




def 	_a      (						SCREAMING_SNAKE_CASE_							:				Optional[Any]      ,      SCREAMING_SNAKE_CASE_							:				List[Any]      ,      SCREAMING_SNAKE_CASE_							:				List[str]      ,      SCREAMING_SNAKE_CASE_							:				List[str]     ):
					global f  # a global dp table for knapsack
					if f[i][j] < 0:
										if j < wt[i - 1]:
															__lowerCAmelCase				   =       mf_knapsack(i - 1      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
										else:
															__lowerCAmelCase				   =       max(
															    mf_knapsack(i - 1      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )      ,      mf_knapsack(i - 1      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      j - wt[i - 1]     ) + val[i - 1]      ,      )
										__lowerCAmelCase				   =       val
					return f[i][j]







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Any      ,      SCREAMING_SNAKE_CASE_							:				str      ,      SCREAMING_SNAKE_CASE_							:				Union[str, Any]      ,      SCREAMING_SNAKE_CASE_							:				int     ):
					__lowerCAmelCase				   =       [[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_:
																				__lowerCAmelCase				   =       max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]      ,      dp[i - 1][w_]     )
															else:
																				__lowerCAmelCase				   =       dp[i - 1][w_]

					return dp[n][w_], dp







def 	_a      (						SCREAMING_SNAKE_CASE_							:				int      ,      SCREAMING_SNAKE_CASE_							:				list      ,      SCREAMING_SNAKE_CASE_							:				list     ):
					if not (isinstance(SCREAMING_SNAKE_CASE_      ,      (list, tuple)     ) and isinstance(SCREAMING_SNAKE_CASE_      ,      (list, tuple)     )):
										raise ValueError(
										    "Both the weights and values vectors must be either lists or tuples"     )

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

					__lowerCAmelCase   ,							__lowerCAmelCase				   =       knapsack(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
					__lowerCAmelCase				   =       set()
					_construct_solution(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )

					return optimal_val, example_optional_set







def 	_a      (						SCREAMING_SNAKE_CASE_							:				list      ,      SCREAMING_SNAKE_CASE_							:				list      ,      SCREAMING_SNAKE_CASE_							:				int      ,      SCREAMING_SNAKE_CASE_							:				int      ,      SCREAMING_SNAKE_CASE_							:				set     ):
					# for the current item i at a maximum weight j to be part of an optimal subset,
					# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
					# where i - 1 means considering only the previous items at the given maximum weight
					if i > 0 and j > 0:
										if dp[i - 1][j] == dp[i][j]:
															_construct_solution(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      i - 1      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
										else:
															optimal_set.add(SCREAMING_SNAKE_CASE_     )
															_construct_solution(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      i - 1      ,      j - wt[i - 1]      ,      SCREAMING_SNAKE_CASE_     )


if __name__ == "__main__":
					UpperCamelCase__    			=			[3, 2, 4, 4]
					UpperCamelCase__    			=			[4, 3, 2, 3]
					UpperCamelCase__    			=			4
					UpperCamelCase__    			=			6
					UpperCamelCase__    			=			[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
					UpperCamelCase__			,	UpperCamelCase__    			=			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
					UpperCamelCase__			,	UpperCamelCase__    			=			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)










import os

import torch

from ..logging import get_logger
from .constants import FSDP_PYTORCH_VERSION, MODEL_NAME, OPTIMIZER_NAME
from .versions import is_torch_version


if is_torch_version(""">=""", FSDP_PYTORCH_VERSION):
					import torch.distributed.checkpoint as dist_cp
					from torch.distributed.checkpoint.default_planner import DefaultLoadPlanner, DefaultSavePlanner
					from torch.distributed.checkpoint.optimizer import load_sharded_optimizer_state_dict
					from torch.distributed.fsdp.fully_sharded_data_parallel import FullyShardedDataParallel as FSDP
					from torch.distributed.fsdp.fully_sharded_data_parallel import StateDictType


UpperCamelCase__    			=			get_logger(__name__)







