


'''simple docstring'''





from random import shuffle

import tensorflow as tf
from numpy import array






def 							__lowercase     (				__lowerCAmelCase							:       Dict      ,					__lowerCAmelCase							:       Union[str, Any]     ):
							a__    =  int(__lowerCAmelCase     )
							assert noofclusters < len(__lowerCAmelCase     )

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

							# Will help select random centroids from among the available vectors
							a__    =  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.

							a__    =  tf.Graph()

							with graph.as_default():
														# SESSION OF COMPUTATION

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

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

														##Node for computing Euclidean distances
														# Placeholders for input
														a__    =  tf.placeholder('float'      ,					[dim]     )
														a__    =  tf.placeholder('float'      ,					[dim]     )
														a__    =  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
														a__    =  tf.placeholder('float'      ,					[noofclusters]     )
														a__    =  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.
														a__    =  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.
														a__    =  1_0_0
														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     )     ):
																												a__    =  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.
																												a__    =  [
																												    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
																												a__    =  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
																												a__    =  [
																												    vectors[i]
																												    for i in range(len(__lowerCAmelCase     )     )
																												    if sess.run(assignments[i]     ) == cluster_n
																												]
																												# Compute new centroid location
																												a__    =  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
														a__    =  sess.run(__lowerCAmelCase     )
														a__    =  sess.run(__lowerCAmelCase     )
														return centroids, assignments








def 							__lowercase     (				__lowerCAmelCase							:       int = 2_0_0     ):
							a__    =  [1, 2, 5, 1_0, 2_0, 5_0, 1_0_0, 2_0_0]
							a__    =  [0] * (pence + 1)
							a__    =  1  # base case: 1 way to make 0 pence

							for coin in coins:
														for i in range(__lowerCAmelCase      ,					pence + 1      ,					1     ):
																					number_of_ways[i] += number_of_ways[i - coin]
							return number_of_ways[pence]


if __name__ == "__main__":
						assert solution(2_00) == 7_36_82




