curriculum/challenges/english/blocks/learn-interfaces-by-building-an-equation-solver/665460392acb7e91db2afad1.md
When the second-degree coefficient is positive, the parabola has a minimum point and opens upward, or it is called concave upwards. Instead, when the second-degree coefficient is negative, the parabola has a maximum point and opens downward, or it is called concave downwards.
Declare a concavity variable and assign it either the string 'upwards' or 'downwards', depending on the concavity of the parabola. Also, declare a variable named min_max and assign it either the string 'min' or 'max', depending on if the vertex is a minimum or a maximum, respectively.
Finally, add the dictionary to return two keys 'min_max' and 'concavity' with the values of min_max' and concavity, respectively.
Your analyze method should return a dictionary with four keys, 'x', 'y', 'min_max', and 'concavity' and the values of x, y, min_max, and concavity, respectively.
({ test: () => runPython(`
eq1 = QuadraticEquation(16, 2, 1)
eq2 = QuadraticEquation(-16, 2, 1)
assert eq1.analyze() == {'x': -0.0625, 'y': 0.9375, 'min_max': 'min', 'concavity': 'upwards'}
assert eq2.analyze() == {'x': 0.0625, 'y': 1.0625, 'min_max': 'max', 'concavity': 'downwards'}
`) })
from abc import ABC, abstractmethod
import re
class Equation(ABC):
degree: int
def __init__(self, *args):
if (self.degree + 1) != len(args):
raise TypeError(
f"'Equation' object takes {self.degree + 1} positional arguments but {len(args)} were given"
)
if any(not isinstance(arg, (int, float)) for arg in args):
raise TypeError("Coefficients must be of type 'int' or 'float'")
if args[0] == 0:
raise ValueError("Highest degree coefficient must be different from zero")
self.coefficients = {(len(args) - n - 1): arg for n, arg in enumerate(args)}
def __init_subclass__(cls):
if not hasattr(cls, "degree"):
raise AttributeError(
f"Cannot create '{cls.__name__}' class: missing required attribute 'degree'"
)
def __str__(self):
terms = []
for n, coefficient in self.coefficients.items():
if not coefficient:
continue
if n == 0:
terms.append(f'{coefficient:+}')
elif n == 1:
terms.append(f'{coefficient:+}x')
else:
terms.append(f"{coefficient:+}x**{n}")
equation_string = ' '.join(terms) + ' = 0'
return re.sub(r"(?<!\d)1(?=x)", "", equation_string.strip("+"))
@abstractmethod
def solve(self):
pass
@abstractmethod
def analyze(self):
pass
class LinearEquation(Equation):
degree = 1
def solve(self):
a, b = self.coefficients.values()
x = -b / a
return [x]
def analyze(self):
slope, intercept = self.coefficients.values()
return {'slope': slope, 'intercept': intercept}
class QuadraticEquation(Equation):
degree = 2
def __init__(self, *args):
super().__init__(*args)
a, b, c = self.coefficients.values()
self.delta = b**2 - 4 * a * c
def solve(self):
if self.delta < 0:
return []
a, b, _ = self.coefficients.values()
x1 = (-b + (self.delta) ** 0.5) / (2 * a)
x2 = (-b - (self.delta) ** 0.5) / (2 * a)
if self.delta == 0:
return [x1]
return [x1, x2]
--fcc-editable-region--
def analyze(self):
a, b, c = self.coefficients.values()
x = -b / (2 * a)
y = a * x**2 + b * x + c
return {'x': x, 'y': y}
--fcc-editable-region--
lin_eq = LinearEquation(2, 3)
print(lin_eq)
quadr_eq = QuadraticEquation(1, 2, 1)
print(quadr_eq)
print(quadr_eq.solve())