Python homework regarding prime numbers - python

My homework is simple, declare a function named printPrimeNumbersTo with a single argument named to
I created the skeleton of the code itself, however, I needed some help from the net.
GeeksforGeeks was the site where I "borrowed" a line of code, which I don't completely understand. (Site: https://www.geeksforgeeks.org/python-program-to-print-all-prime-numbers-in-an-interval/)
My code looks like this (I have comments on nearly every line, describing what I think that the line of code does):
def printPrimeNumbersTo(to):
x = 0
prime_list = [] # This was a string, however, I changed it to a list so I won't have to convert the numbers to a string every time I wanted to append it to the list
for i in range(x, to + 1): # Create a for loop, using the function range an starting the loop at number 0. Add 1 to 'to', because range excludes the end integer
if i == 0 or i == 1:
continue
else:
for j in range(2, i // 2 + 1): # <--
if i % j == 0: # If 'j' is divided by any number in the list and remainder is 0, then the number is not a prime number, which means I can break the loop
break
else:
prime_list.append(i) # Append the prime number to the list
return str(prime_list)[1:-1] # Returns '[2,3,5,7..]', I use the square brackets the get rid of the brackets themselves
print(printPrimeNumbersTo(7)) # >>> 2, 3, 5, 7
The one line I don't understand is marked with an arrow, it's the 8th line of the code.
Why am I dividing the number by 2? And then making it an integer? When I do the calculations, it works, but... where is the logic? Anybody help?

The biggest number which could possibly be an even factor of a number is the half of that number. The integer division operator // produces this number as an integer.
Because of how range works, the ending index needs to be the desired number plus one.

There are two points to note:
the code needs to be indented correctly, in Python indentation matters as it forms the code blocks.
aside from this and specifically adressing the question: the range function that you refer to requires integers otherwise it would throw an typeerror like this: 'float' object cannot be interpreted as an integer .
# this will throw an error
for i in range(1, 10.5):
print(i)
# this will work
for i in range(1, 10):
print(i)
So the reason why the line of code you queried was written like that was to ensure that the upper bound of the range was an integer.
You should also note that the // has a meaning, for example try this:
x = 5//2
print(x)
y = 5/2
print(y)
x is the integer part only (x=2)
y is the full number (y=2.5)
In terms of implementaiton, there are a number of methods that would be better (suggested here):
Print series of prime numbers in python

Dividing the number by 2 is done to reduce the number of iterations. For example, the number 12 you can divide it without a remainder by 1,2,3,4,6. Notice that there is no number bigger than (6) which is 12 / 2. And this goes on with all of the numbers.
16 ---> 1,2,8 no number bigger than its half (8)

Related

How do I write an iterative function that computes the sum of the first n odd numbers it returns 1 + 3 + .... + (2n - 1), using a for loop?

Assuming that n is a positive integer
this is my code:
def sum_odd_n(n):
x =1
for x in range(n):
if x%2==1:
continue
return x + 2
but when I run it on Python it gives me the answer 2. Could you help me by telling me what's wrong and what I should do to solve this?
Since you want to find the sum of first 'n' odd numbers, I suggest you to use range function with step=2. I'll elaborate:
def sum_n(n):
addition=0
for x in range(1,2*n,2):
addition+=x
return addition
s=sum_n(5)
print(s)
This gives output as: 25
Here, in range function, 1st attribute provides starting point, 2nd attribute provides the end point, and 3rd attribute gives the Difference between each number in the sequence.
I hope this helps.
There are a few problems with your code.
The first is that you have a return statement inside the for loop.
Secondly, you just visit the first n integers and check which of them are odd. You won't visit all the first n odd integers.
A list comprehension solution solution is as follows.
def sum_odd_n(n):
# sum up the first n odd numbers
return sum([2*i + 1 for i in range(n)])
Check this program it will work:
a=int(input("how many first odd number sum you want"))
x=1
i=0
def OddSum():
global i
global x
while i<=a:
x+=2
i+=1
print(x)
OddSum()

