Modifying a generator using send - python

I want to modify a generator by only changing the manipulate_generator function below. This is a HR challenge that has had me scratching my head throughout the day. I got the idea of using send from a previous SO question on even numbers. I cannot get to work using a primality checker. The algorithm should print the first 10 non-primes. It's currently printing 3.
from math import sqrt
from itertools import count, islice
def is_prime(n):
if n < 2:
return False
for number in islice(count(2), int(sqrt(n) - 1)):
if n % number == 0:
return False
return True
# this is the only portion of the code that can be changed
def manipulate_generator(generator, n):
if not is_prime(n):
generator.send(n+1)
#all the code below cannot be changed
def positive_integers_generator():
n = 1
while True:
x = yield n
if x is not None:
n = x
else:
n += 1
k = int(input())
g = positive_integers_generator()
for _ in range(k):
n = next(g)
print(n)
manipulate_generator(g, n)

Related

Create a mathematical sequence

i need to create a mathematical sequence of type:
P(n)= P(n-1) + P(n-2)
We know that P(0)=0 and P(1)=1
I really struggle creating a sequence, i tried to create it, here is some of what I’ve written...
def fibonacci(n):
number = 0
if n == 0:
number = 0
return (number)
if n == 1:
number = 1
return (number)
if n > 1:
def compute(limit):
for x in range(2, limit):
fibonacci(x) = fibonacci(x-1) + fibonacci(x-2)
for i in range(0, n):
number += compute(i)
First: you don't need to use brackets when you use 'return' statement
Solution:
def fibonacci(n):
number = 0
if n == 0:
number = 0
return number
if n == 1:
number = 1
return number
if n > 1:
return fibonacci(n-1)+fibonacci(n-2)
This code works fine, but u can calculate fibonacci more effective if u will use dynamic programming
Example:
fibonacci = [0,1]
for i in range(2,n+1):
fibonacci.append(fibonacci[i-1]+fibonacci[i-2])
print(fibonacci[-1])

Python print non-prime numbers

I have a hackkerank coding challenge to print first n non prime numbers, i have the working code but the problem is that they have a locked code which prints numbers from 1 to n along with the output, in order to pass the test i need to print only the non prime numbers not 1...n numbers along with it. I cant comment the printing part of 1...n as it is blocked. please let me know the idea to print only 1st n non prime numbers:
here is my solution:
def manipulate_generator(generator, n):
if n>1:
ls=[1]
for elm in generator:
if elm>3 and len(ls)<n:
for k in range(2,elm):
if elm%k==0 and elm not in ls:
ls.append(elm)
print(elm)
if len(ls)==n:
return ls
That's the code I added but here is the code that's locked on which I have to write the code above to make it print the number one at a time
def positive_integers_generator():
n = 1
while True:
x = yield n
if x is not None:
n = x
else:
n += 1
k = int(input())
g = positive_integers_generator()
for _ in range(k):
n = next(g)
print(n)
manipulate_generator(g, n)
the point is the for _ in range(k): already prints out number which includes numbers I don't want printed out: This is the desired kind of output I want:for n=10 I want it to print out:
output:
1
4
6
8
9
10
12
14
15
16
I can't change this code but the one above is what I wrote and can be changed... Pleae help me out... Thanks in anticipation
Why not to throw away the numbers which we don't need? Look at this solution which I implemented...
def is_prime(n):
for i in range(2, n):
if n%i == 0:
return False
return True
def manipulate_generator(generator, n):
if is_prime(n+1):
next(generator)
manipulate_generator(generator, n+1)
Note: I understand that the logic can be improved to make it more efficient. But, its the idea of skipping unnecessary number printing which is important here !
You can print all the numbers from 1 up to the first prime number and then from that first number to the next one until you reach n.
I'm not sure of your hackerrank situation, but printing the first N non-prime numbers efficiently can be done this way.
def non_prime_numbers_till_n(n):
primes = set()
for num in range(2,number + 1):
if num > 1:
for i in range(2, math.sqrt(num)):
if (num % i) == 0:
break
else:
primes.add(num)
result = []
for i in range(1, n):
if i not in primes:
result.append(i)
return result
Depending on what your online editor expects you can either print them, or store them in a list and return the list.
Also bear in mind, you can only check upto the sqrt of the number to determine if its a prime or not.
I eventually came up with this answer which I believe should solve it but id there;s a better way to solve it please add your answers:
def manipulate_generator(generator, n):
for num in range(3,100000):
for q in range(2,num):
if num%q==0 and num>n:
generator.send(num-1)
return
this link python generator helped me to understand python generator
I just solved that right now. Like Swapnil Godse said you need to deal with all special cases to optimize computations. This link might be helpful: click here.
Here is the solution:
from math import sqrt
def is_prime(n):
if (n <= 1):
return False
if (n == 2):
return True
if (n % 2 == 0):
return False
i = 3
while i <= sqrt(n):
if n % i == 0:
return False
i = i + 2
return True
def manipulate_generator(g, n):
if is_prime(n+1):
next(g)
manipulate_generator(g, n+1)
prime = int(input('Please enter the range: '))
prime_number = []
for num in range(prime):
if num > 1:
for i in range(2,num):
if num % i == 0:
break
else:
prime_number.append(num)
print(f'Prime numbers in range {prime} is {prime_number}')
all_number = []
for i in range(2,prime+1):
all_number.append(i)
Non_prime_number = []
for element in all_number:
if element not in prime_number:
Non_prime_number.append(element)
print(f'Non Prime numbers in range {prime} is {Non_prime_number}')

