



'''simple docstring'''







import heapq





def 						snake_case__ (lowerCAmelCase_					,  lowerCAmelCase_					,  lowerCAmelCase_	):
    UpperCamelCase__      =			[(0, start)]  # cost from start node,end node
    UpperCamelCase__      =			set()
    while heap:
        ((UpperCamelCase__)    ,  (UpperCamelCase__))      =			heapq.heappop(lowerCAmelCase_	)
        if u in visited:
            continue
        visited.add(lowerCAmelCase_	)
        if u == end:
            return cost
        for v, c in graph[u]:
            if v in visited:
                continue
            UpperCamelCase__      =			cost + c
            heapq.heappush(lowerCAmelCase_					,  (next_item, v)	)
    return -1


lowercase__     :  Any    					=			{
    'A': [['B', 2], ['C', 5]],
    'B': [['A', 2], ['D', 3], ['E', 1], ['F', 1]],
    'C': [['A', 5], ['F', 3]],
    'D': [['B', 3]],
    'E': [['B', 4], ['F', 3]],
    'F': [['C', 3], ['E', 3]],
}
lowercase__     :  Optional[int]    					=			{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['F', 3]],
    'F': [],
}
lowercase__     :  Union[str, Any]    					=			{
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}

lowercase__     :  Union[str, Any]    					=			dijkstra(G, 'E', 'C')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

lowercase__     :  Optional[int]    					=			dijkstra(Ga, 'E', 'F')
print(short_distance)  # E -- 3 --> F == 3

lowercase__     :  Any    					=			dijkstra(Ga, 'E', 'F')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
      import doctest

      doctest.testmod()









'''simple docstring'''







from math import radians as angle_to_radians
from math import sin

# Acceleration Constant on Earth (unit m/s^2)
lowercase__     :  str    					=			9.8_0_6_6_5





def 						snake_case__ (lowerCAmelCase_					,  lowerCAmelCase_	):

    # Ensure valid instance
    if not isinstance(lowerCAmelCase_					,  (int, float)	):
        raise TypeError("Invalid velocity. Should be a positive number."	)

    if not isinstance(lowerCAmelCase_					,  (int, float)	):
        raise TypeError("Invalid angle. Range is 1-90 degrees."	)

    # Ensure valid angle
    if angle > 90 or angle < 1:
        raise ValueError("Invalid angle. Range is 1-90 degrees."	)

    # Ensure valid velocity
    if init_velocity < 0:
        raise ValueError("Invalid velocity. Should be a positive number."	)





def 						snake_case__ (lowerCAmelCase_					,  lowerCAmelCase_	):
    check_args(lowerCAmelCase_					,  lowerCAmelCase_	)
    UpperCamelCase__      =			angle_to_radians(2 * angle	)
    return round(init_velocity**2 * sin(lowerCAmelCase_	) / g					,  2	)





def 						snake_case__ (lowerCAmelCase_					,  lowerCAmelCase_	):
    check_args(lowerCAmelCase_					,  lowerCAmelCase_	)
    UpperCamelCase__      =			angle_to_radians(lowerCAmelCase_	)
    return round(init_velocity**2 * sin(lowerCAmelCase_	) ** 2 / (2 * g)					,  2	)





def 						snake_case__ (lowerCAmelCase_					,  lowerCAmelCase_	):
    check_args(lowerCAmelCase_					,  lowerCAmelCase_	)
    UpperCamelCase__      =			angle_to_radians(lowerCAmelCase_	)
    return round(2 * init_velocity * sin(lowerCAmelCase_	) / g					,  2	)





def 						snake_case__ ():
    UpperCamelCase__    ,  UpperCamelCase__      =			25, 20
    assert horizontal_distance(lowerCAmelCase_					,  lowerCAmelCase_	) == 40.97
    assert max_height(lowerCAmelCase_					,  lowerCAmelCase_	) == 3.73
    assert total_time(lowerCAmelCase_					,  lowerCAmelCase_	) == 1.74


if __name__ == "__main__":
      from doctest import testmod

      testmod()

      # Get input from user
      lowercase__     :  Union[str, Any]    					=			float(input('Initial Velocity: ').strip())

      # Get input from user
      lowercase__     :  Any    					=			float(input('angle: ').strip())

      # Print results
      print()
      print('Results: ')
      print(F'''Horizontal Distance: {horizontal_distance(init_vel, angle)!s} [m]''')
      print(F'''Maximum Height: {max_height(init_vel, angle)!s} [m]''')
      print(F'''Total Time: {total_time(init_vel, angle)!s} [s]''')




