У вас уже есть свой ответ, но я должен был решить этот вид упражнения для собеседования некоторое время назад. Это не сложно, и мне не потребовалось много времени, чтобы прийти к следующему решению.
Прочитайте это, и это должно быть само за себя.
Создайте модуль Python, который решает треугольники, применяя теоремы sin и cosin.
Модуль получает в качестве параметров некоторые значения треугольника и, если возможно, возвращает значения всех его углов и длины сторон.
Параметры принимаются как dict, и его следует вызывать как автономный из командной строки.
from __future__ import division
import sys, logging
from math import radians, degrees, acos, cos, sin, sqrt, asin
class InconsistentDataError(TypeError):
pass
class InsufficientDataError(TypeError):
pass
class NonUpdatable(dict):
"""Dictionary whose items can be set only once."""
def __setitem__(self, i, y):
if self.get(i, None):
raise InconsistentDataError()
super(NonUpdatable, self).__setitem__(i, y)
def get_known_sides(**kwarg):
"""Filter from the input elements the Side elements."""
return dict([i for i in kwarg.iteritems() if i[0].isupper()])
def get_known_angles(**kwarg):
"""Filter from the input elements the Angle elements."""
return dict([i for i in kwarg.iteritems() if i[0].islower()])
def get_opposite_angle(C, B, A):
"""
Get the angle corresponding to C.
Keyword arguments:
A -- right side of the angle (real number > 0)
B -- left side of the angle (real number > 0)
C -- side opposite to the angle (real number > 0)
Returns:
angle opposite to C
"""
return degrees(acos((A**2 + B**2 - C**2) / (2 * A * B)))
def get_side(A, B, c):
"""
Calculate the Side corresponding to the Angle c.
Keyword arguments:
A -- left side of C (real number > 0)
B -- right side of C (real number > 0)
c -- angle opposite to side C (real number)
Returns:
side C, opposite to c
"""
return sqrt(A**2 + B**2 - 2*A*B*cos(radians(c)))
def get_overlapping_angle(known_angles, known_sides):
"""
Calculate the Angle of a known side, knowing the angle to another known side.
Keyword arguments:
known_angles -- (dict of angles)
known_sides -- (dict of sides)
Returns:
angle of the known side, to which there is no known angle
"""
a = (set([i.lower() for i in known_sides.iterkeys()]) -
set([i.lower() for i in known_angles.iterkeys()])).pop()
b = (set([i.lower() for i in known_sides.iterkeys()]) &
set([i.lower() for i in known_angles.iterkeys()])).pop()
y = (known_sides[a.upper()]/known_sides[b.upper()]) * sin(radians(known_angles[b.lower()]))
if y > 1: y = 1 #Rounding error fix --- y = 1.000000000001; asin(y) -> Exception
return {a.lower(): degrees(asin(y))}
def get_angles(A, B, C):
"""
Calculate all the angles, given the length of all the sides.
Keyword arguments:
A -- side A (real number > 0)
B -- side B (real number > 0)
C -- side C (real number > 0)
Returns:
dict of angles
"""
sides = {"A":A,"B":B,"C":C}
_sides = sides.keys()
angles = {}
for side in sides.keys():
angles[side.lower()] = get_opposite_angle(
sides[_sides[0]],
sides[_sides[1]],
sides[_sides[2]])
_sides.append(_sides.pop(0))
return angles
def get_triangle_values(**kwargs):
"""Calculate the missing values of a triangle based on the known values."""
known_params = kwargs
angles = NonUpdatable({
"a":0,
"b":0,
"c":0,
})
sides = NonUpdatable({
"A":0,
"B":0,
"C":0,
})
if len(known_params) < 3:
raise InsufficientDataError("Three parameters are needed to calculate triangle's values.")
if str(known_params.keys()).islower():
raise TypeError("At least one length needed.")
known_sides = NonUpdatable(get_known_sides(**known_params))
sides.update(known_sides)
known_angles = NonUpdatable(get_known_angles(**known_params))
angles.update(known_angles)
if len(known_angles) == 3 and sum(known_angles.itervalues()) != 180:
raise InconsistentDataError("One of the sides is too long.")
if len(known_sides) == 3:
x=[side for side in known_sides.itervalues() if (sum(known_sides.itervalues()) - side) < side]
if len(x):
raise InconsistentDataError("One of the sides is too long.")
for angle, value in get_angles(**known_sides).iteritems():
# Done this way to force exception when overwriting a
# user input angle, otherwise it would be a simple assignment.
# >>> angles = get_angles(**known_sides)
# This means inconsistent input data.
angles[angle] = value
else: # There are angles given and not enough sides.
if len(known_angles) > 1:
#2 angles given. Get last angle and calculate missing sides
for angle, val in angles.iteritems():
if val == 0:
angles[angle] = 180. - sum(angles.itervalues())
known_sides = known_sides.items()
for side, length in sides.iteritems():
if length == 0:
sides[side] = known_sides[0][1] / \
sin(radians(angles[known_sides[0][0].lower()])) * \
sin(radians(angles[side.lower()]))
else:
unknown_side = (set(sides.keys()) - set(known_sides.keys())).pop()
chars = [ord(i.lower()) for i in known_params.iterkeys()]
chars.sort()
if chars[0] < chars[1] < chars[2]:
sides[unknown_side] = get_side(known_sides.values()[0], known_sides.values()[1], known_angles[unknown_side.lower()])
angles = get_angles(**sides)
else:
known_angles.update(get_overlapping_angle(known_angles, known_sides))
angles.update(known_angles)
for angle, val in angles.iteritems():
if val == 0:
angles[angle] = 180. - sum(angles.itervalues())
sides[unknown_side] = get_side(known_sides.values()[0], known_sides.values()[1], angles[unknown_side.lower()])
angles.update(sides)
return angles
if __name__ == "__main__":
try:
values = get_triangle_values( **eval(sys.argv[1], {}, {}) )
except IndexError, e:
values = get_triangle_values(A=10,B=10,C=10)
except InsufficientDataError, e:
print "Not enough data!"
exit(1)
except InconsistentDataError, e:
print "Data is inconsistent!"
exit(1)
print values
A, B и C - длины сторон, a, b и c - углы, поэтому c - угол, противоположный стороне C.
Тесты