






from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
__UpperCAmelCase										=		{
    '1': ['2', '3', '4', '5'],
    '2': ['1', '3', '4', '5'],
    '3': ['1', '2', '4', '5', '10'],
    '4': ['1', '2', '3', '5', '6'],
    '5': ['1', '2', '3', '4', '7'],
    '6': ['7', '8', '9', '10', '4'],
    '7': ['6', '8', '9', '10', '5'],
    '8': ['6', '7', '9', '10'],
    '9': ['6', '7', '8', '10'],
    '10': ['6', '7', '8', '9', '3'],
}




def   lowercase__   (  __snake_case					:							dict[str, list[str]]						):


					'''simple docstring'''


					UpperCAmelCase_					:   List[str]   =		{node: {node} for node in graph}

					UpperCAmelCase_					:   List[Any]   =		{node: graph[node][:] for node in graph}

					while len(__snake_case						) > 2:
										# Choose a random edge.
										UpperCAmelCase_					:   Any   =		random.choice(list(graph_copy.keys()						)						)
										UpperCAmelCase_					:   Union[str, Any]   =		random.choice(graph_copy[u]						)

										# Contract edge (u, v) to new node uv
										UpperCAmelCase_					:   Any   =		u + v
										UpperCAmelCase_					:   Any   =		list(set(graph_copy[u] + graph_copy[v]						)						)
										uv_neighbors.remove(__snake_case						)
										uv_neighbors.remove(__snake_case						)
										UpperCAmelCase_					:   Optional[int]   =		uv_neighbors
										for neighbor in uv_neighbors:
															graph_copy[neighbor].append(__snake_case						)

										UpperCAmelCase_					:   List[Any]   =		set(contracted_nodes[u].union(contracted_nodes[v]						)						)

										# Remove nodes u and v.
										del graph_copy[u]
										del graph_copy[v]
										for neighbor in uv_neighbors:
															if u in graph_copy[neighbor]:
																				graph_copy[neighbor].remove(__snake_case						)
															if v in graph_copy[neighbor]:
																				graph_copy[neighbor].remove(__snake_case						)

    # Find cutset.
					UpperCAmelCase_					:   Tuple   =		[contracted_nodes[node] for node in graph_copy]
					return {
					    (node, neighbor)
					    for node in groups[0]
					    for neighbor in graph[node]
					    if neighbor in groups[1]
					}


if __name__ == "__main__":
		print(partition_graph(TEST_GRAPH))














import torch.nn as nn

from .imports import is_fpa_available


if is_fpa_available():
		import transformer_engine.pytorch as te




def   lowercase__   (  __snake_case					:							List[str]  , __snake_case					:							List[Any]=True  , __snake_case					:							str=True  , __snake_case					:							Tuple=True						):


					'''simple docstring'''


					if not is_fpa_available():
										raise ImportError('Using `convert_model` requires transformer_engine to be installed.'						)
					for name, module in model.named_children():
										if isinstance(__snake_case  , nn.Linear						) and to_transformer_engine and _convert_linear:
															# Return early if the linear layer weights are not multiples of 16
															if any(p % 16 != 0 for p in module.weight.shape						):
																				return
															UpperCAmelCase_					:   Optional[int]   =		module.bias is not None
															UpperCAmelCase_					:   Optional[int]   =		te.Linear(
															    module.in_features  , module.out_features  , bias=__snake_case  , params_dtype=module.weight.dtype						)
															UpperCAmelCase_					:   List[str]   =		module.weight.data.clone()
															if has_bias:
																				UpperCAmelCase_					:   List[Any]   =		module.bias.data.clone()

															setattr(__snake_case  , __snake_case  , __snake_case						)
										elif isinstance(__snake_case  , nn.LayerNorm						) and to_transformer_engine and _convert_ln:
															UpperCAmelCase_					:   int   =		te.LayerNorm(module.normalized_shape[0]  , eps=module.eps  , params_dtype=module.weight.dtype						)
															UpperCAmelCase_					:   Any   =		module.weight.data.clone()
															UpperCAmelCase_					:   Any   =		module.bias.data.clone()

															setattr(__snake_case  , __snake_case  , __snake_case						)
										elif isinstance(__snake_case  , te.Linear						) and not to_transformer_engine and _convert_linear:
															UpperCAmelCase_					:   int   =		module.bias is not None
															UpperCAmelCase_					:   Tuple   =		nn.Linear(
															    module.in_features  , module.out_features  , bias=__snake_case  , params_dtype=module.weight.dtype						)
															UpperCAmelCase_					:   str   =		module.weight.data.clone()
															if has_bias:
																				UpperCAmelCase_					:   Dict   =		module.bias.data.clone()

															setattr(__snake_case  , __snake_case  , __snake_case						)
										elif isinstance(__snake_case  , te.LayerNorm						) and not to_transformer_engine and _convert_ln:
															UpperCAmelCase_					:   List[Any]   =		nn.LayerNorm(module.normalized_shape[0]  , eps=module.eps  , params_dtype=module.weight.dtype						)
															UpperCAmelCase_					:   List[str]   =		module.weight.data.clone()
															UpperCAmelCase_					:   Tuple   =		module.bias.data.clone()

															setattr(__snake_case  , __snake_case  , __snake_case						)
										else:
															convert_model(
															    __snake_case  , to_transformer_engine=__snake_case  , _convert_linear=_convert_linear  , _convert_ln=_convert_ln  , )






def   lowercase__   (  __snake_case					:							List[Any]						):


					'''simple docstring'''


					if not is_fpa_available():
										raise ImportError('Using `has_transformer_engine_layers` requires transformer_engine to be installed.'						)
					for m in model.modules():
										if isinstance(__snake_case  , (te.LayerNorm, te.Linear)						):
															return True
					return False