Counting how many times I used one equation until it reaches a specific result in python

import math
#entrada
x=int(input("Put a number here:"))
#processo
num1=int(math.sqrt(x))
num2=round(num1,0)
num3=num2**2
remaining=x-num3
#saída
print("The remaining is:",remaining)
I made this code to get the remaining of a perfect square, for any "int" number, now I want to improve on this code so it keeps doing the equation using the last answer(stored in "remaining")is "0"(and stop calculating after that).
And then, after it finishes calculating, I want to count how many times I used the equation until it reaches "0"
I know this is hard to understand put ill try with one example:
For the number 87, the remaining will be 6 in this code because 87-(9²)=6, I want to use this result(6)and make the same equation and then the result will be (2) because 6-(2²)=2, then doing it again (1), then stop once it returns (0).
After that, I want to count how many times the equation was used to reach (0), in this example, it would be 4 (87 6)(6 2)(2 1)(1 0). And I want to print that counting...in this case(4)
I know it is a lot to ask to help me in this(it's a big request), but I'm just staring programming now(10 days ago)and I couldn't find what I wanted anywhere else in the internet. Thanks for the help. Also, if there is any way to make mine original code better tell me please.
I think you need something like this:
def count_squares(x):
count = 0
remaining = 1
while remaining:
min_square = (int(x**0.5) // 1) **2
remaining = x - min_square
count +=1
print('X = {}, remaining = {}, count = {}'.format(x, remaining, count))
x = remaining
return count
print(count_squares(87))
Explaining:
** operator — for exponentiation.
// operator — for floor division. In this case it is similiar to "int" and "round" bound, that you used for calculating num2, because "//1" will throw away all digits after dot. By the way int() function is not necessary in this case at all.
we will exit from while loop as soon as remaining value will be equal to zero, because zero integer value is interpreted as false.
format is method of strings used to do formatting(surprisingly). All {} will be filled with arguments passed to the "format" method. There are other ways to do formatting in python( % operator, and formatted strings).
Output is:
X = 87, remaining = 6, Count = 1
X = 6, remaining = 2, Count = 2
X = 2, remaining = 1, Count = 3
X = 1, remaining = 0, Count = 4
4

