





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
snake_case__									=				{
    "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 lowerCAmelCase__(__snake_case							)    ->				set[tuple[str, str]]:







	'''simple docstring'''







	lowerCamelCase__        =		{node: {node} for node in graph}

	lowerCamelCase__        =		{node: graph[node][:] for node in graph}

	while len(__snake_case							) > 2:
		# Choose a random edge.
		lowerCamelCase__        =		random.choice(list(graph_copy.keys()							)							)
		lowerCamelCase__        =		random.choice(graph_copy[u]							)

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

		lowerCamelCase__        =		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.
	lowerCamelCase__        =		[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))










from ...configuration_utils import PretrainedConfig
from ...utils import logging


_a									=				logging.get_logger(__name__)

_a									=				{
    "google/pegasus-x-base": "https://huggingface.co/google/pegasus-x-base/resolve/main/config.json",
    "google/pegasus-x-large": "https://huggingface.co/google/pegasus-x-large/resolve/main/config.json",
    # See all PEGASUS-X models at https://huggingface.co/models?filter=pegasus-x
}






class  __A   (   lowerCAmelCase			):

			'''simple docstring'''







			lowerCAmelCase_												=						"""pegasus_x"""
			lowerCAmelCase_												=						["""past_key_values"""]
			lowerCAmelCase_												=						{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}





			def __init__(   self	,  __lowerCAmelCase=9_6_1_0_3	,  __lowerCAmelCase=1_6_3_8_4	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=4_0_9_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=4_0_9_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=True	,  __lowerCAmelCase="gelu"	,  __lowerCAmelCase=1_0_2_4	,  __lowerCAmelCase=0.1	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.02	,  __lowerCAmelCase=0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=0	,  __lowerCAmelCase=1	,  __lowerCAmelCase=1	,  __lowerCAmelCase=3_2	,  __lowerCAmelCase=5_1_2	,  __lowerCAmelCase=True	,  **__lowerCAmelCase	,  ):



				'''simple docstring'''







				lowerCamelCase__        =		vocab_size
				lowerCamelCase__        =		max_position_embeddings
				lowerCamelCase__        =		d_model
				lowerCamelCase__        =		encoder_ffn_dim
				lowerCamelCase__        =		encoder_layers
				lowerCamelCase__        =		encoder_attention_heads
				lowerCamelCase__        =		decoder_ffn_dim
				lowerCamelCase__        =		decoder_layers
				lowerCamelCase__        =		decoder_attention_heads
				lowerCamelCase__        =		dropout
				lowerCamelCase__        =		attention_dropout
				lowerCamelCase__        =		activation_dropout
				lowerCamelCase__        =		activation_function
				lowerCamelCase__        =		init_std
				lowerCamelCase__        =		encoder_layerdrop
				lowerCamelCase__        =		decoder_layerdrop
				lowerCamelCase__        =		use_cache
				lowerCamelCase__        =		encoder_layers
				lowerCamelCase__        =		scale_embedding  # scale factor will be sqrt(d_model) if True

				lowerCamelCase__        =		num_global_tokens
				lowerCamelCase__        =		block_size
				lowerCamelCase__        =		stagger_local_blocks

				super().__init__(
				    pad_token_id=__lowerCAmelCase	,  eos_token_id=__lowerCAmelCase	,  is_encoder_decoder=__lowerCAmelCase	,  decoder_start_token_id=__lowerCAmelCase	,  forced_eos_token_id=__lowerCAmelCase	,  **__lowerCAmelCase	,  )





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.encoder_attention_heads





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.d_model