Optimizing a python Code

I'm trying to optimize this code (Given two integers m, n (1 <= m <= n) we want to find all integers between m and n whose sum of squared divisors is itself a square). I'm new to coding and I'm having a hard time with this concept
def list_squared(m, n):
# your code
import math
MyList = []
for i in range(m,n):
A=[]
for k in range(1,i+1):
if i%k == 0:
A.append(k**2)
if round(math.sqrt(sum(A))) == math.sqrt(sum(A)):
B =[]
B.append(i)
B.append(sum(A))
MyList.append(B)
return MyList
import math
def list_squared(m, n):
MyList = []
for i in range(m,n):
res=0
for k in range(1,i+1):
if i%k == 0:
res+=k**2
if res == int(math.sqrt(res))**2
MyList.append(i)
return MyList
First thing that i note you can optimize is range(1,i+1). You can set initially res=1 and start the range from 2 avoiding the first cycle. The important optimization is in the end: you can stop after i/2 because there are not integer divisors after it but remember to include the dispair case (for example 3/2 = 1.5 is not a valid input for range) so wrap the result of division around ceil function. In conclusion a simple optimization is range(2, ceil(i/2)+1) with res=1

Surprised about good recursion performance in python

I wrote this rather poor Python function for prime factorization:
import math
def factor(n):
for i in range(2, int(math.sqrt(n)+1)):
if not n % i:
return [i] + factor(n//i)
return [n]
and it worked as expected, now I was interested in whether the performance could be better when using an iterative approach:
def factor_it(n):
r = []
i = 2
while i < int(math.sqrt(n)+1):
while not n % i:
r.append(i)
n //= i
i +=1
if n > 1:
r.append(n)
return r
But what I observed (while the functions gave the same results) was that the iterative function took longer to run. At least I had the feeling, when doing this:
number = 31123478114123
print(factor(number))
print(factor_it(number))
so I measured:
setup = '''
import math
def factor(n):
for i in range(2, int(math.sqrt(n)+1)):
if not n % i:
return [i] + factor(n//i)
return [n]
def factor_it(n):
r = []
i = 2
while i < int(math.sqrt(n)+1):
while not n % i:
r.append(i)
n //= i
i +=1
if n > 1:
r.append(n)
return r
'''
import timeit
exec(setup)
number = 66666667*952381*290201
print(factor(number))
print(factor_it(number))
print(timeit.Timer('factor('+str(number)+')',setup=setup).repeat(1,1))
print(timeit.Timer('factor_it('+str(number)+')',setup=setup).repeat(1,1))
And this is what I got:
[290201, 952381, 66666667]
[290201, 952381, 66666667]
[0.19888348945642065]
[0.7451271022307537]
Why is the recursive approach in this case faster than the iterative one?
I use WinPython-64bit-3.4.4.2 (Python 3.4.4 64bits).
It’s because you’re recomputing sqrt each time. This modification runs as fast as your recursive version:
def factor_it2(n):
r = []
i = 2
lim = int(math.sqrt(n)+1)
while i < lim:
while not n % i:
r.append(i)
n //= i
lim = int(math.sqrt(n)+1)
i += 1
if n > 1:
r.append(n)
return r
timeit gives me these times:
factor 0.13133816363922143
factor_it 0.5705408816539869
factor_it2 0.14267319543853973
I think the tiny difference that remains is due to for … in range(…) being faster than the equivalent while loop, as the for loop can use a generator instead of having to execute a bunch of comparisons.