I need help finding a smart solution to shorten the time this code runs

2 days ago i started practicing python 2.7 on Codewars.com and i came across a really interesting problem, the only thing is i think it's a bit too much for my level of python knowledge. I actually did solve it in the end but the site doesn't accept my solution because it takes too much time to complete when you call it with large numbers, so here is the code:
from itertools import permutations
def next_bigger(n):
digz =list(str(n))
nums =permutations(digz, len(digz))
nums2 = []
for i in nums:
z =''
for b in range(0,len(i)):
z += i[b]
nums2.append(int(z))
nums2 = list(set(nums2))
nums2.sort()
try:
return nums2[nums2.index(n)+1]
except:
return -1
"You have to create a function that takes a positive integer number and returns the next bigger number formed by the same digits" - These were the original instructions
Also, at one point i decided to forgo the whole permutations idea, and in the middle of this second attempt i realized that there's no way it would work:
def next_bigger(n):
for i in range (1,11):
c1 = n % (10**i) / (10**(i-1))
c2 = n % (10**(i+1)) / (10**i)
if c1 > c2:
return ((n /(10**(i+1)))*10**(i+1)) + c1 *(10**i) + c2*(10**(i-1)) + n % (10**(max((i-1),0)))
break
if anybody has any ideas, i'm all-ears and if you hate my code, please do tell, because i really want to get better at this.
stolen from http://www.geeksforgeeks.org/find-next-greater-number-set-digits/
Following are few observations about the next greater number.
1) If all digits sorted in descending order, then output is always “Not Possible”. For example, 4321.
2) If all digits are sorted in ascending
order, then we need to swap last two digits. For example, 1234.
3) For
other cases, we need to process the number from rightmost side (why?
because we need to find the smallest of all greater numbers)
You can now try developing an algorithm yourself.
Following is the algorithm for finding the next greater number.
I)
Traverse the given number from rightmost digit, keep traversing till
you find a digit which is smaller than the previously traversed digit.
For example, if the input number is “534976”, we stop at 4 because 4
is smaller than next digit 9. If we do not find such a digit, then
output is “Not Possible”.
II) Now search the right side of above found digit ‘d’ for the
smallest digit greater than ‘d’. For “534976″, the right side of 4
contains “976”. The smallest digit greater than 4 is 6.
III) Swap the above found two digits, we get 536974 in above example.
IV) Now sort all digits from position next to ‘d’ to the end of
number. The number that we get after sorting is the output. For above
example, we sort digits in bold 536974. We get “536479” which is the
next greater number for input 534976.
"formed by the same digits" - there's a clue that you have to break the number into digits: n = list(str(n))
"next bigger". The fact that they want the very next item means that you want to make the least change. Focus on changing the 1s digit. If that doesn't work, try the 10's digit, then the 100's, etc. The smallest change you can make is to exchange two furthest digits to the right that will increase the value of the integer. I.e. exchange the two right-most digits in which the more right-most is bigger.
def next_bigger(n):
n = list(str(n))
for i in range(len(n)-1, -1, -1):
for j in range(i-1, -1, -1):
if n[i] > n[j]:
n[i], n[j] = n[j], n[i]
return int("".join(n))
print next_bigger(123)
Oops. This fails for next_bigger(1675). I'll leave the buggy code here for a while, for whatever it is worth.
How about this? See in-line comments for explanations. Note that the way this is set up, you don't end up with any significant memory use (we're not storing any lists).
from itertools import permutations
#!/usr/bin/python3
def next_bigger(n):
# set next_bigger to an arbitrarily large value to start: see the for-loop
next_bigger = float('inf')
# this returns a generator for all the integers that are permutations of n
# we want a generator because when the potential number of permutations is
# large, we don't want to store all of them in memory.
perms = map(lambda x: int(''.join(x)), permutations(str(n)))
for p in perms:
if (p > n) and (p <= next_bigger):
# we can find the next-largest permutation by going through all the
# permutations, selecting the ones that are larger than n, and then
# selecting the smallest from them.
next_bigger = p
return next_bigger
Note that this is still a brute-force algorithm, even if implemented for speed. Here is an example result:
time python3 next_bigger.py 3838998888
3839888889
real 0m2.475s
user 0m2.476s
sys 0m0.000s
If your code needs to be faster yet, then you'll need a smarter, non-brute-force algorithm.
You don't need to look at all the permutations. Take a look at the two permutations of the last two digits. If you have an integer greater than your integer, that's it. If not, take a look at the permutations of the last three digits, etc.
from itertools import permutations
def next_bigger(number):
check = 2
found = False
digits = list(str(number))
if sorted(digits, reverse=True) == digits:
raise ValueError("No larger number")
while not found:
options = permutations(digits[-1*check:], check)
candidates = list()
for option in options:
new = digits.copy()[:-1*check]
new.extend(option)
candidate = int(''.join(new))
if candidate > number:
candidates.append(candidate)
if candidates:
result = sorted(candidates)[0]
found = True
return result
check += 1

Writing a Python program that finds the square of a number without using multiplication or exponents?

thank you for reading and hopefully responding to my question. I'm stuck trying to write this Python program that finds a number's square without using multiplication or exponents. Instead, I have to get the summation of the first odd n numbers starting from 1. This is what I have so far:
def square():
print("This program calculates the square of a given number")
print("WITHOUT using multiplication! ")
odd = 1
n = eval(input("Enter a number: "))
for odd in range(0, n + 1, 2):
odd = odd + 2
final_square = n + odd
print(n, "squared is", final_square, ".")
EDIT: Hi guys, I can't do 4 + 4 + 4 + 4. I have to do 1 + 3 + 5 + 7, and I'm not sure how. It gives me 4 squared is 11 or something.
Just some tips:
Try not to use eval(), it will evaluate any input given and so it can do something you don't want to do. Instead, use int().
Remember that, say 4*4, is just 4 + 4 + 4 + 4. You're on the right track with a for-loop, but now make the loop iterate n times adding n to itself.
new = 0
for _ in range(n):
new += n
Note that this won't work with negative numbers. If you're going to be dealing with those, perhaps get the absolute value of n at the beginning:
def square(n):
n = abs(n)
....
Since you have been told you have to get the answer by producing the first n odd numbers, then you need to think about how to do that - certainly your loop isn't doing that :
several issues :
you do odd =1, and then use odd in your for loop, the two can't co-exist, so the initial value of odd = 1 is overwritten.
Your loop doesn't produce the first n odd numbers that I can see.
My suggest would be to rework your loop : the first 'n' odd numbers are in the form :
1, 3, 5, ... n*2-1
(Counting from 1 not from zero)
so a loop like this :
final = 0
for c in range(1, n+1): #start counting from 1 to do 1 to n+1
odd = c*2 -1 #Use the series above to generate each odd number.
final += odd
should work
a much more 'pythonic' way to do this is :
final = sum(c*2-1 for c in range(1,n))
This uses a generator to create all of the odd numbers (the equivalent of the loop), and sum the values as they get created.
Go back to the original definition of multiplication.
Just add the number n to itself n times. What's so hard? It's inefficient has hell, but it'll work.
I'm sure there's a more Pythonic way:
def square(n):
sum = 0
for i in range(0,n):
sum = sum + n
return sum

