




from random import shuffle

import tensorflow as tf
from numpy import array







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



       """simple docstring"""

       A__       =    int(lowercase_						)
       assert noofclusters < len(lowercase_						)

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

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

       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(lowercase_						)
              ]
              ##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(lowercase_ ,				lowercase_						)						)

              ##Variables for cluster assignments of individual vectors(initialized
              ##to 0 at first)
              A__       =    [tf.Variable(0						) for i in range(len(lowercase_						)						)]
              ##These nodes will assign an assignment Variable the appropriate
              ##value
              A__       =    tf.placeholder('''int32'''						)
              A__       =    []
              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
              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(lowercase_ ,				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(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
              A__       =    tf.placeholder('''float''' ,				[noofclusters]						)
              A__       =    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.
              A__       =    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.
              A__       =    100
              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_						)						):
                            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(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
                            A__       =    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
                            A__       =    [
                                vectors[i]
                                for i in range(len(lowercase_						)						)
                                if sess.run(assignments[i]						) == cluster_n
                            ]
                            # Compute new centroid location
                            A__       =    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
              A__       =    sess.run(lowercase_						)
              A__       =    sess.run(lowercase_						)
              return centroids, assignments








def SCREAMING_SNAKE_CASE				(       lowercase_						)   ->       "list[int]":



       """simple docstring"""

       if upper_limit < 0:
              raise ValueError('''Limit for the Catalan sequence must be ≥ 0'''						)

       A__       =    [0] * (upper_limit + 1)

       # Base case: C(0) = C(1) = 1
       A__       =    1
       if upper_limit > 0:
              A__       =    1

       # Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
       for i in range(2 ,				upper_limit + 1						):
              for j in range(lowercase_						):
                     catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

       return catalan_list


if __name__ == "__main__":
  print("""\n********* Catalan Numbers Using Dynamic Programming ************\n""")
  print("""\n*** Enter -1 at any time to quit ***""")
  print("""\nEnter the upper limit (≥ 0) for the Catalan number sequence: """, end="""""")
  try:
    while True:
      _lowerCamelCase	:		List[Any]							       =   int(input().strip())
      if N < 0:
        print("""\n********* Goodbye!! ************""")
        break
      else:
        print(F'''The Catalan numbers from 0 through {N} are:''')
        print(catalan_numbers(N))
        print("""Try another upper limit for the sequence: """, end="""""")
  except (NameError, ValueError):
    print("""\n********* Invalid input, goodbye! ************\n""")

  import doctest

  doctest.testmod()


