



'''simple docstring'''
from random import shuffle

import tensorflow as tf
from numpy import array





def 	_a(					UpperCamelCase__			:  int,		UpperCamelCase__			:  Optional[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=int(UpperCamelCase__							)
      assert noofclusters < len(UpperCamelCase__							)

      # Find out the dimensionality
      SCREAMING_SNAKE_CASE__       :			Any													=len(vectors[0]							)

      # Will help select random centroids from among the available vectors
      SCREAMING_SNAKE_CASE__       :			Dict													=list(range(len(UpperCamelCase__							)							)							)
      shuffle(UpperCamelCase__							)

      # 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.

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=tf.Graph()

      with graph.as_default():
            # SESSION OF COMPUTATION

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

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

            ##Now lets construct the node that will compute the mean
            # The placeholder for the input
            SCREAMING_SNAKE_CASE__       :			int													=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
            SCREAMING_SNAKE_CASE__       :			List[str]													=tf.reduce_mean(UpperCamelCase__,		0							)

            ##Node for computing Euclidean distances
            # Placeholders for input
            SCREAMING_SNAKE_CASE__       :			Optional[int]													=tf.placeholder('''float''',		[dim]							)
            SCREAMING_SNAKE_CASE__       :			Any													=tf.placeholder('''float''',		[dim]							)
            SCREAMING_SNAKE_CASE__       :			str													=tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(UpperCamelCase__,		UpperCamelCase__							),		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
            SCREAMING_SNAKE_CASE__       :			Any													=tf.placeholder('''float''',		[noofclusters]							)
            SCREAMING_SNAKE_CASE__       :			List[Any]													=tf.argmin(UpperCamelCase__,		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.
            SCREAMING_SNAKE_CASE__       :			Any													=tf.initialize_all_variables()

            # Initialize all variables
            sess.run(UpperCamelCase__							)

            ##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.
            SCREAMING_SNAKE_CASE__       :			int													=1_0_0
            for _ in range(UpperCamelCase__							):
                  ##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(UpperCamelCase__							)							):
                        SCREAMING_SNAKE_CASE__       :			Union[str, Any]													=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.
                        SCREAMING_SNAKE_CASE__       :			List[Any]													=[
                            sess.run(UpperCamelCase__,		feed_dict={va: vect, va: sess.run(UpperCamelCase__							)}							)
                            for centroid in centroids
                        ]
                        # Now use the cluster assignment node, with the distances
                        # as the input
                        SCREAMING_SNAKE_CASE__       :			Tuple													=sess.run(
                            UpperCamelCase__,		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(UpperCamelCase__							):
                        # Collect all the vectors assigned to this cluster
                        SCREAMING_SNAKE_CASE__       :			Any													=[
                            vectors[i]
                            for i in range(len(UpperCamelCase__							)							)
                            if sess.run(assignments[i]							) == cluster_n
                        ]
                        # Compute new centroid location
                        SCREAMING_SNAKE_CASE__       :			List[str]													=sess.run(
                            UpperCamelCase__,		feed_dict={mean_input: array(UpperCamelCase__							)}							)
                        # Assign value to appropriate variable
                        sess.run(
                            cent_assigns[cluster_n],		feed_dict={centroid_value: new_location}							)

        # Return centroids and assignments
            SCREAMING_SNAKE_CASE__       :			List[Any]													=sess.run(UpperCamelCase__							)
            SCREAMING_SNAKE_CASE__       :			str													=sess.run(UpperCamelCase__							)
            return centroids, assignments







'''simple docstring'''
from __future__ import annotations

import os
from collections.abc import Mapping

a_					=	tuple[int, int]






class        __SCREAMING_SNAKE_CASE :




 def __init__( self		:							Any   , __lowercase		:							set[int]   , __lowercase		:							Mapping[EdgeT, int] )		->  None:
       SCREAMING_SNAKE_CASE__       :			set[int]													=vertices
       SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={
           (min(__lowercase ), max(__lowercase )): weight for edge, weight in edges.items()
       }




 def        __magic_name__		( self		:							Union[str, Any]   , __lowercase		:							EdgeT   , __lowercase		:							int )		->  None:
       self.vertices.add(edge[0] )
       self.vertices.add(edge[1] )
       SCREAMING_SNAKE_CASE__       :			List[str]													=weight




 def        __magic_name__		( self		:							Optional[Any] )		->  Graph:
       SCREAMING_SNAKE_CASE__       :			Graph													=Graph({min(self.vertices )}   , {} )
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int
       SCREAMING_SNAKE_CASE__       :			EdgeT
       SCREAMING_SNAKE_CASE__       :			int

       while len(subgraph.vertices ) < len(self.vertices ):
             SCREAMING_SNAKE_CASE__       :			Any													=max(self.edges.values() ) + 1
             for edge, weight in self.edges.items():
                   if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                         if weight < min_weight:
                               SCREAMING_SNAKE_CASE__       :			List[str]													=edge
                               SCREAMING_SNAKE_CASE__       :			Any													=weight

             subgraph.add_edge(__lowercase   , __lowercase )

       return subgraph





def 	_a(					UpperCamelCase__			:  str = "p107_network.txt"							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__       :			str													=os.path.abspath(os.path.dirname(UpperCamelCase__							)							)
      SCREAMING_SNAKE_CASE__       :			str													=os.path.join(UpperCamelCase__,		UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__       :			dict[EdgeT, int]													={}
      SCREAMING_SNAKE_CASE__       :			list[str]
      SCREAMING_SNAKE_CASE__       :			int
      SCREAMING_SNAKE_CASE__       :			int

      with open(UpperCamelCase__							) as f:
            SCREAMING_SNAKE_CASE__       :			Any													=f.read().strip().split('''\n'''							)

      SCREAMING_SNAKE_CASE__       :			Optional[Any]													=[line.split(''','''							) for line in data]

      for edgea in range(1,		len(UpperCamelCase__							)							):
            for edgea in range(UpperCamelCase__							):
                  if adjaceny_matrix[edgea][edgea] != "-":
                        SCREAMING_SNAKE_CASE__       :			List[Any]													=int(adjaceny_matrix[edgea][edgea]							)

      SCREAMING_SNAKE_CASE__       :			Graph													=Graph(set(range(len(UpperCamelCase__							)							)							),		UpperCamelCase__							)

      SCREAMING_SNAKE_CASE__       :			Graph													=graph.prims_algorithm()

      SCREAMING_SNAKE_CASE__       :			int													=sum(graph.edges.values()							)
      SCREAMING_SNAKE_CASE__       :			int													=sum(subgraph.edges.values()							)

      return initial_total - optimal_total


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