
from random import shuffle

import tensorflow as tf
from numpy import array

def 		UpperCamelCase						(   lowercase_			,			lowercase_ )		->						Optional[int]:


  '''simple docstring'''






  lowercase__	: Union[str, Any]     		=   int(lowercase_ )
  assert noofclusters < len(lowercase_ )

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

  # Will help select random centroids from among the available vectors
  lowercase__	: Tuple     		=   list(range(len(lowercase_ ) ) )
  shuffle(lowercase_ )

  # 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__	: str     		=   tf.Graph()

  with graph.as_default():
    # SESSION OF COMPUTATION

    lowercase__	: Union[str, Any]     		=   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__	: Tuple     		=   [
        tf.Variable(vectors[vector_indices[i]] ) for i in range(lowercase_ )
    ]
    ##These nodes will assign the centroid Variables the appropriate
    ##values
    lowercase__	: int     		=   tf.placeholder("""float64"""			,			[dim] )
    lowercase__	: str     		=   []
    for centroid in centroids:
      cent_assigns.append(tf.assign(lowercase_			,			lowercase_ ) )

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

    ##Now lets construct the node that will compute the mean
    # The placeholder for the input
    lowercase__	: Union[str, Any]     		=   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__	: Optional[int]     		=   tf.reduce_mean(lowercase_			,			0 )

    ##Node for computing Euclidean distances
    # Placeholders for input
    lowercase__	: Any     		=   tf.placeholder("""float"""			,			[dim] )
    lowercase__	: Optional[Any]     		=   tf.placeholder("""float"""			,			[dim] )
    lowercase__	: Optional[int]     		=   tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(lowercase_			,			lowercase_ )			,			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__	: int     		=   tf.placeholder("""float"""			,			[noofclusters] )
    lowercase__	: Dict     		=   tf.argmin(lowercase_			,			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__	: Optional[Any]     		=   tf.initialize_all_variables()

    # Initialize all variables
    sess.run(lowercase_ )

    ##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__	: int     		=   1_00
    for _ in range(lowercase_ ):
      ##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(lowercase_ ) ):
        lowercase__	: List[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.
        lowercase__	: Optional[Any]     		=   [
            sess.run(lowercase_			,			feed_dict={va: vect, va: sess.run(lowercase_ )} )
            for centroid in centroids
        ]
        # Now use the cluster assignment node, with the distances
        # as the input
        lowercase__	: Any     		=   sess.run(
            lowercase_			,			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(lowercase_ ):
        # Collect all the vectors assigned to this cluster
        lowercase__	: Optional[Any]     		=   [
            vectors[i]
            for i in range(len(lowercase_ ) )
            if sess.run(assignments[i] ) == cluster_n
        ]
        # Compute new centroid location
        lowercase__	: Dict     		=   sess.run(
            lowercase_			,			feed_dict={mean_input: array(lowercase_ )} )
        # Assign value to appropriate variable
        sess.run(
            cent_assigns[cluster_n]			,			feed_dict={centroid_value: new_location} )

        # Return centroids and assignments
    lowercase__	: Optional[Any]     		=   sess.run(lowercase_ )
    lowercase__	: List[str]     		=   sess.run(lowercase_ )
    return centroids, assignments








def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ )		->						List[str]:


  '''simple docstring'''






  global f  # a global dp table for knapsack
  if f[i][j] < 0:
    if j < wt[i - 1]:
      lowercase__	: str     		=   mf_knapsack(i - 1			,			lowercase_			,			lowercase_			,			lowercase_ )
    else:
      lowercase__	: List[str]     		=   max(
          mf_knapsack(i - 1			,			lowercase_			,			lowercase_			,			lowercase_ )			,			mf_knapsack(i - 1			,			lowercase_			,			lowercase_			,			j - wt[i - 1] ) + val[i - 1]			,			)
    lowercase__	: List[Any]     		=   val
  return f[i][j]

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ )		->						str:


  '''simple docstring'''






  lowercase__	: Any     		=   [[0] * (w + 1) for _ in range(n + 1 )]

  for i in range(1			,			n + 1 ):
    for w_ in range(1			,			w + 1 ):
      if wt[i - 1] <= w_:
        lowercase__	: List[Any]     		=   max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]			,			dp[i - 1][w_] )
      else:
        lowercase__	: Tuple     		=   dp[i - 1][w_]

  return dp[n][w_], dp

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_ )		->						Optional[Any]:


  '''simple docstring'''






  if not (isinstance(lowercase_			,			(list, tuple) ) and isinstance(lowercase_			,			(list, tuple) )):
    raise ValueError(
        """Both the weights and values vectors must be either lists or tuples""" )

  lowercase__	: str     		=   len(lowercase_ )
  if num_items != len(lowercase_ ):
    lowercase__	: Optional[int]     		=   (
        """The number of weights must be the same as the number of values.\n"""
        F'But got {num_items} weights and {len(lowercase_ )} values'
    )
    raise ValueError(lowercase_ )
  for i in range(lowercase_ ):
    if not isinstance(wt[i]			,			lowercase_ ):
      lowercase__	: int     		=   (
          """All weights must be integers but got weight of """
          F'type {type(wt[i] )} at index {i}'
      )
      raise TypeError(lowercase_ )

  lowercase__		,     lowercase__	: Tuple     		=   knapsack(lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ )
  lowercase__	: set     		=   set()
  _construct_solution(lowercase_			,			lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ )

  return optimal_val, example_optional_set

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_			,			lowercase_			,			lowercase_ )		->						Any:


  '''simple docstring'''






  if i > 0 and j > 0:
    if dp[i - 1][j] == dp[i][j]:
      _construct_solution(lowercase_			,			lowercase_			,			i - 1			,			lowercase_			,			lowercase_ )
    else:
      optimal_set.add(lowercase_ )
      _construct_solution(lowercase_			,			lowercase_			,			i - 1			,			j - wt[i - 1]			,			lowercase_ )


if __name__ == "__main__":
     lowerCamelCase__     :		Dict        = [3, 2, 4, 4]
     lowerCamelCase__     :		List[Any]        = [4, 3, 2, 3]
     lowerCamelCase__     :		Optional[int]        = 4
     lowerCamelCase__     :		Dict        = 6
     lowerCamelCase__     :		Optional[int]        = [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
     lowerCamelCase__   ,    lowerCamelCase__     :		int        = knapsack(w, wt, val, n)
     print(optimal_solution)
     print(mf_knapsack(n, wt, val, w))  # switched the n and w

     # testing the dynamic programming problem with example
     # the optimal subset for the above example are items 3 and 4
     lowerCamelCase__   ,    lowerCamelCase__     :		Optional[int]        = knapsack_with_example_solution(w, wt, val)
     assert optimal_solution == 8
     assert optimal_subset == {3, 4}
     print("""optimal_value = """, optimal_solution)
     print("""An optimal subset corresponding to the optimal value""", optimal_subset)






