
from random import shuffle

import tensorflow as tf
from numpy import array



def        UpperCamelCase    (							lowerCAmelCase__ ,			lowerCAmelCase__		):
					'''simple docstring'''
					lowercase							=						int(lowerCAmelCase__		)
					assert noofclusters < len(lowerCAmelCase__		)

					# Find out the dimensionality
					lowercase							=						len(vectors[0]		)

					# Will help select random centroids from among the available vectors
					lowercase							=						list(range(len(lowerCAmelCase__		)		)		)
					shuffle(lowerCAmelCase__		)

					# GRAPH OF COMPUTATION
					# We initialize a new graph and set it as the default during each run
					# of this algorithm. This ensures that as this function is called
					# multiple times, the default graph doesn't keep getting crowded with
					# unused ops and Variables from previous function calls.

					lowercase							=						tf.Graph()

					with graph.as_default():
										# SESSION OF COMPUTATION

										lowercase							=						tf.Session()

										##CONSTRUCTING THE ELEMENTS OF COMPUTATION

										##First lets ensure we have a Variable vector for each centroid,
										##initialized to one of the vectors from the available data points
										lowercase							=						[
										    tf.Variable(vectors[vector_indices[i]]		) for i in range(lowerCAmelCase__		)
										]
										##These nodes will assign the centroid Variables the appropriate
										##values
										lowercase							=						tf.placeholder('''float64''' ,			[dim]		)
										lowercase							=						[]
										for centroid in centroids:
															cent_assigns.append(tf.assign(lowerCAmelCase__ ,			lowerCAmelCase__		)		)

										##Variables for cluster assignments of individual vectors(initialized
										##to 0 at first)
										lowercase							=						[tf.Variable(0		) for i in range(len(lowerCAmelCase__		)		)]
										##These nodes will assign an assignment Variable the appropriate
										##value
										lowercase							=						tf.placeholder('''int32'''		)
										lowercase							=						[]
										for assignment in assignments:
															cluster_assigns.append(tf.assign(lowerCAmelCase__ ,			lowerCAmelCase__		)		)

										##Now lets construct the node that will compute the mean
										# The placeholder for the input
										lowercase							=						tf.placeholder('''float''' ,			[None, dim]		)
										# The Node/op takes the input and computes a mean along the 0th
										# dimension, i.e. the list of input vectors
										lowercase							=						tf.reduce_mean(lowerCAmelCase__ ,			0		)

										##Node for computing Euclidean distances
										# Placeholders for input
										lowercase							=						tf.placeholder('''float''' ,			[dim]		)
										lowercase							=						tf.placeholder('''float''' ,			[dim]		)
										lowercase							=						tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(lowerCAmelCase__ ,			lowerCAmelCase__		) ,			2		)		)		)

										##This node will figure out which cluster to assign a vector to,
										##based on Euclidean distances of the vector from the centroids.
										# Placeholder for input
										lowercase							=						tf.placeholder('''float''' ,			[noofclusters]		)
										lowercase							=						tf.argmin(lowerCAmelCase__ ,			0		)

										##INITIALIZING STATE VARIABLES

										##This will help initialization of all Variables defined with respect
										##to the graph. The Variable-initializer should be defined after
										##all the Variables have been constructed, so that each of them
										##will be included in the initialization.
										lowercase							=						tf.initialize_all_variables()

										# Initialize all variables
										sess.run(lowerCAmelCase__		)

										##CLUSTERING ITERATIONS

										# Now perform the Expectation-Maximization steps of K-Means clustering
										# iterations. To keep things simple, we will only do a set number of
										# iterations, instead of using a Stopping Criterion.
										lowercase							=						100
										for _ in range(lowerCAmelCase__		):
															##EXPECTATION STEP
															##Based on the centroid locations till last iteration, compute
															##the _expected_ centroid assignments.
															# Iterate over each vector
															for vector_n in range(len(lowerCAmelCase__		)		):
																				lowercase							=						vectors[vector_n]
																				# Compute Euclidean distance between this vector and each
																				# centroid. Remember that this list cannot be named
																				#'centroid_distances', since that is the input to the
																				# cluster assignment node.
																				lowercase							=						[
																				    sess.run(lowerCAmelCase__ ,			feed_dict={va: vect, va: sess.run(lowerCAmelCase__		)}		)
																				    for centroid in centroids
																				]
																				# Now use the cluster assignment node, with the distances
																				# as the input
																				lowercase							=						sess.run(
																				    lowerCAmelCase__ ,			feed_dict={centroid_distances: distances}		)
																				# Now assign the value to the appropriate state variable
																				sess.run(
																				    cluster_assigns[vector_n] ,			feed_dict={assignment_value: assignment}		)

