




'''simple docstring'''







def 						snake_case_							(_a	:							Tuple     ):
    UpperCAmelCase			       =		[0] * len(_a     )
    UpperCAmelCase			       =		[]
    UpperCAmelCase			       =		[1] * len(_a     )

    for values in graph.values():
        for i in values:
            indegree[i] += 1

    for i in range(len(_a     )     ):
        if indegree[i] == 0:
            queue.append(_a     )

    while queue:
        UpperCAmelCase			       =		queue.pop(0     )
        for x in graph[vertex]:
            indegree[x] -= 1

            if long_dist[vertex] + 1 > long_dist[x]:
                UpperCAmelCase			       =		long_dist[vertex] + 1

            if indegree[x] == 0:
                queue.append(_a     )

    print(max(_a     )     )


# Adjacency list of Graph
A     ={0: [2, 3, 4], 1: [2, 7], 2: [5], 3: [5, 7], 4: [7], 5: [6], 6: [7], 7: []}







longest_distance(graph)










'''simple docstring'''







from queue import PriorityQueue
from typing import Any

import numpy as np





def 						snake_case_							(_a	:							dict    ,   _a	:							str    ,   _a	:							set    ,   _a	:							set    ,   _a	:							dict    ,   _a	:							dict    ,   _a	:							PriorityQueue    ,   _a	:							dict    ,   _a	:							float | int    ,   ):
    for nxt, d in graph[v]:
        if nxt in visited_forward:
            continue
        UpperCAmelCase			       =		cst_fwd.get(_a    ,   np.inf     )
        UpperCAmelCase			       =		cst_fwd[v] + d
        if new_cost_f < old_cost_f:
            queue.put((new_cost_f, nxt)     )
            UpperCAmelCase			       =		new_cost_f
            UpperCAmelCase			       =		v
        if nxt in visited_backward:
            if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
                UpperCAmelCase			       =		cst_fwd[v] + d + cst_bwd[nxt]
    return shortest_distance





def 						snake_case_							(_a	:							str    ,   _a	:							str    ,   _a	:							dict    ,   _a	:							dict     ):
    UpperCAmelCase			       =		-1

    UpperCAmelCase			       =		set()
    UpperCAmelCase			       =		set()
    UpperCAmelCase			       =		{source: 0}
    UpperCAmelCase			       =		{destination: 0}
    UpperCAmelCase			       =		{source: None}
    UpperCAmelCase			       =		{destination: None}
    UpperCAmelCase			       =		PriorityQueue()
    UpperCAmelCase			       =		PriorityQueue()

    UpperCAmelCase			       =		np.inf

    queue_forward.put((0, source)     )
    queue_backward.put((0, destination)     )

    if source == destination:
        return 0

    while not queue_forward.empty() and not queue_backward.empty():
        UpperCAmelCase       ,     UpperCAmelCase			       =		queue_forward.get()
        visited_forward.add(_a     )

        UpperCAmelCase       ,     UpperCAmelCase			       =		queue_backward.get()
        visited_backward.add(_a     )

        UpperCAmelCase			       =		pass_and_relaxation(
            _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   )

        UpperCAmelCase			       =		pass_and_relaxation(
            _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   _a    ,   )

        if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
            break

    if shortest_distance != np.inf:
        UpperCAmelCase			       =		shortest_distance
    return shortest_path_distance


A     ={
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
A     ={
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
   import doctest

   doctest.testmod()