How can I get this Python code to run more quickly? [Project Euler Problem #7]

I'm trying to complete this Project Euler challenge:
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can
see that the 6th prime is 13.
What is the 10 001st prime number?
My code seem to be right because it works with small numbers, e.g 6th prime is 13.
How can i improve it so that the code will run much more quickly for larger numbers such as 10 001.
Code is below:
#Checks if a number is a prime
def is_prime(n):
count = 0
for i in range(2, n):
if n%i == 0:
return False
break
else:
count += 1
if count == n-2:
return True
#Finds the value for the given nth term
def term(n):
x = 0
count = 0
while count != n:
x += 1
if is_prime(x) == True:
count += 1
print x
term(10001)
UPDATE:
Thanks for your responses. I should have been more clear, I am not looking to speed up the interpreter or finding a faster interpreter, because i know my code isn't great, so i was looking for ways of make my code more efficient.
A few questions to ponder:
Do you really need to check the division until n-1? How earlier can you stop?
Apart from 2, do you really need to check the division by all the multiples of two ?
What about the multiples of 3? 5? Is there a way to extend this idea to all the multiples of previously tested primes?
The purpose of Project Euler is not really to think learn programming, but to think about algorithms. On problem #10, your algorithm will need to be even faster than on #7, etc. etc. So you need to come up with a better way to find prime numbers, not a faster way to run Python code. People solve these problems under the time limit with far slower computers that you're using now by thinking about the math.
On that note, maybe ask about your prime number algorithm on https://math.stackexchange.com/ if you really need help thinking about the problem.
A faster interpreter won't cut it. Even an implementation written in C or assembly language won't be fast enough (to be in the "about one second" timeframe of project Euler). To put it bluntly, your algorithm is pathetic. Some research and thinking will help you write an algorithm that runs faster in a dog-slow interpreter than your current algorithm implemented in native code (I won't name any specifics, partly because that's your job and partly because I can't tell offhand how much optimization will be needed).
Many of the Euler problems (including this one) are designed to have a solution that computes in acceptable time on pretty much any given hardware and compiler (well, not INTERCAL on a PDP-11 maybe).
You algorithm works, but it has quadratic complexity. Using a faster interpreter will give you a linear performance boost, but the quadratic complexity will dwarf it long before you calculate 10,000 primes. There are algorithms with much lower complexity; find them (or google them, no shame in that and you'll still learn a lot) and implement them.
Without discussing your algorithm, the PyPy interpreter can be ridiculously faster than the normal CPython one for tight numerical computation like this. You might want to try it out.
to check the prime number you dont have to run till n-1 or n/2....
To run it more faster,you can check only until square root of n
And this is the fastest algorithm I know
def isprime(number):
if number<=1:
return False
if number==2:
return True
if number%2==0:
return False
for i in range(3,int(sqrt(number))+1):
if number%i==0:
return False
return True
As most people have said, it's all about coming up with the correct algorithm. Have you considered looking at a
Sieve of Eratosthenes
import time
t=time.time()
def n_th_prime(n):
b=[]
b.append(2)
while len(b)<n :
for num in range(3,n*11,2):
if all(num%i!=0 for i in range(2,int((num)**0.5)+1)):
b.append(num)
print list(sorted(b))[n-1]
n_th_prime(10001)
print time.time()-t
prints
104743
0.569000005722 second
A pythonic Answer
import time
t=time.time()
def prime_bellow(n):
b=[]
num=2
j=0
b.append(2)
while len(b)-1<n:
if all(num%i!=0 for i in range(2,int((num)**0.5)+1)):
b.append(num)
num += 1
print b[n]
prime_bellow(10001)
print time.time()-t
Prints
104743
0.702000141144 second
import math
count = 0 <br/> def is_prime(n):
if n % 2 == 0 and n > 2:
return False
for i in range(3, int(math.sqrt(n)) + 1, 2):
if n % i == 0:
return False
return True
for i in range(2,2000000):
if is_prime(i):
count += 1
if count == 10001:
print i
break