def 	_a      (						SCREAMING_SNAKE_CASE_							:				List[str]      ,      SCREAMING_SNAKE_CASE_							:				Tuple      ,      SCREAMING_SNAKE_CASE_							:				Tuple      ,      SCREAMING_SNAKE_CASE_							:				Optional[Any]      ,      SCREAMING_SNAKE_CASE_							:				str=0     ):
					os.makedirs(SCREAMING_SNAKE_CASE_      ,      exist_ok=SCREAMING_SNAKE_CASE_     )
					with FSDP.state_dict_type(
					    SCREAMING_SNAKE_CASE_      ,      fsdp_plugin.state_dict_type      ,      fsdp_plugin.state_dict_config      ,      fsdp_plugin.optim_state_dict_config     ):
										__lowerCAmelCase				   =       model.state_dict()
										if fsdp_plugin.state_dict_type == StateDictType.FULL_STATE_DICT:
															__lowerCAmelCase				   =       F"""{MODEL_NAME}.bin""" if model_index == 0 else F"""{MODEL_NAME}_{model_index}.bin"""
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															if accelerator.process_index == 0:
																				logger.info(F"""Saving model to {output_model_file}"""     )
																				torch.save(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
																				logger.info(F"""Model saved to {output_model_file}"""     )
										elif fsdp_plugin.state_dict_type == StateDictType.LOCAL_STATE_DICT:
															__lowerCAmelCase				   =       (
															    F"""{MODEL_NAME}_rank{accelerator.process_index}.bin"""
															    if model_index == 0
															    else F"""{MODEL_NAME}_{model_index}_rank{accelerator.process_index}.bin"""
															)
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Saving model to {output_model_file}"""     )
															torch.save(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Model saved to {output_model_file}"""     )
										elif fsdp_plugin.state_dict_type == StateDictType.SHARDED_STATE_DICT:
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      F"""{MODEL_NAME}_{model_index}"""     )
															os.makedirs(SCREAMING_SNAKE_CASE_      ,      exist_ok=SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Saving model to {ckpt_dir}"""     )
															__lowerCAmelCase				   =       {"model": state_dict}

															dist_cp.save_state_dict(
															    state_dict=SCREAMING_SNAKE_CASE_      ,      storage_writer=dist_cp.FileSystemWriter(SCREAMING_SNAKE_CASE_     )      ,      planner=DefaultSavePlanner()      ,      )
															logger.info(F"""Model saved to {ckpt_dir}"""     )







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Dict      ,      SCREAMING_SNAKE_CASE_							:				int      ,      SCREAMING_SNAKE_CASE_							:				Optional[int]      ,      SCREAMING_SNAKE_CASE_							:				List[str]      ,      SCREAMING_SNAKE_CASE_							:				Any=0     ):
					accelerator.wait_for_everyone()
					with FSDP.state_dict_type(
					    SCREAMING_SNAKE_CASE_      ,      fsdp_plugin.state_dict_type      ,      fsdp_plugin.state_dict_config      ,      fsdp_plugin.optim_state_dict_config     ):
										if fsdp_plugin.state_dict_type == StateDictType.FULL_STATE_DICT:
															if type(SCREAMING_SNAKE_CASE_     ) != FSDP and accelerator.process_index != 0:
																				if not fsdp_plugin.sync_module_states:
																									raise ValueError(
																									    "Set the `sync_module_states` flag to `True` so that model states are synced across processes when "
																									    "initializing FSDP object"     )
																				return
															__lowerCAmelCase				   =       F"""{MODEL_NAME}.bin""" if model_index == 0 else F"""{MODEL_NAME}_{model_index}.bin"""
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Loading model from {input_model_file}"""     )
															__lowerCAmelCase				   =       torch.load(SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Model loaded from {input_model_file}"""     )
										elif fsdp_plugin.state_dict_type == StateDictType.LOCAL_STATE_DICT:
															__lowerCAmelCase				   =       (
															    F"""{MODEL_NAME}_rank{accelerator.process_index}.bin"""
															    if model_index == 0
															    else F"""{MODEL_NAME}_{model_index}_rank{accelerator.process_index}.bin"""
															)
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Loading model from {input_model_file}"""     )
															__lowerCAmelCase				   =       torch.load(SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Model loaded from {input_model_file}"""     )
										elif fsdp_plugin.state_dict_type == StateDictType.SHARDED_STATE_DICT:
															__lowerCAmelCase				   =       (
															    os.path.join(SCREAMING_SNAKE_CASE_      ,      F"""{MODEL_NAME}_{model_index}"""     )
															    if F"""{MODEL_NAME}""" not in input_dir
															    else input_dir
															)
															logger.info(F"""Loading model from {ckpt_dir}"""     )
															__lowerCAmelCase				   =       {"model": model.state_dict()}
															dist_cp.load_state_dict(
															    state_dict=SCREAMING_SNAKE_CASE_      ,      storage_reader=dist_cp.FileSystemReader(SCREAMING_SNAKE_CASE_     )      ,      planner=DefaultLoadPlanner()      ,      )
															__lowerCAmelCase				   =       state_dict["model"]
															logger.info(F"""Model loaded from {ckpt_dir}"""     )
										model.load_state_dict(SCREAMING_SNAKE_CASE_     )







