


def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     global f  # a global dp table for knapsack
     if f[i][j] < 0:
          if j < wt[i - 1]:
               snake_case					=    mf_knapsack(i - 1							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )
          else:
               snake_case					=    max(
                   mf_knapsack(i - 1							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )							,mf_knapsack(i - 1							,UpperCamelCase_							,UpperCamelCase_							,j - wt[i - 1]    ) + val[i - 1]							,)
          snake_case					=    val
     return f[i][j]
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     snake_case					=    [[0] * (w + 1) for _ in range(n + 1    )]

     for i in range(1							,n + 1    ):
          for w_ in range(1							,w + 1    ):
               if wt[i - 1] <= w_:
                    snake_case					=    max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]							,dp[i - 1][w_]    )
               else:
                    snake_case					=    dp[i - 1][w_]

     return dp[n][w_], dp
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     if not (isinstance(UpperCamelCase_							,(list, tuple)    ) and isinstance(UpperCamelCase_							,(list, tuple)    )):
          raise ValueError(
              '''Both the weights and values vectors must be either lists or tuples'''    )

     snake_case					=    len(UpperCamelCase_    )
     if num_items != len(UpperCamelCase_    ):
          snake_case					=    (
              '''The number of weights must be the same as the number of values.\n'''
              F'''But got {num_items} weights and {len(UpperCamelCase_    )} values'''
          )
          raise ValueError(UpperCamelCase_    )
     for i in range(UpperCamelCase_    ):
          if not isinstance(wt[i]							,UpperCamelCase_    ):
               snake_case					=    (
                   '''All weights must be integers but got weight of '''
                   F'''type {type(wt[i]    )} at index {i}'''
               )
               raise TypeError(UpperCamelCase_    )

     snake_case			,  snake_case					=    knapsack(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )
     snake_case					=    set()
     _construct_solution(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )

     return optimal_val, example_optional_set
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     if i > 0 and j > 0:
          if dp[i - 1][j] == dp[i][j]:
               _construct_solution(UpperCamelCase_							,UpperCamelCase_							,i - 1							,UpperCamelCase_							,UpperCamelCase_    )
          else:
               optimal_set.add(UpperCamelCase_    )
               _construct_solution(UpperCamelCase_							,UpperCamelCase_							,i - 1							,j - wt[i - 1]							,UpperCamelCase_    )


if __name__ == "__main__":
 _SCREAMING_SNAKE_CASE      :			Tuple      				=   [3, 2, 4, 4]
 _SCREAMING_SNAKE_CASE      :			Dict      				=   [4, 3, 2, 3]
 _SCREAMING_SNAKE_CASE      :			Optional[int]      				=   4
 _SCREAMING_SNAKE_CASE      :			str      				=   6
 _SCREAMING_SNAKE_CASE      :			str      				=   [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 _SCREAMING_SNAKE_CASE      :			Union[str, Any]      				=   knapsack(w, wt, val, n)
 print(optimal_solution)
 print(mf_knapsack(n, wt, val, w))  # switched the n and w

 # testing the dynamic programming problem with example
 # the optimal subset for the above example are items 3 and 4
 _SCREAMING_SNAKE_CASE      :			Any      				=   knapsack_with_example_solution(w, wt, val)
 assert optimal_solution == 8
 assert optimal_subset == {3, 4}
 print("optimal_value = ", optimal_solution)
 print("An optimal subset corresponding to the optimal value", optimal_subset)








# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
_SCREAMING_SNAKE_CASE      :			Union[str, Any]      				=   abspath(join(dirname(dirname(dirname(__file__))), "src"))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action="ignore", category=FutureWarning)
def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     from transformers.testing_utils import pytest_addoption_shared

     pytest_addoption_shared(UpperCamelCase_    )

def       UpperCAmelCase__						(UpperCamelCase_    ):



     """simple docstring"""






     from transformers.testing_utils import pytest_terminal_summary_main

     snake_case					=    terminalreporter.config.getoption('''--make-reports'''    )
     if make_reports:
          pytest_terminal_summary_main(UpperCamelCase_							,id=UpperCamelCase_    )




