Clash Royale CLAN TAG

Polynomials and dictionaries

i have this exercise about polynomials and dictionaries which i did (see below) but i am sure there is a better and easier way to solve it (for question 2 and 3). can anyone show me another way to approach question 2 or 3? Thanks.

here is the exercice:

In this exercise we want to work with polynomials of any degree. Each polynomial can be represented by a dictionary, whose keys correspond to the powers of x, and the values ​​to the coefficients. For example, to represent the polynomial x ^ 6 + 3 * x ^ 2, we can use the dictionary: {6: 1, 2: 3}

1. Write a function evaluer(p, x) that takes a polynomial p and a number x into arguments, and returns the value of polynomial at point x.

Execution example:

evaluer({3: 1, 1: 2, 0: -1}, 2)

OUT: 11

2. Write a function somme_polynomes(p1, p2) which takes two polynomials (dictionaries) into arguments and which
returns a new dictionary representing the sum of the two polynomials p1 and p2.

Execution example:

somme_polynomes ({3: 1, 2: 1, 0: 1}, {4: 2, 2: 3})

OUT: {0: 1, 2: 4, 3: 1, 4: 2}

3. Write a function produit_polynomes(p1, p2) that takes two polynomials as arguments and returns the product of two polynomials in a new dictionary.

Execution example:

produit_polynomes ({3: 1, 2: 1, 0: 1}, {4: 2, 2: 3})

OUT: {2: 3, 4: 5, 5: 3, 6: 2, 7: 2}

here is what i did:

# 1)

def evaluer(p,x):
c = 0
for key,value in p.items():
c += value*(x**key)
return c

# 2)

def somme_polynomes(p1,p2):
p3 = {}

for key,value in p1.items():
for k,v in p2.items():
p3.update({key:value})
p3.update({k:v})

for key in p1:
if key in p2:
add = p1[key]+p2[key]
p3.update({key:add})
if add == 0:
del p3[key]
return p3

# 3)

def produit_polynomes(p1,p2):
p3 = {}
for key,value in p1.items():
for k,v in p2.items():
if key+k in p3:
p3[key+k] += value*v
else:
p3.update({key+k:value*v})

return p3


2 Answers
2

Your code is fine, here are alternative ways of doing it using more of Python's language (generator expression, dict comprehension) and library (itertools, collections):

itertools

collections

def evaluer(p, x):
return sum(v * x**k for k, v in p.items())

def somme_polynomes(p1, p2):
return {k: p1.get(k, 0) + p2.get(k, 0) for k in set(p1) | set(p2)}

import itertools as it
from collection import defaultdict

def produit_polynomes(p1, p2):
p3 = defaultdict(int)
for k1, k2 in it.product(p1, p2):
p3[k1+k2] += p1[k1]*p2[k2]
return dict(p3)


If you want to avoid importing any modules then produit_polnomes() could be written without the conditional as:

produit_polnomes()

def produit_polynomes(p1,p2):
p3 = {}
for k1, v1 in p1.items():
for k2, v2 in p2.items():
p3[k1+k2] = p3.get(k1+k2, 0) + v1*v2
return p3


Exercise 2 can be done in a more Pythonic way by using set union for keys and dict comprehension for sums:

def somme_polynomes(p1, p2):
return {p: p1.get(p, 0) + p2.get(p, 0) for p in set(p1) | set (p2)}


Exercise 3 on the other hand is best done using nested loops aggregating products to the sum of keys, which is what you are already doing. The only slight enhancement I would make is to use the setdefault method to avoid the if statement:

setdefault

if

def produit_polynomes(p1,p2):
p3 = {}
for key,value in p1.items():
for k,v in p2.items():
p3[key + k] = p3.get(key + k, 0) + value * v
return p3


setdefault()

setdefault()

get()

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