
def    A (      lowercase				)     ->						str:
		'''simple docstring'''

		UpperCamelCase						=  generate_pascal_triangle(lowerCAmelCase_				)
		for row_idx in range(lowerCAmelCase_				):
				# Print left spaces
				for _ in range(num_rows - row_idx - 1				):
						print(end=' '				)
				# Print row values
				for col_idx in range(row_idx + 1				):
						if col_idx != row_idx:
								print(triangle[row_idx][col_idx]					, end=' '				)
						else:
								print(triangle[row_idx][col_idx]					, end=''				)
				print()


def    A (      lowercase				)     ->						Tuple:
		'''simple docstring'''

		if not isinstance(lowerCAmelCase_					, lowerCAmelCase_				):
				raise TypeError('The input value of \'num_rows\' should be \'int\''				)

		if num_rows == 0:
				return []
		elif num_rows < 0:
				raise ValueError(
				    'The input value of \'num_rows\' should be greater than or equal to 0'				)

		UpperCamelCase						=  []
		for current_row_idx in range(lowerCAmelCase_				):
				UpperCamelCase						=  populate_current_row(lowerCAmelCase_					, lowerCAmelCase_				)
				triangle.append(lowerCAmelCase_				)
		return triangle


def    A (      lowercase					, lowercase				)     ->						int:
		'''simple docstring'''

		UpperCamelCase						=  [-1] * (current_row_idx + 1)
		# first and last elements of current row are equal to 1
		UpperCamelCase						=  1, 1
		for current_col_idx in range(1					, lowerCAmelCase_				):
				calculate_current_element(
				    lowerCAmelCase_					, lowerCAmelCase_					, lowerCAmelCase_					, lowerCAmelCase_				)
		return current_row


def    A (      lowercase					, lowercase					, lowercase					, lowercase					, )     ->						Optional[Any]:
		'''simple docstring'''

		UpperCamelCase						=  triangle[current_row_idx - 1][current_col_idx - 1]
		UpperCamelCase						=  triangle[current_row_idx - 1][current_col_idx]
		UpperCamelCase						=  above_to_left_elt + above_to_right_elt


def    A (      lowercase				)     ->						Any:
		'''simple docstring'''

		if not isinstance(lowerCAmelCase_					, lowerCAmelCase_				):
				raise TypeError('The input value of \'num_rows\' should be \'int\''				)

		if num_rows == 0:
				return []
		elif num_rows < 0:
				raise ValueError(
				    'The input value of \'num_rows\' should be greater than or equal to 0'				)

		UpperCamelCase						=  [[1]]

		for row_index in range(1					, lowerCAmelCase_				):
				UpperCamelCase						=  [0] + result[-1] + [0]
				UpperCamelCase						=  row_index + 1
				# Calculate the number of distinct elements in a row
				UpperCamelCase						=  sum(divmod(lowerCAmelCase_					, 2				)				)
				UpperCamelCase						=  [
				    temp_row[i - 1] + temp_row[i] for i in range(1					, distinct_elements + 1				)
				]
				UpperCamelCase						=  row_first_half[: (row_index + 1) // 2]
				row_second_half.reverse()
				UpperCamelCase						=  row_first_half + row_second_half
				result.append(lowerCAmelCase_				)

		return result


def    A (      )     ->						int:
		'''simple docstring'''

		from collections.abc import Callable
		from timeit import timeit

		def benchmark_a_function(lowercase					, lowercase				) -> None:
				UpperCamelCase						=  f'''{func.__name__}({value})'''
				UpperCamelCase						=  timeit(f'''__main__.{call}'''					, setup='import __main__'				)
				# print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
				print(f'''{call:38} -- {timing:.4f} seconds'''				)

		for value in range(15				):  # (1, 7, 14):
				for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
						benchmark_a_function(lowerCAmelCase_					, lowerCAmelCase_				)
				print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()


from random import shuffle

import tensorflow as tf
from numpy import array


def    A (      lowercase					, lowercase				)     ->						Optional[Any]:
		'''simple docstring'''

		UpperCamelCase						=  int(lowercase				)
		assert noofclusters < len(lowercase				)

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

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

		UpperCamelCase						=  tf.Graph()

		with graph.as_default():
				# SESSION OF COMPUTATION

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

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

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