I approached it a different way. We know that all multiples of 2 are not going to be prime (except 2) we also know that all non-prime numbers can be broken down to prime constituents.
i.e.
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 3 x 2
Therefore I iterated through a list of odd numbers, accumulating a list of primes, and only attempting to find the modulus of the odd numbers with primes in this list.
#First I create a helper method to determine if it's a prime that
#iterates through the list of primes I already have
def is_prime(number, list):
for prime in list:
if number % prime == 0:
return False
return True
EDIT: Originally I wrote this recursively, but I think the iterative case is much simpler
def find_10001st_iteratively():
number_of_primes = 0
current_number = 3
list_of_primes = [2]
while number_of_primes <= 10001:
if is_prime(current_number, list_of_primes):
list_of_primes.append(current_number)
number_of_primes += 1
current_number += 2
return current_number
A different quick Python solution:
import math
prime_number = 4 # Because 2 and 3 are already prime numbers
k = 3 # It is the 3rd try after 2 and 3 prime numbers
milestone = 10001
while k <= milestone:
divisible = 0
for i in range(2, int(math.sqrt(prime_number)) + 1):
remainder = prime_number % i
if remainder == 0: #Check if the number is evenly divisible (not prime) by i
divisible += 1
if divisible == 0:
k += 1
prime_number += 1
print(prime_number-1)
import time
t = time.time()
def is_prime(n): #check primes
prime = True
for i in range(2, int(n**0.5)+1):
if n % i == 0:
prime = False
break
return prime
def number_of_primes(n):
prime_list = []
counter = 0
num = 2
prime_list.append(2)
while counter != n:
if is_prime(num):
prime_list.append(num)
counter += 1
num += 1
return prime_list[n]
print(number_of_primes(10001))
print(time.time()-t)
104743
0.6159017086029053
based on the haskell code in the paper: The Genuine Sieve of Eratosthenes by Melissa E. O'Neill
from itertools import cycle, chain, tee, islice
wheel2357 = [2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10]
def spin(wheel, n):
for x in wheel:
yield n
n = n + x
import heapq
def insertprime(p,xs,t):
heapq.heappush(t,(p*p,(p*v for v in xs)))
def adjust(t,x):
while True:
n, ns = t[0]
if n <= x:
n, ns = heapq.heappop(t)
heapq.heappush(t, (ns.next(), ns))
else:
break
def sieve(it):
t = []
x = it.next()
yield x
xs0, xs1 = tee(it)
insertprime(x,xs1,t)
it = xs0
while True:
x = it.next()
if t[0][0] <= x:
adjust(t,x)
continue
yield x
xs0, xs1 = tee(it)
insertprime(x,xs1,t)
it = xs0
primes = chain([2,3,5,7], sieve(spin(cycle(wheel2357), 11)))
from time import time
s = time()
print list(islice(primes, 10000, 10001))
e = time()
print "%.8f seconds" % (e-s)
prints:
[104743]
0.18839407 seconds
from itertools import islice
from heapq import heappush, heappop
wheel2357 = [2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,
4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10]
class spin(object):
__slots__ = ('wheel','o','n','m')
def __init__(self, wheel, n, o=0, m=1):
self.wheel = wheel
self.o = o
self.n = n
self.m = m
def __iter__(self):
return self
def next(self):
v = self.m*self.n
self.n += self.wheel[self.o]
self.o = (self.o + 1) % len(self.wheel)
return v
def copy(self):
return spin(self.wheel, self.n, self.o, self.m)
def times(self, x):
return spin(self.wheel, self.n, self.o, self.m*x)
def adjust(t,x):
while t[0][0] <= x:
n, ns = heappop(t)
heappush(t, (ns.next(), ns))
def sieve_primes():
for p in [2,3,5,7]:
yield p
it = spin(wheel2357, 11)
t = []
p = it.next()
yield p
heappush(t, (p*p, it.times(p)))
while True:
p = it.next()
if t[0][0] <= p:
adjust(t,p)
continue
yield p
heappush(t, (p*p, it.times(p)))
from time import time
s = time()
print list(islice(sieve_primes(), 10000, 10001))[-1]
e = time()
print "%.8f seconds" % (e-s)
prints:
104743
0.22022200 seconds
import time
from math import sqrt
wheel2357 = [2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10]
list_prime = [2,3,5,7]
def isprime(num):
limit = sqrt(num)
for prime in list_prime:
if num % prime == 0: return 0
if prime > limit: break
return 1
def generate_primes(no_of_primes):
o = 0
n = 11
w = wheel2357
l = len(w)
while len(list_prime) < no_of_primes:
i = n
n = n + w[o]
o = (o + 1) % l
if isprime(i):
list_prime.append(i)
t0 = time.time()
generate_primes(10001)
print list_prime[-1] # 104743
t1 = time.time()
print t1-t0 # 0.18 seconds
prints:
104743
0.307313919067

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