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!
Related
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)
I was recently trying to solve a HackerEarth problem. The code worked on the sample inputs and some custom inputs that I gave. But, when I submitted, it showed errors for exceeding the time limit. Can someone explain how I can make the code run faster?
Problem Statement: Cyclic shift
A large binary number is represented by a string A of size N and comprises of 0s and 1s. You must perform a cyclic shift on this string. The cyclic shift operation is defined as follows:
If the string A is [A0, A1,..., An-1], then after performing one cyclic shift, the string becomes [A1, A2,..., An-1, A0].
You performed the shift infinite number of times and each time you recorded the value of the binary number represented by the string. The maximum binary number formed after performing (possibly 0) the operation is B. Your task is to determine the number of cyclic shifts that can be performed such that the value represented by the string A will be equal to B for the Kth time.
Input format:
First line: A single integer T denoting the number of test cases
For each test case:
First line: Two space-separated integers N and K
Second line: A denoting the string
Output format:
For each test case, print a single line containing one integer that represents the number of cyclic shift operations performed such that the value represented by string A is equal to B for the Kth time.
Code:
import math
def value(s):
u = len(s)
d = 0
for h in range(u):
d = d + (int(s[u-1-h]) * math.pow(2, h))
return d
t = int(input())
for i in range(t):
x = list(map(int, input().split()))
n = x[0]
k = x[1]
a = input()
v = 0
for j in range(n):
a = a[1:] + a[0]
if value(a) > v:
b = a
v = value(a)
ctr = 0
cou = 0
while ctr < k:
a = a[1:] + a[0]
cou = cou + 1
if a == b:
ctr = ctr + 1
print(cou)
In the problem, the constraint on n is 0<=n<=1e5. In the function value(), you calculating integer from the binary string whose length can go up to 1e5. so the integer calculating by you can go as high as pow(2, 1e5). This surely impractical.
As mentioned by Prune, you must use some efficient algorithms for finding a subsequence, say sub1, whose repetitions make up the given string A. If you solve this by brute-force, the time complexity will be O(n*n), as maximum value of n is 1e5, time limit will exceed. so use some efficient algorithm.
I can't do much with the code you posted, since you obfuscated it with meaningless variables and a lack of explanation. When I scan it, I get the impression that you've made the straightforward approach of doing a single-digit shift in a long-running loop. You count iterations until you hit B for the Kth time.
This is easy to understand, but cumbersome and inefficient.
Since the cycle repeats every N iterations, you gain no new information from repeating that process. All you need to do is find where in the series of N iterations you encounter B ... which could be multiple times.
In order for B to appear multiple times, A must consist of a particular sub-sequence of bits, repeated 2 or more times. For instance, 101010 or 011011. You can detect this with a simple addition to your current algorithm: at each iteration, check to see whether the current string matches the original. The first time you hit this, simply compute the repetition factor as rep = len(a) / j. At this point, exit the shifting loop: the present value of b is the correct one.
Now that you have b and its position in the first j rotations, you can directly compute the needed result without further processing.
I expect that you can finish the algorithm and do the coding from here.
Ah -- taken as a requirements description, the wording of your problem suggests that B is a given. If not, then you need to detect the largest value.
To find B, append A to itself. Find the A-length string with the largest value. You can hasten this by finding the longest string of 1s, applying other well-known string-search algorithms for the value-trees after the first 0 following those largest strings.
Note that, while you iterate over A, you look for the first place in which you repeat the original value: this is the desired repetition length, which drives the direct-computation phase in the first part of my answer.
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
What I'm trying to figure out is when I run this code for smaller numbers it returns the list just fine, but for larger numbers (I would call this small in the context of what I'm working on.) like 29996299, it will run for a long time, I've waited for 45 minutes with no results and had to end up killing the program. What I was wondering was whether there was a more efficient way to handle numbers whose scale was larger than 4 or 5 digits. I've tested a few permutations of the range function to see if there was a better way to handle the limits of the list I want to produce but nothing seems to have any effect on the amount of time it takes to do the computation. I'm new to python and am not that experienced as a programmer. Thank you for your time.
ran the program again before submitting this post and it took an hour and a half or so.
function of the program is to take the User selected number, use it to generate a lower bound, find all primes between the bound and input and append to list, then generate a secound upper bound and find all primes and then append to list, to create a list that extends forwards and backwards from the initial number.
the program works like I expect it to but not as quickly as I need it to since the numbers I'm going to be dealing with are going to get large quickly, almost doubling at each phase.
initial_num = input("Please enter a number. ")
lower_1 = int(initial_num) - 1000
upper_1 = int(initial_num)
list_1 = []
for num in range(lower_1,upper_1):
if num > 1:
for i in range(2,num):
if (num % i) == 0:
break
else:
list_1.append(num)
lower_2 = list_1[-1]
upper_2 = list_1[-1] + 2000
list_2 = []
for num in range(lower_2,upper_2 +1):
if num > 1:
for i in range(2,num):
if (num % i) == 0:
break
else:
list_2.append(num)
list_3 = list_1 + list_2[1:]
print list_3
You can use a more efficient algorithm to generate the entire list of prime numbers up to N. This is the Sieve of Erathostenes. Please have a look at the linked article, it even includes an example pseudocode. The basic idea of the algorithm is:
maintain L, a list of potentially prime numbers (initially all numbers from 2 to N)
pick the next prime number (p) as the first element of L (intially 2)
remove all numbers that are a multiple of p, up to N, since they cannot be prime
repeat from step 2
At the end you are left with a list of prime numbers.
An implementation in Pyhton from here
def eratosthenes2(n):
multiples = set()
for i in range(2, n+1):
if i not in multiples:
yield i
multiples.update(range(i*i, n+1, i))
print(list(eratosthenes2(100)))
To reduce memory consumpution you could consider usgin a bitset, storing one bit for each number. That should reduce memory usage by between 32 - 64 times. A bitset implementation is available for python here.
I've got, what I think is a valid solution to problem 2 of Project Euler (finding all even numbers in the Fibonacci sequence up to 4,000,000). This works for lower numbers, but crashes when I run it with 4,000,000. I understand that this is computationally difficult, but shouldn't it just take a long time to compute rather than crash? Or is there an issue in my code?
import functools
def fib(limit):
sequence = []
for i in range(limit):
if(i < 3):
sequence.append(i)
else:
sequence.append(sequence[i-1] + sequence[i-2])
return sequence
def add_even(x, y):
if(y % 2 == 0):
return x + y
return x + 0
print(functools.reduce(add_even,fib(4000000)))
The problem is about getting the Fibonacci numbers that are smaller than 4000000. Your code tries to find the first 4000000 Fibonacci values instead. Since Fibonacci numbers grow exponentially, this will reach numbers too large to fit in memory.
You need to change your function to stop when the last calculated value is more than 4000000.
Another possible improvement is to add the numbers as you are calculating them instead of storing them in a list, but this won't be necessary if you stop at the appropriate time.