'''simple docstring'''




# 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   _lowercase:



   """simple docstring"""





   def __init__(							self:    str			,a:    Any			,a:    Optional[Any]	):
    __UpperCAmelCase         =					key
    __UpperCAmelCase         =					freq





   def __str__(							self:    Any	):
    return f"""Node(key={self.key}, freq={self.freq})"""




def 						__snake_case (       lowerCAmelCase       :     Union[str, Any]      ,  lowerCAmelCase       :     Dict      ,  lowerCAmelCase       :     List[Any]      ,  lowerCAmelCase       :     str      ,  lowerCAmelCase       :     int      ,  lowerCAmelCase       :     Tuple			):
 if i > j or i < 0 or j > len(lowerCAmelCase			) - 1:
  return

 __UpperCAmelCase         =					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(lowerCAmelCase      ,  lowerCAmelCase      ,  lowerCAmelCase      ,  node - 1      ,  key[node]      ,  lowerCAmelCase			)
 print_binary_search_tree(lowerCAmelCase      ,  lowerCAmelCase      ,  node + 1      ,  lowerCAmelCase      ,  key[node]      ,  lowerCAmelCase			)



def 						__snake_case (       lowerCAmelCase       :     Tuple			):
 nodes.sort(key=lambda lowerCAmelCase			: node.key			)

 __UpperCAmelCase         =					len(lowerCAmelCase			)

 __UpperCAmelCase         =					[nodes[i].key for i in range(lowerCAmelCase			)]
 __UpperCAmelCase         =					[nodes[i].freq for i in range(lowerCAmelCase			)]

 # 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.
 __UpperCAmelCase         =					[[freqs[i] if i == j else 0 for j in range(lowerCAmelCase			)] for i in range(lowerCAmelCase			)]
 # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
 # array
 __UpperCAmelCase         =					[[freqs[i] if i == j else 0 for j in range(lowerCAmelCase			)] for i in range(lowerCAmelCase			)]
 # stores tree roots that will be used later for constructing binary search tree
 __UpperCAmelCase         =					[[i if i == j else 0 for j in range(lowerCAmelCase			)] for i in range(lowerCAmelCase			)]

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

   __UpperCAmelCase         =					sys.maxsize  # set the value to "infinity"
   __UpperCAmelCase         =					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
    __UpperCAmelCase         =					dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
    __UpperCAmelCase         =					dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
    __UpperCAmelCase         =					left + total[i][j] + right

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

 print('Binary search tree nodes:'			)
 for node in nodes:
  print(lowerCAmelCase			)

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



def 						__snake_case (       ):
 # A sample binary search tree
 __UpperCAmelCase         =					[Node(lowerCAmelCase      ,  randint(1      ,  50			)			) for i in range(10      ,  0      ,  -1			)]
 find_optimal_binary_search_tree(lowerCAmelCase			)


if __name__ == "__main__":
     main()




'''simple docstring'''




import unittest
from pathlib import Path

from transformers import is_vision_available, load_tool
from transformers.testing_utils import get_tests_dir

from .test_tools_common import ToolTesterMixin


if is_vision_available():
     from PIL import Image

class   _lowercase(     unittest.TestCase   ,_lowerCamelCase				):



   """simple docstring"""





   def 			snake_case	(							self:    Optional[int]	):
    __UpperCAmelCase         =					load_tool('image-captioning'	)
    self.tool.setup()
    __UpperCAmelCase         =					load_tool('image-captioning'			,remote=a	)





   def 			snake_case	(							self:    List[Any]	):
    __UpperCAmelCase         =					Image.open(Path(get_tests_dir('fixtures/tests_samples/COCO'	)	) / '000000039769.png'	)
    __UpperCAmelCase         =					self.tool(a	)
    self.assertEqual(a			,'two cats sleeping on a couch'	)





   def 			snake_case	(							self:    List[Any]	):
    __UpperCAmelCase         =					Image.open(Path(get_tests_dir('fixtures/tests_samples/COCO'	)	) / '000000039769.png'	)
    __UpperCAmelCase         =					self.remote_tool(a	)
    self.assertEqual(a			,'two cats sleeping on a couch'	)





   def 			snake_case	(							self:    Optional[Any]	):
    __UpperCAmelCase         =					Image.open(Path(get_tests_dir('fixtures/tests_samples/COCO'	)	) / '000000039769.png'	)
    __UpperCAmelCase         =					self.tool(image=a	)
    self.assertEqual(a			,'two cats sleeping on a couch'	)





   def 			snake_case	(							self:    Tuple	):
    __UpperCAmelCase         =					Image.open(Path(get_tests_dir('fixtures/tests_samples/COCO'	)	) / '000000039769.png'	)
    __UpperCAmelCase         =					self.remote_tool(image=a	)
    self.assertEqual(a			,'two cats sleeping on a couch'	)



