





'''simple docstring'''





from random import shuffle

import tensorflow as tf
from numpy import array





def    __UpperCamelCase      (    a,     a) ->int:
					lowerCamelCase__       =       int(a)
					assert noofclusters < len(a)

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

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

					# 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.

					lowerCamelCase__       =       tf.Graph()

					with graph.as_default():
										# SESSION OF COMPUTATION

										lowerCamelCase__       =       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
										lowerCamelCase__       =       [
										    tf.Variable(vectors[vector_indices[i]]) for i in range(a)
										]
										##These nodes will assign the centroid Variables the appropriate
										##values
										lowerCamelCase__       =       tf.placeholder("float64",     [dim])
										lowerCamelCase__       =       []
										for centroid in centroids:
															cent_assigns.append(tf.assign(a,     a))

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

										##Now lets construct the node that will compute the mean
										# The placeholder for the input
										lowerCamelCase__       =       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
										lowerCamelCase__       =       tf.reduce_mean(a,     0)

										##Node for computing Euclidean distances
										# Placeholders for input
										lowerCamelCase__       =       tf.placeholder("float",     [dim])
										lowerCamelCase__       =       tf.placeholder("float",     [dim])
										lowerCamelCase__       =       tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(a,     a),     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
										lowerCamelCase__       =       tf.placeholder("float",     [noofclusters])
										lowerCamelCase__       =       tf.argmin(a,     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.
										lowerCamelCase__       =       tf.initialize_all_variables()

										# Initialize all variables
										sess.run(a)

										##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.
										lowerCamelCase__       =       100
										for _ in range(a):
															##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(a)):
																				lowerCamelCase__       =       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.
																				lowerCamelCase__       =       [
																				    sess.run(a,     feed_dict={va: vect, va: sess.run(a)})
																				    for centroid in centroids
																				]
																				# Now use the cluster assignment node, with the distances
																				# as the input
																				lowerCamelCase__       =       sess.run(
																				    a,     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(a):
																				# Collect all the vectors assigned to this cluster
																				lowerCamelCase__       =       [
																				    vectors[i]
																				    for i in range(len(a))
																				    if sess.run(assignments[i]) == cluster_n
																				]
																				# Compute new centroid location
																				lowerCamelCase__       =       sess.run(
																				    a,     feed_dict={mean_input: array(a)})
																				# Assign value to appropriate variable
																				sess.run(
																				    cent_assigns[cluster_n],     feed_dict={centroid_value: new_location})

        # Return centroids and assignments
										lowerCamelCase__       =       sess.run(a)
										lowerCamelCase__       =       sess.run(a)
										return centroids, assignments








def    __UpperCamelCase      (    a = 100) ->int:
					lowerCamelCase__       =       (n * (n + 1) // 2) ** 2
					lowerCamelCase__       =       n * (n + 1) * (2 * n + 1) // 6
					return sum_cubes - sum_squares


if __name__ == "__main__":
						print(f"""{solution() = }""")

