class Polynomial:
"""Represents a polynomial as a collection of terms and stores in a Vector"""
def __init__(self, poly_string=""):
"""Builds a polynomial
If a string is given in the right format it will split it to build the polynomial"""
self.terms = Vector()
if poly_string != "":
poly_pieces = Vector()
poly_pieces.build_from_list(poly_string.split(" "))
for i in range(0, len(poly_pieces), 2):
coef = poly_pieces[i]
exponent = poly_pieces[i + 1]
self.terms.insert_rear(Term(int(coef), int(exponent)))
#condense similar terms
self.combine_like_terms()
# Sort the terms
self.sort_terms()
def __add__(self, other):
"""Overloaded addition operator"""
temp = Vector()
for term in self.terms:
temp.append(term)
for term in other.terms:
temp.append(term)
new_poly = Polynomial()
new_poly.terms = temp
new_poly.combine_like_terms()
new_poly.sort_terms()
return new_poly
def __radd__(self, other):
return self.__add__(other)
def __sub__(self, other):
"""Overlaoded subtraction operator"""
p = Polynomial("-1 0")
return (self + (p * other))
def __mul__(self, other):
"""Overloaded multiplication operator"""
temp = Vector()
for term in self.terms:
for item in other.terms:
new_coef = term.coef * item.coef
new_exp = term.exponent + item.exponent
temp.append(Term(new_coef, new_exp))
new_poly = Polynomial()
new_poly.terms = temp
new_poly.combine_like_terms()
new_poly.sort_terms()
return new_poly
def __rmul__(self, other):
return self.__mul__(other)
def sort_terms(self):
"""Sorts the terms of the polynomial in O(n^2) time"""
temp = Vector()
for i in range(len(self.terms)):
max_exp = self.terms[0].exponent
max_exp_index = 0
for index, term in enumerate(self.terms):
if term.exponent > max_exp:
max_exp = term.exponent
max_exp_index = index
temp.append(self.terms[max_exp_index])
self.terms.erase(max_exp_index)
self.terms = temp
def combine_like_terms(self):
max_exponent = 0
temp = Vector()
for term in self.terms:
max_exponent = max(max_exponent, term.exponent)
for exponent in range(max_exponent + 1):
new_coef = 0
for term in self.terms:
if term.exponent == exponent:
new_coef += term.coef
if (new_coef != 0):
temp.append(Term(new_coef, exponent))
self.terms = temp
self.sort_terms
def __str__(self):
"""Returns a string representation of the polynomial"""
temp = ""
if len(self.terms) > 0:
if self.terms[0].coef < 0:
temp += "-"
temp += str(abs(self.terms[0].coef))
if self.terms[0].exponent != 0:
temp += "x^" + str(self.terms[0].exponent)
for i in range(1, len(self.terms)):
if self.terms[i].coef > 0:
temp += " + "
else:
temp += " - "
temp += str(abs(self.terms[i].coef))
if self.terms[i].exponent != 0:
temp += "x^" + str(self.terms[i].exponent)
return temp
class Polynomial:
"""Represents a polynomial as a collection of terms and stores in a Vector"""
def __init__(self, poly_string=""):
"""Builds a polynomial
If a string is given in the right format it will split it to build the polynomial"""
self.terms = Vector()
if poly_string != "":
poly_pieces = Vector()
poly_pieces.build_from_list(poly_string.split(" "))
for i in range(0, len(poly_pieces), 2):
coef = poly_pieces[i]
exponent = poly_pieces[i + 1]
self.terms.insert_rear(Term(int(coef), int(exponent)))
#condense similar terms
self.combine_like_terms()
# Sort the terms
self.sort_terms()
def __add__(self, other):
"""Overloaded addition operator"""
temp = Vector()
for term in self.terms:
temp.append(term)
for term in other.terms:
temp.append(term)
new_poly = Polynomial()
new_poly.terms = temp
new_poly.combine_like_terms()
new_poly.sort_terms()
return new_poly
def __radd__(self, other):
return self.__add__(other)
def __sub__(self, other):
"""Overlaoded subtraction operator"""
p = Polynomial("-1 0")
return (self + (p * other))
def __mul__(self, other):
"""Overloaded multiplication operator"""
temp = Vector()
for term in self.terms:
for item in other.terms:
new_coef = term.coef * item.coef
new_exp = term.exponent + item.exponent
temp.append(Term(new_coef, new_exp))
new_poly = Polynomial()
new_poly.terms = temp
new_poly.combine_like_terms()
new_poly.sort_terms()
return new_poly
def __rmul__(self, other):
return self.__mul__(other)
def sort_terms(self):
"""Sorts the terms of the polynomial in O(n^2) time"""
temp = Vector()
for i in range(len(self.terms)):
max_exp = self.terms[0].exponent
max_exp_index = 0
for index, term in enumerate(self.terms):
if term.exponent > max_exp:
max_exp = term.exponent
max_exp_index = index
temp.append(self.terms[max_exp_index])
self.terms.erase(max_exp_index)
self.terms = temp
def combine_like_terms(self):
max_exponent = 0
temp = Vector()
for term in self.terms:
max_exponent = max(max_exponent, term.exponent)
for exponent in range(max_exponent + 1):
new_coef = 0
for term in self.terms:
if term.exponent == exponent:
new_coef += term.coef
if (new_coef != 0):
temp.append(Term(new_coef, exponent))
self.terms = temp
self.sort_terms
def __str__(self):
"""Returns a string representation of the polynomial"""
temp = ""
if len(self.terms) > 0:
if self.terms[0].coef < 0:
temp += "-"
temp += str(abs(self.terms[0].coef))
if self.terms[0].exponent != 0:
temp += "x^" + str(self.terms[0].exponent)
for i in range(1, len(self.terms)):
if self.terms[i].coef > 0:
temp += " + "
else:
temp += " - "
temp += str(abs(self.terms[i].coef))
if self.terms[i].exponent != 0:
temp += "x^" + str(self.terms[i].exponent)
return temp
