




# 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 				__UpperCamelCase      :





				'''simple docstring'''



				def __init__(			self							,			UpperCAmelCase_							,			UpperCAmelCase_    ):
											lowerCAmelCase =		key
											lowerCAmelCase =		freq






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




def    UpperCAmelCase							(  _snake_case    ,			_snake_case    ,			_snake_case    ,			_snake_case    ,			_snake_case    ,			_snake_case				):
							if i > j or i < 0 or j > len(_snake_case				) - 1:
														return

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



def    UpperCAmelCase							(  _snake_case				):
							nodes.sort(key=lambda _snake_case				: node.key				)

							lowerCAmelCase =		len(_snake_case				)

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

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

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

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

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

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

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



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


if __name__ == "__main__":
		main()









import sacrebleu as scb
from packaging import version

import datasets


UpperCAmelCase_    ="""\
@inproceedings{post-2018-call,
    title = \"A Call for Clarity in Reporting {BLEU} Scores\",
    author = \"Post, Matt\",
    booktitle = \"Proceedings of the Third Conference on Machine Translation: Research Papers\",
    month = oct,
    year = \"2018\",
    address = \"Belgium, Brussels\",
    publisher = \"Association for Computational Linguistics\",
    url = \"https://www.aclweb.org/anthology/W18-6319\",
    pages = \"186--191\",
}
"""

UpperCAmelCase_    ="""\
SacreBLEU provides hassle-free computation of shareable, comparable, and reproducible BLEU scores.
Inspired by Rico Sennrich's `multi-bleu-detok.perl`, it produces the official WMT scores but works with plain text.
It also knows all the standard test sets and handles downloading, processing, and tokenization for you.

See the [README.md] file at https://github.com/mjpost/sacreBLEU for more information.
"""

UpperCAmelCase_    ="""
Produces BLEU scores along with its sufficient statistics
from a source against one or more references.

Args:
    predictions (`list` of `str`): list of translations to score. Each translation should be tokenized into a list of tokens.
    references (`list` of `list` of `str`): A list of lists of references. The contents of the first sub-list are the references for the first prediction, the contents of the second sub-list are for the second prediction, etc. Note that there must be the same number of references for each prediction (i.e. all sub-lists must be of the same length).
    smooth_method (`str`): The smoothing method to use, defaults to `'exp'`. Possible values are:
        - `'none'`: no smoothing
        - `'floor'`: increment zero counts
        - `'add-k'`: increment num/denom by k for n>1
        - `'exp'`: exponential decay
    smooth_value (`float`): The smoothing value. Only valid when `smooth_method='floor'` (in which case `smooth_value` defaults to `0.1`) or `smooth_method='add-k'` (in which case `smooth_value` defaults to `1`).
    tokenize (`str`): Tokenization method to use for BLEU. If not provided, defaults to `'zh'` for Chinese, `'ja-mecab'` for Japanese and `'13a'` (mteval) otherwise. Possible values are:
        - `'none'`: No tokenization.
        - `'zh'`: Chinese tokenization.
        - `'13a'`: mimics the `mteval-v13a` script from Moses.
        - `'intl'`: International tokenization, mimics the `mteval-v14` script from Moses
        - `'char'`: Language-agnostic character-level tokenization.
        - `'ja-mecab'`: Japanese tokenization. Uses the [MeCab tokenizer](https://pypi.org/project/mecab-python3).
    lowercase (`bool`): If `True`, lowercases the input, enabling case-insensitivity. Defaults to `False`.
    force (`bool`): If `True`, insists that your tokenized input is actually detokenized. Defaults to `False`.
    use_effective_order (`bool`): If `True`, stops including n-gram orders for which precision is 0. This should be `True`, if sentence-level BLEU will be computed. Defaults to `False`.

