



import math
import sys



class 			_lowercase							:





	"""simple docstring"""




	def __init__(self	):
						"""simple docstring"""

						a        =     0
						a        =     []
						a        =     {}  # To store the pos of node in array




	def   UpperCamelCase_ (self	):
						"""simple docstring"""

						return self.cur_size == 0




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     self.left(lowerCAmelCase_	)
						a        =     self.right(lowerCAmelCase_	)
						if lc < self.cur_size and self.array(lowerCAmelCase_	)[0] < self.array(lowerCAmelCase_	)[0]:
											a        =     lc
						else:
											a        =     idx
						if rc < self.cur_size and self.array(lowerCAmelCase_	)[0] < self.array(lowerCAmelCase_	)[0]:
											a        =     rc
						if smallest != idx:
											self.swap(lowerCAmelCase_	, lowerCAmelCase_	)
											self.min_heapify(lowerCAmelCase_	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     self.cur_size
						self.cur_size += 1
						self.array.append((sys.maxsize, tup[1])	)
						self.decrease_key((sys.maxsize, tup[1])	, tup[0]	)




	def   UpperCamelCase_ (self	):
						"""simple docstring"""

						a        =     self.array[0][1]
						a        =     self.array[self.cur_size - 1]
						self.cur_size -= 1
						self.min_heapify(1	)
						del self.pos[min_node]
						return min_node




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						return 2 * i + 1




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						return 2 * i + 2




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						return math.floor(i / 2	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     j
						a        =     i
						a        =     self.array[i]
						a        =     self.array[j]
						a        =     temp




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     self.pos[tup[1]]
						# assuming the new_d is atmost old_d
						a        =     (new_d, tup[1])
						while idx > 0 and self.array[self.par(lowerCAmelCase_	)][0] > self.array[idx][0]:
											self.swap(lowerCAmelCase_	, self.par(lowerCAmelCase_	)	)
											a        =     self.par(lowerCAmelCase_	)




class 			_lowercase							:





	"""simple docstring"""




	def __init__(self	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     {}  # To store graph: u -> (v,w)
						a        =     num  # Number of nodes in graph
						# To store the distance from source vertex
						a        =     [0] * self.num_nodes
						a        =     [-1] * self.num_nodes  # To store the path




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	):
						"""simple docstring"""

						if u in self.adjList:
											self.adjList[u].append((v, w)	)
						else:
											a        =     [(v, w)]

						# Assuming undirected graph
						if v in self.adjList:
											self.adjList[v].append((u, w)	)
						else:
											a        =     [(u, w)]




	def   UpperCamelCase_ (self	):
						"""simple docstring"""

						for u in self.adjList:
											print(lowerCAmelCase_	, "->"	, " -> ".join(str(F'''{v}({w})'''	) for v, w in self.adjList[u]	)	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     [-1] * self.num_nodes
						# src is the source node
						a        =     0
						a        =     PriorityQueue()
						q.insert((0, src)	)  # (dist from src, node)
						for u in self.adjList:
											if u != src:
																a        =     sys.maxsize  # Infinity
																a        =     -1

						while not q.is_empty():
											a        =     q.extract_min()  # Returns node with the min dist from source
											# Update the distance of all the neighbours of u and
											# if their prev dist was INFINITY then push them in Q
											for v, w in self.adjList[u]:
																a        =     self.dist[u] + w
																if self.dist[v] > new_dist:
																					if self.dist[v] == sys.maxsize:
																										q.insert((new_dist, v)	)
																					else:
																										q.decrease_key((self.dist[v], v)	, lowerCAmelCase_	)
																					a        =     new_dist
																					a        =     u

        # Show the shortest distances from src
						self.show_distances(lowerCAmelCase_	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	):
						"""simple docstring"""

						print(F'''Distance from node: {src}'''	)
						for u in range(self.num_nodes	):
											print(F'''Node {u} has distance: {self.dist[u]}'''	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	):
						"""simple docstring"""

						a        =     []
						a        =     0
						a        =     dest
						# Backtracking from dest to src
						while self.par[temp] != -1:
											path.append(lowerCAmelCase_	)
											if temp != src:
																for v, w in self.adjList[temp]:
																					if v == self.par[temp]:
																										cost += w
																										break
											a        =     self.par[temp]
						path.append(lowerCAmelCase_	)
						path.reverse()

						print(F'''----Path to reach {dest} from {src}----'''	)
						for u in path:
											print(F'''{u}'''	, end=" "	)
											if u != dest:
																print("-> "	, end=""	)

						print("\nTotal cost of path: "	, lowerCAmelCase_	)


if __name__ == "__main__":
				_lowercase:				List[Any]       =	Graph(9)
				graph.add_edge(0, 1, 4)
				graph.add_edge(0, 7, 8)
				graph.add_edge(1, 2, 8)
				graph.add_edge(1, 7, 11)
				graph.add_edge(2, 3, 7)
				graph.add_edge(2, 8, 2)
				graph.add_edge(2, 5, 4)
				graph.add_edge(3, 4, 9)
				graph.add_edge(3, 5, 14)
				graph.add_edge(4, 5, 10)
				graph.add_edge(5, 6, 2)
				graph.add_edge(6, 7, 1)
				graph.add_edge(6, 8, 6)
				graph.add_edge(7, 8, 7)
				graph.show_graph()
				graph.dijkstra(0)
				graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21





# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left



@flax.struct.dataclass
class 			_lowercase							:





	"""simple docstring"""
	# setable values
	__A					=							None
	__A					=							None
	__A					=							None




	@classmethod
	def   UpperCamelCase_ (cls	):
						"""simple docstring"""

						return cls()




@dataclass
class 			_lowercase							(     lowerCAmelCase			):





	"""simple docstring"""
	__A					=							42
	__A					=							42
	__A					=							None




class 			_lowercase							(     lowerCAmelCase,   lowerCAmelCase			):





	"""simple docstring"""




	@property
	def   UpperCamelCase_ (self	):
						"""simple docstring"""

						return True




	@register_to_config
	def __init__(self	, lowerCamelCase_ = 2000	, lowerCamelCase_ = 0.15	, lowerCamelCase_ = 0.01	, lowerCamelCase_ = 1348.0	, lowerCamelCase_ = 1E-5	, lowerCamelCase_ = 1	, ):
						"""simple docstring"""

						pass




	def   UpperCamelCase_ (self	):
						"""simple docstring"""

						a        =     ScoreSdeVeSchedulerState.create()
						return self.set_sigmas(
						    lowerCamelCase_	, self.config.num_train_timesteps	, self.config.sigma_min	, self.config.sigma_max	, self.config.sampling_eps	, )




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_ = ()	, lowerCamelCase_ = None	):
						"""simple docstring"""

						a        =     sampling_eps if sampling_eps is not None else self.config.sampling_eps

						a        =     jnp.linspace(1	, lowerCamelCase_	, lowerCamelCase_	)
						return state.replace(timesteps=lowerCamelCase_	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_ = None	, lowerCamelCase_ = None	, lowerCamelCase_ = None	, ):
						"""simple docstring"""

						a        =     sigma_min if sigma_min is not None else self.config.sigma_min
						a        =     sigma_max if sigma_max is not None else self.config.sigma_max
						a        =     sampling_eps if sampling_eps is not None else self.config.sampling_eps
						if state.timesteps is None:
											a        =     self.set_timesteps(lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	)

						a        =     jnp.exp(jnp.linspace(jnp.log(lowerCamelCase_	)	, jnp.log(lowerCamelCase_	)	, lowerCamelCase_	)	)
						a        =     jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]	)

						return state.replace(discrete_sigmas=lowerCamelCase_	, sigmas=lowerCamelCase_	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	):
						"""simple docstring"""

						return jnp.where(timesteps == 0	, jnp.zeros_like(lowerCamelCase_	)	, state.discrete_sigmas[timesteps - 1]	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_ = True	, ):
						"""simple docstring"""

						if state.timesteps is None:
											raise ValueError(
											    "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"	)

						a        =     timestep * jnp.ones(
						    sample.shape[0]	, )
						a        =     (timestep * (len(state.timesteps	) - 1)).long()

						a        =     state.discrete_sigmas[timesteps]
						a        =     self.get_adjacent_sigma(lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	)
						a        =     jnp.zeros_like(lowerCamelCase_	)
						a        =     (sigma**2 - adjacent_sigma**2) ** 0.5

						# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
						# also equation 47 shows the analog from SDE models to ancestral sampling methods
						a        =     diffusion.flatten()
						a        =     broadcast_to_shape_from_left(lowerCamelCase_	, sample.shape	)
						a        =     drift - diffusion**2 * model_output

						#  equation 6: sample noise for the diffusion term of
						a        =     random.split(lowerCamelCase_	, num=1	)
						a        =     random.normal(key=lowerCamelCase_	, shape=sample.shape	)
						a        =     sample - drift  # subtract because `dt` is a small negative timestep
						# TODO is the variable diffusion the correct scaling term for the noise?
						a        =     prev_sample_mean + diffusion * noise  # add impact of diffusion field g

						if not return_dict:
											return (prev_sample, prev_sample_mean, state)

						return FlaxSdeVeOutput(prev_sample=lowerCamelCase_	, prev_sample_mean=lowerCamelCase_	, state=lowerCamelCase_	)




	def   UpperCamelCase_ (self	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_	, lowerCamelCase_ = True	, ):
						"""simple docstring"""

						if state.timesteps is None:
											raise ValueError(
											    "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"	)

						# For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
						# sample noise for correction
						a        =     random.split(lowerCamelCase_	, num=1	)
						a        =     random.normal(key=lowerCamelCase_	, shape=sample.shape	)

						# compute step size from the model_output, the noise, and the snr
						a        =     jnp.linalg.norm(lowerCamelCase_	)
						a        =     jnp.linalg.norm(lowerCamelCase_	)
						a        =     (self.config.snr * noise_norm / grad_norm) ** 2 * 2
						a        =     step_size * jnp.ones(sample.shape[0]	)

						# compute corrected sample: model_output term and noise term
						a        =     step_size.flatten()
						a        =     broadcast_to_shape_from_left(lowerCamelCase_	, sample.shape	)
						a        =     sample + step_size * model_output
						a        =     prev_sample_mean + ((step_size * 2) ** 0.5) * noise

						if not return_dict:
											return (prev_sample, state)

						return FlaxSdeVeOutput(prev_sample=lowerCamelCase_	, state=lowerCamelCase_	)




	def __len__(self	):
						"""simple docstring"""

						return self.config.num_train_timesteps