Debugging IndexError: Trivial sum generation problem

I can't wrap my head around what's causing the index error here, not exactly looking for a quick fix. Let me know however if my code repulses you/is incredibly ineffectual. The goal is to generate palindromes produced by the product of two four digit numbers.
Code:
for x in range(10000):
for y in range(10000):
product = str(x*y)
lengthprod = len(str(product))
for digit in range(lengthprod+1):
if (product[digit]==product[lengthprod-digit]):
print x,"x",y,"=",product
Traceback:
Traceback (most recent call last):
File "<pyshell#31>", line 6, in <module>
if (product[digit]==product[lengthprod-digit]):
IndexError: string index out of range
Converting a number to a string is generally a slow operation, since there are many possibilities in general (integers, floating point, scientific notation, maybe something exotic like fractions or imaginary numbers, not to mention things like handling leading zero or overwidth numbers or rounding to two decimal places). Thus, it is often a better approach for checking if a positive integer is a palindrome to reverse the digits numerically by repeatedly taking the input modulo 10 to extract the last digit, adding the digit to an accumulator that is multiplied by 10 at each step, then dividing the input number by 10 before looping. I don't speak Python, so here is my Scheme program to reverse a number:
(define (rev n)
(let loop ((n n) (r 0))
(if (zero? n) r
(loop (quotient n 10)
(+ (* r 10) (modulo n 10))))))
Then you can check if the number is a palindrome by checking if the input number equals its reversal.
Edit: Here it is in Python:
def rev(n):
r = 0
while n > 0:
r = r * 10 + n % 10
n = n // 10
return r
You iterate over values 0...lengthprod , but the legal subscripts for product are 0...lengthprod-1.
The last index is out of bounds. It references an element that is one byte beyond the end of the string.
Two changes:
1: range(0, lengthprod+1) should be range(0, lengthprod)
See documentation on range()
2: product[lengthprod-digit] should be product[lengthprod-digit-1]
Off by one error since lengthprod is a length (1 based) and digit is an index (0 based).
Note, this will only give you valid "single digit" palindromes, but gets you past the index out of range error.
Your code repulses me!
(Sorry, I wouldn't normally be so rude, but since you asked for it... ;)
Use xrange rather than range for long loops like this.
Start the range from 1 rather than 0 unless you don't mind all the duplicated trivial results.
Since multiplication commutes, you might want to loop over a "triangle" rather than a "square" to avoid duplicates.
Your variable name product shadows a function from numeric core.
The question says you're interested in the "product of two four digit numbers", but your code has no such restrictions on the number of digits in the numbers. If you want the four digit numbers as input, just start your xrange(start, stop) from 1000.
Since your stated "goal is to generate palindromes", how about to try it with the correct tool for the job: generators!
def pairs(n):
for x in xrange(n):
for y in xrange(n):
yield (x,y)
pairs_generator = pairs(100)
filter(None, ['{x}*{y}={xy}'.format(x=x,y=y,xy=x*y) if str(x*y) == str(x*y)[::-1] else None for x,y in pairs_generator])
I kept my generator simple for clarity's purpose. I will leave it as an exercise for you to simply make a generator to spit out the palindromes. This will involve moving the logic which I have put in my list comprehension into the generator (or you could make a new palindrome_generator which uses a pairs_generator).
Have fun!

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