A Python code of a program that reads an integer, and prints the integer is a multiple of either 2 or 5 but not both.
First off, SO is not a forum to ask people to solve your homework without first putting effort yourself. you could have written a simple naive solution with if-else statements and posted that in your question, asking for a better way to do this.
That being said, I'm still adding my approach because I think you should know that a beautiful and simple way would be to just use an XOR check:
n = int(input("Input a number: "))
answer = True if (n % 2 == 0) != (n % 5 == 0) else False
print(answer)
I'm assuming the user will always input a value that can be cast as an integer. You can take care of the error handling process. Once the number has been read, I do a simple XOR check to return True if the number is only divisible by either 2 or 5 but not both, and False in all other cases. This works because bool(a)!=bool(b) gives True only when bool(a) and bool(b) evaluate to different things.
Demonstration:
def check(n):
return (n%2 == 0) != (n%5 ==0)
print(check(2)) # Out: True
print(check(5)) # Out: True
print(check(10)) # Out: False
print(check(3)) # Out: False
sum = 2
x=3
y=5000
for i in range (x,y):
for j in range (2,i):
if i%j==0:
break
elif i%j!=0 and j==i-1:
sum += i
if i==y-1 and y<2000000:
x=y
y+=5000
else:
continue
print(sum)
**I am not getting what is wrong in this code. By running this I came to know that the Last If and Else statement are not running **
Given your code, there are a couple of things wrong. First, sum is a python function name and should never be used as a variable name. It will get you into trouble in more ways than I care to think about. Second, the last else statement is not needed, because whether the if clause above it is or is not executed executed, the for loop will be executed again. Third, I don't understand the purpose of y and the magical value 5000, unless you are trying to provide an end value for your loop. The problem with this approach is you seem to try and extend it's range in increments of 5000. The problem is that once the initial for loop is executed, it creates a local iterable from x to 5000, and subsequent changes to y do not affect the for loops range.
I would approach the problem differently, by creating a list of primes and then use the python sum method to add all the values. Here is the code:
def sum_primes(max_prime):
""" Return Sum of primes Less than max_prime"""
primes = [2]
indx_num = 3
while primes[-1] <= max_prime:
update = True
for prime in primes:
if indx_num == prime or indx_num % prime == 0:
update = False
break
if update:
primes.append(indx_num)
indx_num += 2
#return summ of all values except the last
return sum(primes[:-1])
Executing sum_primes(2000000)
yields 1709600813
I have a question in regard to time complexity (big-O) in Python. I want to understand the general method I would need to implement when trying to find the big-O of a complex algorithm. I have understood the reasoning behind calculating the time complexity of simple algorithms, such as a for loop iterating over a list of n elements having a O(n), or having two nested for loops each iterating over 2 lists of n elements each having a big-O of n**2. But, for more complex algorithms that implement multiple if-elif-else statements coupled with for loops, I would want to see if there is a strategy to, simply based on the code, in an iterative fashion, to determine the big-O of my code using simple heuristics (such as, ignoring constant time complexity if statements or always squaring the n upon going over a for loop, or doing something specific when encountering an else statement).
I have created a battleship game, for which I would like to find the time complexity, using such an aforementioned strategy.
from random import randint
class Battle:
def __init__(self):
self.my_grid = [[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False],[False,False,False,False,False,False,False,False,False,False]]
def putting_ship(self,x,y):
breaker = False
while breaker == False:
r1=x
r2=y
element = self.my_grid[r1][r2]
if element == True:
continue
else:
self.my_grid[r1][r2] = True
break
def printing_grid(self):
return self.my_grid
def striking(self,r1,r2):
element = self.my_grid[r1][r2]
if element == True:
print("STRIKE!")
self.my_grid[r1][r2] = False
return True
elif element == False:
print("Miss")
return False
def game():
battle_1 = Battle()
battle_2 = Battle()
score_player1 = 0
score_player2 = 0
turns = 5
counter_ships = 2
while True:
input_x_player_1 = input("give x coordinate for the ship, player 1\n")
input_y_player_1 = input("give y coordinate for the ship, player 1\n")
battle_1.putting_ship(int(input_x_player_1),int(input_y_player_1))
input_x_player_2 = randint(0,9)
input_y_player_2 = randint(0,9)
battle_2.putting_ship(int(input_x_player_2),int(input_y_player_2))
counter_ships -= 1
if counter_ships == 0:
break
while True:
input_x_player_1 = input("give x coordinate for the ship\n")
input_y_player_1 = input("give y coordinate for the ship\n")
my_var = battle_1.striking(int(input_x_player_1),int(input_y_player_1))
if my_var == True:
score_player1 += 1
print(score_player1)
input_x_player_2 = randint(0,9)
input_y_player_2 = randint(0,9)
my_var_2 = battle_2.striking(int(input_x_player_2),int(input_y_player_2))
if my_var_2 == True:
score_player2 += 1
print(score_player2)
counter_ships -= 1
if counter_ships == 0:
break
print("the score for player 1 is",score_player1)
print("the score for player 2 is",score_player2)
print(game())
If it's just nested for loops and if/else statements, you can take the approach ibonyun has suggested - assume all if/else cases are covered and look at the deepest loops (being aware that some operations like sorting, or copying an array, might hide loops of their own.)
