





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
_a									=				{
    "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))










import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
			import torch

if is_vision_available():
			from PIL import Image

			from transformers import ViltImageProcessor






class  __A   (   unittest.TestCase			):

			'''simple docstring'''







			def __init__(   self	,  __lowerCAmelCase	,  __lowerCAmelCase=7	,  __lowerCAmelCase=3	,  __lowerCAmelCase=1_8	,  __lowerCAmelCase=3_0	,  __lowerCAmelCase=4_0_0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=None	,  __lowerCAmelCase=2	,  __lowerCAmelCase=True	,  __lowerCAmelCase=[0.5, 0.5, 0.5]	,  __lowerCAmelCase=[0.5, 0.5, 0.5]	,  ):



				'''simple docstring'''







				lowerCamelCase__        =		size if size is not None else {'''shortest_edge''': 3_0}
				lowerCamelCase__        =		parent
				lowerCamelCase__        =		batch_size
				lowerCamelCase__        =		num_channels
				lowerCamelCase__        =		image_size
				lowerCamelCase__        =		min_resolution
				lowerCamelCase__        =		max_resolution
				lowerCamelCase__        =		do_resize
				lowerCamelCase__        =		size
				lowerCamelCase__        =		size_divisor
				lowerCamelCase__        =		do_normalize
				lowerCamelCase__        =		image_mean
				lowerCamelCase__        =		image_std





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return {
				    "image_mean": self.image_mean,
				    "image_std": self.image_std,
				    "do_normalize": self.do_normalize,
				    "do_resize": self.do_resize,
				    "size": self.size,
				    "size_divisor": self.size_divisor,
				}





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase=False							):



				'''simple docstring'''







				if not batched:
					lowerCamelCase__        =		self.size['''shortest_edge''']
					lowerCamelCase__        =		image_inputs[0]
					if isinstance(__lowerCAmelCase	,  Image.Image							):
						lowerCamelCase__    ,     lowerCamelCase__        =		image.size
					else:
						lowerCamelCase__    ,     lowerCamelCase__        =		image.shape[1], image.shape[2]
					lowerCamelCase__        =		size / min(__lowerCAmelCase	,  __lowerCAmelCase							)
					if h < w:
						lowerCamelCase__    ,     lowerCamelCase__        =		size, scale * w
					else:
						lowerCamelCase__    ,     lowerCamelCase__        =		scale * h, size

					lowerCamelCase__        =		int((1_3_3_3 / 8_0_0) * size							)
					if max(__lowerCAmelCase	,  __lowerCAmelCase							) > max_size:
						lowerCamelCase__        =		max_size / max(__lowerCAmelCase	,  __lowerCAmelCase							)
						lowerCamelCase__        =		newh * scale
						lowerCamelCase__        =		neww * scale

					lowerCamelCase__    ,     lowerCamelCase__        =		int(newh + 0.5							), int(neww + 0.5							)
					lowerCamelCase__    ,     lowerCamelCase__        =		(
					    newh // self.size_divisor * self.size_divisor,
					    neww // self.size_divisor * self.size_divisor,
					)

				else:
					lowerCamelCase__        =		[]
					for image in image_inputs:
						lowerCamelCase__    ,     lowerCamelCase__        =		self.get_expected_values([image]							)
						expected_values.append((expected_height, expected_width)							)
					lowerCamelCase__        =		max(__lowerCAmelCase	,  key=lambda __lowerCAmelCase							: item[0]							)[0]
					lowerCamelCase__        =		max(__lowerCAmelCase	,  key=lambda __lowerCAmelCase							: item[1]							)[1]

				return expected_height, expected_width






@require_torch
@require_vision
class  __A   (   lowerCAmelCase      ,    unittest.TestCase			):

			'''simple docstring'''







			lowerCAmelCase_												=						ViltImageProcessor if is_vision_available() else None





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		ViltImageProcessingTester(self							)





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.image_processor_tester.prepare_image_processor_dict()





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''image_mean'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''image_std'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''do_normalize'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''do_resize'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''size'''							)							)
				self.assertTrue(hasattr(__lowerCAmelCase	,  '''size_divisor'''							)							)





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class.from_dict(self.image_processor_dict							)
				self.assertEqual(image_processor.size	,  {'''shortest_edge''': 3_0}							)

				lowerCamelCase__        =		self.image_processing_class.from_dict(self.image_processor_dict	,  size=4_2							)
				self.assertEqual(image_processor.size	,  {'''shortest_edge''': 4_2}							)





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				pass





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random PIL images
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  Image.Image							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random numpy tensors
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase	,  numpify=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  np.ndarray							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.image_processing_class(**self.image_processor_dict							)
				# create random PyTorch tensors
				lowerCamelCase__        =		prepare_image_inputs(self.image_processor_tester	,  equal_resolution=__lowerCAmelCase	,  torchify=__lowerCAmelCase							)
				for image in image_inputs:
					self.assertIsInstance(__lowerCAmelCase	,  torch.Tensor							)

				# Test not batched input
				lowerCamelCase__        =		image_processing(image_inputs[0]	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (1, self.image_processor_tester.num_channels, expected_height, expected_width)	,  )

				# Test batched
				lowerCamelCase__        =		image_processing(__lowerCAmelCase	,  return_tensors='''pt'''							).pixel_values

				lowerCamelCase__    ,     lowerCamelCase__        =		self.image_processor_tester.get_expected_values(__lowerCAmelCase	,  batched=__lowerCAmelCase							)
				self.assertEqual(
				    encoded_images.shape	,  (
				        self.image_processor_tester.batch_size,
				        self.image_processor_tester.num_channels,
				        expected_height,
				        expected_width,
				    )	,  )



