




# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint




class     a__ :







     def __init__(			self						,	A						,	A				)						->					str:



          '''simple docstring'''



          a											=   key
          a											=   freq







     def __str__(			self				)						->					List[Any]:



          '''simple docstring'''



          return F'''Node(key={self.key}, freq={self.freq})'''







def       SCREAMING_SNAKE_CASE							(     __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase)    ->  List[Any]:
     if i > j or i < 0 or j > len(__UpperCamelCase) - 1:
          return

     a											=   root[i][j]
     if parent == -1:  # root does not have a parent
          print(f'''{key[node]} is the root of the binary search tree.''')
     elif is_left:
          print(f'''{key[node]} is the left child of key {parent}.''')
     else:
          print(f'''{key[node]} is the right child of key {parent}.''')

     print_binary_search_tree(__UpperCamelCase	,      __UpperCamelCase	,      __UpperCamelCase	,      node - 1	,      key[node]	,      __UpperCamelCase)
     print_binary_search_tree(__UpperCamelCase	,      __UpperCamelCase	,      node + 1	,      __UpperCamelCase	,      key[node]	,      __UpperCamelCase)

def       SCREAMING_SNAKE_CASE							(     __UpperCamelCase)    ->  Union[str, Any]:
     nodes.sort(key=lambda __UpperCamelCase: node.key)

     a											=   len(__UpperCamelCase)

     a											=   [nodes[i].key for i in range(__UpperCamelCase)]
     a											=   [nodes[i].freq for i in range(__UpperCamelCase)]

     # This 2D array stores the overall tree cost (which's as minimized as possible);
     # for a single key, cost is equal to frequency of the key.
     a											=   [[freqs[i] if i == j else 0 for j in range(__UpperCamelCase)] for i in range(__UpperCamelCase)]
     # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
     # array
     a											=   [[freqs[i] if i == j else 0 for j in range(__UpperCamelCase)] for i in range(__UpperCamelCase)]
     # stores tree roots that will be used later for constructing binary search tree
     a											=   [[i if i == j else 0 for j in range(__UpperCamelCase)] for i in range(__UpperCamelCase)]

     for interval_length in range(2	,      n + 1):
          for i in range(n - interval_length + 1):
               a											=   i + interval_length - 1

               a											=   sys.maxsize  # set the value to "infinity"
               a											=   total[i][j - 1] + freqs[j]

               # Apply Knuth's optimization
               # Loop without optimization: for r in range(i, j + 1):
               for r in range(root[i][j - 1]	,      root[i + 1][j] + 1):  # r is a temporal root
                    a											=   dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                    a											=   dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
                    a											=   left + total[i][j] + right

                    if dp[i][j] > cost:
                         a											=   cost
                         a											=   r

     print("Binary search tree nodes:")
     for node in nodes:
          print(__UpperCamelCase)

     print(f'''\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.''')
     print_binary_search_tree(__UpperCamelCase	,      __UpperCamelCase	,      0	,      n - 1	,      -1	,      __UpperCamelCase)

def       SCREAMING_SNAKE_CASE							(     )    ->  Union[str, Any]:
     # A sample binary search tree
     a											=   [Node(__UpperCamelCase	,      randint(1	,      50)) for i in range(10	,      0	,      -1)]
     find_optimal_binary_search_tree(__UpperCamelCase)


if __name__ == "__main__":
   main()







import unittest

from transformers.image_processing_utils import get_size_dict




class     a__ (      unittest.TestCase   ):







     def     lowerCAmelCase_       (			self				)						->					Optional[int]:



          '''simple docstring'''



          a											=   {"wrong_key": 224}
          with self.assertRaises(A				):
               get_size_dict(A				)

          a											=   {"height": 224}
          with self.assertRaises(A				):
               get_size_dict(A				)

          a											=   {"width": 224, "shortest_edge": 224}
          with self.assertRaises(A				):
               get_size_dict(A				)

          # Test a dict with the correct keys is returned as is
          a											=   {"height": 224, "width": 224}
          a											=   get_size_dict(A				)
          self.assertEqual(A						,	A				)

          a											=   {"shortest_edge": 224}
          a											=   get_size_dict(A				)
          self.assertEqual(A						,	{"shortest_edge": 224}				)

          a											=   {"longest_edge": 224, "shortest_edge": 224}
          a											=   get_size_dict(A				)
          self.assertEqual(A						,	{"longest_edge": 224, "shortest_edge": 224}				)

          # Test a single int value which  represents (size, size)
          a											=   get_size_dict(224				)
          self.assertEqual(A						,	{"height": 224, "width": 224}				)

          # Test a single int value which represents the shortest edge
          a											=   get_size_dict(224						,	default_to_square=A				)
          self.assertEqual(A						,	{"shortest_edge": 224}				)

          # Test a tuple of ints which represents (height, width)
          a											=   get_size_dict((150, 200)				)
          self.assertEqual(A						,	{"height": 150, "width": 200}				)

          # Test a tuple of ints which represents (width, height)
          a											=   get_size_dict((150, 200)						,	height_width_order=A				)
          self.assertEqual(A						,	{"height": 200, "width": 150}				)

          # Test an int representing the shortest edge and max_size which represents the longest edge
          a											=   get_size_dict(224						,	max_size=256						,	default_to_square=A				)
          self.assertEqual(A						,	{"shortest_edge": 224, "longest_edge": 256}				)

          # Test int with default_to_square=True and max_size fails
          with self.assertRaises(A				):
               get_size_dict(224						,	max_size=256						,	default_to_square=A				)