However, your code also has while loops. In this particular example it's not too hard to replace them with fors, but for code containing nontrivial whiles there is no general strategy that will always give you the complexity - this is a consequence of the halting problem.
For example:
def collatz(n):
n = int(abs(n))
steps = 0
while n != 1:
if n%2 == 1:
n=3*n+1
else:
n=n//2
steps += 1
print(n)
print("Finished in",steps,"steps!")
So far nobody has been able to prove that this will even finish for all n, let alone shown an upper bound to the run-time.
Side note: instead of the screen-breaking
self.my_grid = [[False,False,...False],[False,False,...,False],...,[False,False,...False]]
consider something like:
grid_size = 10
self.my_grid = [[False for i in range(grid_size)] for j in range(grid_size)]
which is easier to read and check.
Empirical:
You could do some time trials while increasing n (so maybe increasing the board size?) and plot the resulting data. You could tell by the curve/slope of the line what the time complexity is.
Theoretical:
Parse the script and keep track of the biggest O() you find for any given line or function call. Any sorting operations will give you nlogn. A for loop inside a for loop will give you n^2 (assuming their both iterating over the input data), etc. Time complexity is about the broad strokes. O(n) and O(n*3) are both linear time, and that's what really matters. I don't think you need to worry about the minutia of all your if-elif-else logic. Maybe just focus on worst case scenario?
In this kata you need to build a function to return either true/True or false/False if a string can be seen as the repetition of a simpler/shorter subpattern or not.
For example:
has_subpattern("a") == False #no repeated pattern
has_subpattern("aaaa") == True #created repeating "a"
has_subpattern("abcd") == False #no repeated pattern
has_subpattern("abababab") == True #created repeating "ab"
has_subpattern("ababababa") == False #cannot be entirely reproduced repeating a pattern
Strings will never be empty and can be composed of any character (just consider upper- and lowercase letters as different entities) and can be pretty long (keep an eye on performances!).
My solution is:
def has_subpattern(string):
string_size = len(string)
for i in range(1, string_size):
slice1 = string[:i]
appearence_count = string.count(slice1)
slice1_len = len(slice1)
if appearence_count > 0:
if appearence_count * slice1_len == string_size:
return True
return False
Obviously there are weak and too slow things like slice1 = string[:i] and string.count() in loop..
Is there better ways to solve an issue or ways to improve performance ?
Short regex approach:
import re
def has_subpattern_re(s):
return bool(re.search(r'^(\w+)\1+$', s))
It'll provide a close (to initial has_subpattern approach) performance on small strings:
import timeit
...
print(timeit.timeit('has_subpattern("abababab")', 'from __main__ import has_subpattern'))
0.7413144190068124
print(timeit.timeit('has_subpattern_re("abababab")', 'from __main__ import re, has_subpattern_re'))
0.856149295999785
But, a significant performance increase (in about 3-5 times faster) on long strings:
print(timeit.timeit('has_subpattern("ababababababababababababababababababababababababa")', 'from __main__ import has_subpattern'))
14.669428467008402
print(timeit.timeit('has_subpattern_re("ababababababababababababababababababababababababa")', 'from __main__ import re, has_subpattern_re'))
4.308312018998549
And one more test for a more longer string:
print(timeit.timeit('has_subpattern("ababababababababababababababababababababababababaababababababababababababababababababababababababab")', 'from __main__ import has_subpattern'))
35.998031173992786
print(timeit.timeit('has_subpattern_re("ababababababababababababababababababababababababaababababababababababababababababababababababababab")', 'from __main__ import re, has_subpattern_re'))
7.010367843002314
Within standard Python, the bottlenecks here will be count, which enjoys C speed implementation and the looping.
The looping itself may be hard to speed-up (althogh Cython may be of some help).
Hence, the most important optimization is to reduce the number of loopings.
