



import numpy as np
import requests



def        __a     (    )      -> Tuple:






						'''simple docstring'''



						UpperCAmelCase_=   requests.get(
						    """https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/"""
						    """master/Week1/ADRvsRating.csv"""				)
						UpperCAmelCase_=   response.text.splitlines()
						UpperCAmelCase_=   []
						for item in lines:
												UpperCAmelCase_=   item.split(""","""				)
												data.append(lowerCAmelCase_				)
						data.pop(0				)  # This is for removing the labels from the list
						UpperCAmelCase_=   np.matrix(lowerCAmelCase_				)
						return dataset



def        __a     (    lowerCAmelCase_   :					List[Any]			,lowerCAmelCase_   :					Dict			,lowerCAmelCase_   :					Any			,lowerCAmelCase_   :					Optional[int]			,lowerCAmelCase_   :					Any				)      -> int:






						'''simple docstring'''



						UpperCAmelCase_=   len_data

						UpperCAmelCase_=   np.dot(lowerCAmelCase_			,data_x.transpose()				)
						prod -= data_y.transpose()
						UpperCAmelCase_=   np.dot(lowerCAmelCase_			,lowerCAmelCase_				)
						UpperCAmelCase_=   theta - (alpha / n) * sum_grad
						return theta



def        __a     (    lowerCAmelCase_   :					Optional[Any]			,lowerCAmelCase_   :					Union[str, Any]			,lowerCAmelCase_   :					List[str]			,lowerCAmelCase_   :					Optional[Any]				)      -> Union[str, Any]:






						'''simple docstring'''



						UpperCAmelCase_=   np.dot(lowerCAmelCase_			,data_x.transpose()				)
						prod -= data_y.transpose()
						UpperCAmelCase_=   np.sum(np.square(lowerCAmelCase_				)				)
						UpperCAmelCase_=   sum_elem / (2 * len_data)
						return error



def        __a     (    lowerCAmelCase_   :					List[Any]			,lowerCAmelCase_   :					int				)      -> Any:






						'''simple docstring'''



						UpperCAmelCase_=   10_00_00
						UpperCAmelCase_=   0.0_001_550

						UpperCAmelCase_=   data_x.shape[1]
						UpperCAmelCase_=   data_x.shape[0] - 1

						UpperCAmelCase_=   np.zeros((1, no_features)				)

						for i in range(0			,lowerCAmelCase_				):
												UpperCAmelCase_=   run_steep_gradient_descent(lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_				)
												UpperCAmelCase_=   sum_of_square_error(lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_			,lowerCAmelCase_				)
												print(F"""At Iteration {i + 1} - Error is {error:.5f}"""				)

						return theta



def        __a     (    lowerCAmelCase_   :					Optional[Any]			,lowerCAmelCase_   :					Dict				)      -> List[Any]:






						'''simple docstring'''



						UpperCAmelCase_=   sum(abs(y - predicted_y[i]				) for i, y in enumerate(lowerCAmelCase_				)				)
						return total / len(lowerCAmelCase_				)



def        __a     (    )      -> List[Any]:






						'''simple docstring'''



						UpperCAmelCase_=   collect_dataset()

						UpperCAmelCase_=   data.shape[0]
						UpperCAmelCase_=   np.c_[np.ones(lowerCAmelCase_				), data[:, :-1]].astype(lowerCAmelCase_				)
						UpperCAmelCase_=   data[:, -1].astype(lowerCAmelCase_				)

						UpperCAmelCase_=   run_linear_regression(lowerCAmelCase_			,lowerCAmelCase_				)
						UpperCAmelCase_=   theta.shape[1]
						print("""Resultant Feature vector : """				)
						for i in range(0			,lowerCAmelCase_				):
												print(F"""{theta[0, i]:.5f}"""				)


if __name__ == "__main__":
	main()









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        __a     (    lowerCAmelCase_   :					dict[str, list[str]]				)      -> set[tuple[str, str]]:






						'''simple docstring'''



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

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

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

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

												UpperCAmelCase_=   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(lowerCAmelCase_				)
																		if v in graph_copy[neighbor]:
																								graph_copy[neighbor].remove(lowerCAmelCase_				)

    # Find cutset.
						UpperCAmelCase_=   [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))