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Dict      ,      SCREAMING_SNAKE_CASE_							:				int      ,      SCREAMING_SNAKE_CASE_							:				List[str]      ,      SCREAMING_SNAKE_CASE_							:				Optional[Any]      ,      SCREAMING_SNAKE_CASE_							:				Optional[int]      ,      SCREAMING_SNAKE_CASE_							:				str=0     ):
					os.makedirs(SCREAMING_SNAKE_CASE_      ,      exist_ok=SCREAMING_SNAKE_CASE_     )
					with FSDP.state_dict_type(
					    SCREAMING_SNAKE_CASE_      ,      fsdp_plugin.state_dict_type      ,      fsdp_plugin.state_dict_config      ,      fsdp_plugin.optim_state_dict_config     ):
										__lowerCAmelCase				   =       FSDP.optim_state_dict(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
										if fsdp_plugin.state_dict_type == StateDictType.FULL_STATE_DICT:
															if accelerator.process_index == 0:
																				__lowerCAmelCase				   =       (
																				    F"""{OPTIMIZER_NAME}.bin""" if optimizer_index == 0 else F"""{OPTIMIZER_NAME}_{optimizer_index}.bin"""
																				)
																				__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
																				logger.info(F"""Saving Optimizer state to {output_optimizer_file}"""     )
																				torch.save(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
																				logger.info(F"""Optimizer state saved in {output_optimizer_file}"""     )
										else:
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      F"""{OPTIMIZER_NAME}_{optimizer_index}"""     )
															os.makedirs(SCREAMING_SNAKE_CASE_      ,      exist_ok=SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Saving Optimizer state to {ckpt_dir}"""     )
															dist_cp.save_state_dict(
															    state_dict={"optimizer": optim_state}      ,      storage_writer=dist_cp.FileSystemWriter(SCREAMING_SNAKE_CASE_     )      ,      planner=DefaultSavePlanner()      ,      )
															logger.info(F"""Optimizer state saved in {ckpt_dir}"""     )







def 	_a      (						SCREAMING_SNAKE_CASE_							:				Dict      ,      SCREAMING_SNAKE_CASE_							:				Dict      ,      SCREAMING_SNAKE_CASE_							:				Tuple      ,      SCREAMING_SNAKE_CASE_							:				List[str]      ,      SCREAMING_SNAKE_CASE_							:				str      ,      SCREAMING_SNAKE_CASE_							:				Dict=0     ):
					accelerator.wait_for_everyone()
					with FSDP.state_dict_type(
					    SCREAMING_SNAKE_CASE_      ,      fsdp_plugin.state_dict_type      ,      fsdp_plugin.state_dict_config      ,      fsdp_plugin.optim_state_dict_config     ):
										if fsdp_plugin.state_dict_type == StateDictType.FULL_STATE_DICT:
															__lowerCAmelCase				   =       None
															# below check should work but currently it isn't working (mostly opytorch issue),
															# in the meantime disabling it at the cost of excess memory usage
															# if accelerator.process_index == 0 or not fsdp_plugin.optim_state_dict_config.rank0_only:
															__lowerCAmelCase				   =       (
															    F"""{OPTIMIZER_NAME}.bin""" if optimizer_index == 0 else F"""{OPTIMIZER_NAME}_{optimizer_index}.bin"""
															)
															__lowerCAmelCase				   =       os.path.join(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Loading Optimizer state from {input_optimizer_file}"""     )
															__lowerCAmelCase				   =       torch.load(SCREAMING_SNAKE_CASE_     )
															logger.info(F"""Optimizer state loaded from {input_optimizer_file}"""     )
										else:
															__lowerCAmelCase				   =       (
															    os.path.join(SCREAMING_SNAKE_CASE_      ,      F"""{OPTIMIZER_NAME}_{optimizer_index}"""     )
															    if F"""{OPTIMIZER_NAME}""" not in input_dir
															    else input_dir
															)
															logger.info(F"""Loading Optimizer from {ckpt_dir}"""     )
															__lowerCAmelCase				   =       load_sharded_optimizer_state_dict(
															    model_state_dict=model.state_dict()      ,      optimizer_key="optimizer"      ,      storage_reader=dist_cp.FileSystemReader(SCREAMING_SNAKE_CASE_     )      ,      )
															__lowerCAmelCase				   =       optim_state["optimizer"]
															logger.info(F"""Optimizer loaded from {ckpt_dir}"""     )
										__lowerCAmelCase				   =       FSDP.optim_state_dict_to_load(SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_      ,      SCREAMING_SNAKE_CASE_     )
										optimizer.load_state_dict(SCREAMING_SNAKE_CASE_     )