One obvious way is to let range() do not exceed half the size of the input (+ 2: + 1 for rounding issues, + 1 for end extrema exclusion in range()):
Also, string is a standard Python module, so better not use it as a variable name.
def has_subpattern_loop(text):
for i in range(1, len(text) // 2 + 2):
subtext = text[:i]
num_subtext = text.count(subtext)
if num_subtext > 1 and num_subtext * len(subtext) == len(text):
return True
return False
A much more effective way of restricting the number of calls to count is to skip computation when i is not a multiple of the length of the input.
def has_subpattern_loop2(text):
for i in range(1, len(text) // 2 + 2):
if len(text) % i == 0:
subtext = text[:i]
num_subtext = text.count(subtext)
if num_subtext > 1 and num_subtext * len(subtext) == len(text):
return True
return False
Even better would be to generate only the divisors of the length of the input.
This could be done using sympy and the approach outlined here:
import sympy as sym
import functools
def get_divisors(n):
if n == 1:
yield 1
return
factors = list(sym.factor_.factorint(n).items())
nfactors = len(factors)
f = [0] * nfactors
while True:
yield functools.reduce(lambda x, y: x * y, [factors[x][0]**f[x] for x in range(nfactors)], 1)
i = 0
while True:
f[i] += 1
if f[i] <= factors[i][1]:
break
f[i] = 0
i += 1
if i >= nfactors:
return
def has_subpattern_divs(text):
for i in get_divisors(len(text)):
subtext = text[:i]
num_subtext = text.count(subtext)
if num_subtext > 1 and num_subtext * len(subtext) == len(text):
return True
return False
A completely different approach is the one proposed in #ВладДавидченко answer:
def has_subpattern_find(text):
return (text * 2).find(text, 1) != len(text)
or the more memory efficient (requires ~50% less additional memory compared to has_subpattern_find2()):
def has_subpattern_find2(text):
return (text + text[:len(text) // 2 + 2]).find(text, 1) > 0
and it is based on the idea that if there is a exactly self-repeating string, the string itself must be found in a circularly extended string:
Input: abab
Extension1: abababab
Found1: |-abab
Extension2: ababab
Found2: |-abab
Input: ababa
Extension1: ababaababa
Found1: |----ababa
Extension2: ababab
Found2: NOT FOUND!
The find-based method are the fastest, with has_subpattern_find() being fastest in the small input size regime, and has_subpattern_find2() gets generally faster in the intermediate and large input size regime (especially in the False case).
For shorter inputs, the direct looping approaches (especially has_subpattern_loop2()) are fastest, closely followed (but sometimes surpassed by has_subpattern_re()), but as soon as the input gets bigger (and especially for the False outcome), the has_subpattern_divs() method gets to be the fastest (aside of find-based ones) by far and large, as shown by the following benchmarks.
For the True outcome, has_subpattern_loop2() gets to be the fastest due to the very small number of loops required, which is independent of the input size.
The input is generated as a function of n using:
def gen_input(n, m=0):
g = string.ascii_lowercase
if not m:
m = n
offset = '!' if n % 2 else ''
return g[:n] * (m // min(n, len(g)) + 2) + offset
so that if n is even, the has_subpattern*() always return True and the opposite for odd n.
Note that, in general, the has_subpattern() function will depend not only on the raw size of the input but also on the length of the repeating string, if any. This is not explored in the benchmarks, except for the odd/even separation.
Even Inputs
Odd Inputs
(Full code available here).
(EDITED to include some more solutions as well as comparison with regex-based solution from #RomanPerekhrest)
(EDITED to include some more solutions based on the find from #ВладДавидченко)
Found another one solution, probably will be useful:
def has_subpattern(string):
return (string * 2).find(string, 1) != len(string)
I need to reach 1,000,000 and for some reason it doesn't give me the output for 1,000,000, I don't know what i am doing wrong. Every time i put a small number like 500 it would give me the correct output but as soon as i put 999,999 or 1,000,000 it just doesn't give out any output and when i do a keyboard interruption it says it stopped at break but I need that break in order for the values to only repeat once.
bachslst=[]
primeslst=[]
q=[]
newlst=[]
z=[]
def goldbach(limit):
primes = dict()
for i in range(2, limit+1):
primes[i] = True
for i in primes:
factors = range(i, limit+1, i)
for f in factors[1:]:
primes[f] = False
for i in primes:
if primes[i]==True:
z.append(i)
for num in range(4,limit+1,2):
for k in range(len(z)):
for j in z:
if (k + j ) == num :
x=(str(k),str(j))
q.append(x)
newlst.append([x,[num]])
break
bachslst.append(num)
print(bachslst,'\n')
return newlst
The break that is referred to is not the break in the code, it is the break caused by the keyboard interrupt.
If you want to get your result in less than 1.5 hours, try to reduce the amount of computing that you are doing. There are many implementations for testing the Goldbach Conjecture if you do a search. Some are in other languages, but you can still use them to influence your algorithm.
I have not looked at it, but here is another implementation in Python: https://codereview.stackexchange.com/questions/99161/function-to-find-two-prime-numbers-that-sum-up-to-a-given-even-number