															##MAXIMIZATION STEP
															# Based on the expected state computed from the Expectation Step,
															# compute the locations of the centroids so as to maximize the
															# overall objective of minimizing within-cluster Sum-of-Squares
															for cluster_n in range(lowerCAmelCase__		):
																				# Collect all the vectors assigned to this cluster
																				lowercase							=						[
																				    vectors[i]
																				    for i in range(len(lowerCAmelCase__		)		)
																				    if sess.run(assignments[i]		) == cluster_n
																				]
																				# Compute new centroid location
																				lowercase							=						sess.run(
																				    lowerCAmelCase__ ,			feed_dict={mean_input: array(lowerCAmelCase__		)}		)
																				# Assign value to appropriate variable
																				sess.run(
																				    cent_assigns[cluster_n] ,			feed_dict={centroid_value: new_location}		)

        # Return centroids and assignments
										lowercase							=						sess.run(lowerCAmelCase__		)
										lowercase							=						sess.run(lowerCAmelCase__		)
										return centroids, assignments







def 					__lowerCamelCase	( ):







							'''simple docstring'''






							return [list(range(1000 - i   ,							-1000 - i   ,							-1      )      ) for i in range(1000      )]


_UpperCAmelCase		:   Union[str, Any]										=       generate_large_matrix()
_UpperCAmelCase		:   Tuple										=       (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							assert all(row == sorted(UpperCamelCase__   ,							reverse=UpperCamelCase__      ) for row in grid      )
							assert all(list(UpperCamelCase__      ) == sorted(UpperCamelCase__   ,							reverse=UpperCamelCase__      ) for col in zip(*UpperCamelCase__      )      )





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_							=    0
							snake_case_							=    len(UpperCamelCase__      ) - 1

							# Edge cases such as no values or all numbers are negative.
							if not array or array[0] < 0:
														return 0

							while right + 1 > left:
														snake_case_							=    (left + right) // 2
														snake_case_							=    array[mid]

														# Num must be negative and the index must be greater than or equal to 0.
														if num < 0 and array[mid - 1] >= 0:
																					return mid

														if num >= 0:
																					snake_case_							=    mid + 1
														else:
																					snake_case_							=    mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
							return len(UpperCamelCase__      )





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_							=    0
							snake_case_							=    len(grid[0]      )

							for i in range(len(UpperCamelCase__      )      ):
														snake_case_							=    find_negative_index(grid[i][:bound]      )
														total += bound
							return (len(UpperCamelCase__      ) * len(grid[0]      )) - total





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							return len([number for row in grid for number in row if number < 0]      )





def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_							=    0
							for row in grid:
														for i, number in enumerate(UpperCamelCase__      ):
																					if number < 0:
																												total += len(UpperCamelCase__      ) - i
																												break
							return total





def 					__lowerCamelCase	( ):







							'''simple docstring'''






							from timeit import timeit

							print('Running benchmarks'      )
							snake_case_							=    (
							    'from __main__ import count_negatives_binary_search, '
							    'count_negatives_brute_force, count_negatives_brute_force_with_break, grid'
							)
							for func in (
							    "count_negatives_binary_search",  # took 0.7727 seconds
							    "count_negatives_brute_force_with_break",  # took 4.6505 seconds
							    "count_negatives_brute_force",  # took 12.8160 seconds
							):
														snake_case_							=    timeit(F'''{func}(grid=grid)'''   ,							setup=UpperCamelCase__   ,							number=500      )
														print(F'''{func}() took {time:0.4f} seconds'''      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()