Returns:
    'score': BLEU score,
    'counts': Counts,
    'totals': Totals,
    'precisions': Precisions,
    'bp': Brevity penalty,
    'sys_len': predictions length,
    'ref_len': reference length,

Examples:

    Example 1:
        >>> predictions = [\"hello there general kenobi\", \"foo bar foobar\"]
        >>> references = [[\"hello there general kenobi\", \"hello there !\"], [\"foo bar foobar\", \"foo bar foobar\"]]
        >>> sacrebleu = datasets.load_metric(\"sacrebleu\")
        >>> results = sacrebleu.compute(predictions=predictions, references=references)
        >>> print(list(results.keys()))
        ['score', 'counts', 'totals', 'precisions', 'bp', 'sys_len', 'ref_len']
        >>> print(round(results[\"score\"], 1))
        100.0

    Example 2:
        >>> predictions = [\"hello there general kenobi\",
        ...                 \"on our way to ankh morpork\"]
        >>> references = [[\"hello there general kenobi\", \"hello there !\"],
        ...                 [\"goodbye ankh morpork\", \"ankh morpork\"]]
        >>> sacrebleu = datasets.load_metric(\"sacrebleu\")
        >>> results = sacrebleu.compute(predictions=predictions,
        ...                             references=references)
        >>> print(list(results.keys()))
        ['score', 'counts', 'totals', 'precisions', 'bp', 'sys_len', 'ref_len']
        >>> print(round(results[\"score\"], 1))
        39.8
"""


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION  ,       _KWARGS_DESCRIPTION	)
class 				__UpperCamelCase      (			datasets.Metric	):





				'''simple docstring'''



				def    __snake_case		(			self    ):
											if version.parse(scb.__version__    ) < version.parse('''1.4.12'''    ):
																		raise ImportWarning(
																		    '''To use `sacrebleu`, the module `sacrebleu>=1.4.12` is required, and the current version of `sacrebleu` doesn\'t match this condition.\n'''
																		    '''You can install it with `pip install "sacrebleu>=1.4.12"`.'''    )
											return datasets.MetricInfo(
											    description=_DESCRIPTION							,			citation=_CITATION							,			homepage='''https://github.com/mjpost/sacreBLEU'''							,			inputs_description=_KWARGS_DESCRIPTION							,			features=datasets.Features(
											        {
											            '''predictions''': datasets.Value('''string'''							,			id='''sequence'''    ),
											            '''references''': datasets.Sequence(datasets.Value('''string'''							,			id='''sequence'''    )							,			id='''references'''    ),
											        }    )							,			codebase_urls=['''https://github.com/mjpost/sacreBLEU''']							,			reference_urls=[
											        '''https://github.com/mjpost/sacreBLEU''',
											        '''https://en.wikipedia.org/wiki/BLEU''',
											        '''https://towardsdatascience.com/evaluating-text-output-in-nlp-bleu-at-your-own-risk-e8609665a213''',
											    ]							,			)






				def    __snake_case		(			self							,			UpperCAmelCase_							,			UpperCAmelCase_							,			UpperCAmelCase_="exp"							,			UpperCAmelCase_=None							,			UpperCAmelCase_=False							,			UpperCAmelCase_=False							,			UpperCAmelCase_=None							,			UpperCAmelCase_=False							,			):
											lowerCAmelCase =		len(references[0]    )
											if any(len(UpperCAmelCase_    ) != references_per_prediction for refs in references    ):
																		raise ValueError('''Sacrebleu requires the same number of references for each prediction'''    )
											lowerCAmelCase =		[[refs[i] for refs in references] for i in range(UpperCAmelCase_    )]
											lowerCAmelCase =		scb.corpus_bleu(
											    UpperCAmelCase_							,			UpperCAmelCase_							,			smooth_method=UpperCAmelCase_							,			smooth_value=UpperCAmelCase_							,			force=UpperCAmelCase_							,			lowercase=UpperCAmelCase_							,			use_effective_order=UpperCAmelCase_							,			**({'''tokenize''': tokenize} if tokenize else {})							,			)
											lowerCAmelCase =		{
											    '''score''': output.score,
											    '''counts''': output.counts,
											    '''totals''': output.totals,
											    '''precisions''': output.precisions,
											    '''bp''': output.bp,
											    '''sys_len''': output.sys_len,
											    '''ref_len''': output.ref_len,
											}
											return output_dict



