for ssa_id in ssa_ids:
            ids[ssa_id:] -= 1
    return path



def linear_to_ssa(path: PathType) -> PathType: