I'm working through this Kata and although I've looked through the solutions none are quite similar enough to mine to answer my question.
Problem Text: The number 89 is the first integer with more than one digit that fulfills the property partially introduced in the title of this kata. What's the use of saying "Eureka"? Because this sum gives the same number.
In effect: 89 = 8^1 + 9^2
The next number in having this property is 135.
See this property again: 135 = 1^1 + 3^2 + 5^3
We need a function to collect these numbers, that may receive two integers a, b that defines the range [a, b] (inclusive) and outputs a list of the sorted numbers in the range that fulfills the property described above.
def sum_dig_pow(a, b): # range(a, b + 1) will be studied by the function
# your code here
lst = []
n = 1
tot = 0
for i in range(a,b):
if i > 9:
spl = str(i).split()
for item in spl:
tot += int(item) ** n
n += 1
if tot == i:
lst.append(i)
else:
lst.append(i)
return lst
Tests are returning "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] should equal [1, 2, 3, 4, 5, 6, 7, 8, 9, 89]".
I cannot figure out why it's passing 10 and not appending 89. I'm sure there's a more efficient way to do this as well but I'm still learning so want to be working in basics of loops, conditionals,etc.
This line is incorrect:
spl = str(i).split()
The split method will split a string on spaces by default and return a list. So passing i=10 gives back spl = ['10'], a list with one element. Instead, just iterate over each of the digits in the string.
for item in str(i):
...
Follow up: you can shorten your code by using enumerate to count the index of each digit.
def sum_dig_pow(a,b):
return [sum(int(y)**(i+1) for i,y in enumerate(str(x))) for x in range(a,b)]
Rather than spending a lot of time converting things from numbers to strings and back, try using arithmetic. To iterate over the digits of a number n, take n modulo ten (to get the least-significant digit) and then divide by ten (to peel off that least-significant digit). For example, the digits of 123 (in reverse order) are [(123 % 10), (12 % 10), (1 % 10)]
Thinking of it in terms of functions, first get the digits:
def digits_of_n(n):
result = []
while n > 0:
result.append(n % 10)
n = n / 10 # in python 3, use 3 // 10 for integer division
return reversed(result) # reverse list to preserve original order
then get the sum of the powers:
def sum_of_ith_powers(numbers):
result = 0
for i, n in enumerate(numbers): # the digits are ordered most-significant to least, as we would expect
result += n ** 1
return result
now you can just call sum_of_ith_powers(digits_of_n(n)) and you have an answer. If you like, you can give that operation a name:
def sum_of_digit_powers(n):
return sum_of_ith_powers(digits_of_n(n))
and you can then name the function that solves the kata:
def solve_kata(a, b):
return [sum_of_digit_powers(n) for n in range (a, b)]
You can use a generator, sum and enumerate in order to simplify your code like this example:
def sum_dig_pow(a,b):
for k in range(a,b+1):
if k > 9:
number_sum = sum(int(j)**i for i,j in enumerate(str(k), 1))
if k is number_sum:
yield k
else:
yield k
print(list(sum_dig_pow(1,10)))
print(list(sum_dig_pow(1,90)))
print(list(sum_dig_pow(1,10000)))
print(list(sum_dig_pow(10,1000)))
print(list(sum_dig_pow(1,900000)))
Output:
[1, 2, 3, 4, 5, 6, 7, 8, 9]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 89]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175]
[89, 135, 175]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175]
li = []
def sum_dig_pow(a, b):
for i in range(a, b+1):
sum1 = 0
for ind, val in enumerate(str(i), 1):
sum1 += pow(int(val), int(ind))
if i == sum1:
li.append(i)
return li
print(sum_dig_pow(1, 11))
Related
I know there is an exhaustive solution that iterates through every single number, but how to implement the divide and conquer approach?
With an array of integers without repeated numbers, and a target product integer number, return a set of numbers that include all pairs that have the product equal to the target number.
def product_pair(num_arr, product):
"""
:type num_arr: List[int]
:type product: int
:rtype: List[int]
"""
Example 1. Product_pair([3, 5, 9, 10, 23, 53], 20) => []
Example 2. Product_pair([10, 2, 9, 30, 5, 1], 10) => [10, 2, 5, 1]
Well I'm not so sure about divide and conquer, but this will be rather efficient and quite simple:
def product_pair(num_arr, product):
value_set = set(num_arr)
sol = [n for n in num_arr if product/n in value_set]
return sol
You can do this as follows:
def f(lst, n):
lst = list(filter(lambda x: x<=n, lst)) # Note 3
res = []
seen = set()
for i, x in enumerate(lst[:-1]): # Note 4
if x in seen:
continue
rem = n / x
if rem in lst[i+1:]: # Note 1, 2
seen.add(rem)
res.extend([x, int(rem)])
return res
which for your examples, produces:
print(f([3, 5, 9, 10, 23, 53], 20)) # -> []
print(f([10, 2, 9, 30, 5, 1], 10)) # -> [10, 1, 2, 5]
Notes
Optimized membership test; you only look for membership in the slice of the list after the current element. If there was something before, you would have already found it.
I am assuming here that your list of candidates only contains integers.
You can filter out numbers that are bigger than the target number. Those are impossible to find an integer complementary to.
It follows from Note 1 that there cannot be anything you haven't found already when reaching the last number on the list.
General
Duplicates in original list: e.g., having two 4s would not return a (4, 4) result for a target number of 16.
This is definitely not the fastest one can do, but it is not too slow either.
Hey this is my first question so I hope I'm doing it right.
I'm trying to write a function that given a list of integers and N as the maximum occurrence, would then return a list with any integer above the maximum occurrence deleted. For example if I input:
[20,37,20,21] #list of integers and 1 #maximum occurrence.
Then as output I would get:
[20,37,21] because the number 20 appears twice and the maximum occurrence is 1, so it is deleted from the list. Here's another example:
Input: [1,1,3,3,7,2,2,2,2], 3
Output: [1,1,3,3,7,2,2,2]
Here's what I wrote so far, how would I be able to optimize it? I keep on getting a timeout error. Thank you very much in advance.
def delete_nth(order,n):
order = Counter(order)
for i in order:
if order[i] > n:
while order[i] > n:
order[i] - 1
return order
print(delete_nth([20,37,20,21], 1))
You can remove building the Counter at the beginning - and just have temporary dictionary as counter:
def delete_nth(order,n):
out, counter = [], {}
for v in order:
counter.setdefault(v, 0)
if counter[v] < n:
out.append(v)
counter[v] += 1
return out
print(delete_nth([20,37,20,21], 1))
Prints:
[20, 37, 21]
You wrote:
while order[i] > n:
order[i] - 1
That second line should presumably be order[i] -= 1, or any code that enters the loop will never leave it.
You could use a predicate with a default argument collections.defaultdict to retain state as your list of numbers is being filtered.
def delete_nth(numbers, n):
from collections import defaultdict
def predicate(number, seen=defaultdict(int)):
seen[number] += 1
return seen[number] <= n
return list(filter(predicate, numbers))
print(delete_nth([1, 1, 3, 3, 7, 2, 2, 2, 2], 3))
Output:
[1, 1, 3, 3, 7, 2, 2, 2]
>>>
I've renamed variables to something that had more meaning for me:
This version, though very short and fairly efficient, will output identical values adjacently:
from collections import Counter
def delete_nth(order, n):
counters = Counter(order)
output = []
for value in counters:
cnt = min(counters[value], n)
output.extend([value] * cnt)
return output
print(delete_nth([1,1,2,3,3,2,7,2,2,2,2], 3))
print(delete_nth([20,37,20,21], 1))
Prints:
[1, 1, 2, 2, 2, 3, 3, 7]
[20, 37, 21]
This version will maintain original order, but run a bit more slowly:
from collections import Counter
def delete_nth(order, n):
counters = Counter(order)
for value in counters:
counters[value] = min(counters[value], n)
output = []
for value in order:
if counters[value]:
output.append(value)
counters[value] -= 1
return output
print(delete_nth([1,1,2,3,3,2,7,2,2,2,2], 3))
print(delete_nth([20,37,20,21], 1))
Prints:
[1, 1, 2, 3, 3, 2, 7, 2]
[20, 37, 21]
I am iterating in a for loop, constructing a list, whilst comparing the last number of that list with another number.
I would like my code to see if the last item of the list is smaller than the item it is being compared to, and if it is, to add it to the end of its list and then to continue.
if the last item of the list is larger, i would like to pop off the last item of the list. i would then like to subject it to the same conditionals.
here is my code, it is not working, it wont re check the conditionals after popping off the last item of the list.
if tempList:
lastNum=tempList[-1]
#############################################
if element < lastNum:
incList.append(tempList)
tempList.pop()
lastNum=tempList[-1]
#############################################
elif lastNum < element:
tempList.append(element)
continue
You can bundle this into a function:
def append_if_lower_else_pop_end_from_list_until_lower(l, num):
"""Add num to l if l[-1] < num, else pop() from l until"""
while l and l[-1] > num:
l.pop()
l.append(num)
# this is not strictly needed - lists are mutable so you are mutating it
# returning it would only make sense for chaining off it with other methods
return l
k = [3,5,7,9,11,13]
print(k)
append_if_lower_else_pop_end_from_list_until_lower(k, 10)
print(k)
append_if_lower_else_pop_end_from_list_until_lower(k, 6)
print(k)
append_if_lower_else_pop_end_from_list_until_lower(k, 10)
print(k)
append_if_lower_else_pop_end_from_list_until_lower(k, 10)
print(k)
append_if_lower_else_pop_end_from_list_until_lower(k, -10)
print(k)
Output:
[3, 5, 7, 9, 11, 13] # start
[3, 5, 7, 9, 10] # after adding 10
[3, 5, 6] # after addding 6
[3, 5, 6, 10] # after adding 10
[3, 5, 6, 10, 10] # after adding 10 again
[-10] # after adding -10
Why return the list as well: example for chaining:
k = [3,5,17,9,11,13]
append_if_lower_else_pop_end_from_list_until_lower(k, 10).sort()
print(k)
Output:
[3, 5, 9, 10, 17]
Try this out:
yourlist = [3,1,4]
n = 1
resultlist = yourlist[:-1] if yourlist[-1]>=n else yourlist+[n]
print(resultlist)
n = 5
resultlist = yourlist[:-1] if yourlist[-1]>=n else yourlist+[n]
print(resultlist)
Output:
[3,1]
[3,1,4,5]
I am trying to do the following..
I have a list of n elements. I want to split this list into 32 separate lists which contain more and more elements as we go towards the end of the original list. For example from:
a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
I want to get something like this:
b = [[1],[2,3],[4,5,6,7],[8,9,10,11,12]]
I've done the following for a list containing 1024 elements:
for i in range (0, 32):
c = a[i**2:(i+1)**2]
b.append(c)
But I am stupidly struggling to find a reliable way to do it for other numbers like 256, 512, 2048 or for another number of lists instead of 32.
Use an iterator, a for loop with enumerate and itertools.islice:
import itertools
def logsplit(lst):
iterator = iter(lst)
for n, e in enumerate(iterator):
yield itertools.chain([e], itertools.islice(iterator, n))
Works with any number of elements. Example:
for r in logsplit(range(50)):
print(list(r))
Output:
[0]
[1, 2]
[3, 4, 5]
[6, 7, 8, 9]
... some more ...
[36, 37, 38, 39, 40, 41, 42, 43, 44]
[45, 46, 47, 48, 49]
In fact, this is very similar to this problem, except it's using enumerate to get variable chunk sizes.
This is incredibly messy, but gets the job done. Note that you're going to get some empty bins at the beginning if you're logarithmically slicing the list. Your examples give arithmetic index sequences.
from math import log, exp
def split_list(_list, divs):
n = float(len(_list))
log_n = log(n)
indices = [0] + [int(exp(log_n*i/divs)) for i in range(divs)]
unfiltered = [_list[indices[i]:indices[i+1]] for i in range(divs)] + [_list[indices[i+1]:]]
filtered = [sublist for sublist in unfiltered if sublist]
return [[] for _ in range(divs- len(filtered))] + filtered
print split_list(range(1024), 32)
Edit: After looking at the comments, here's an example that may fit what you want:
def split_list(_list):
copy, output = _list[:], []
length = 1
while copy:
output.append([])
for _ in range(length):
if len(copy) > 0:
output[-1].append(copy.pop(0))
length *= 2
return output
print split_list(range(15))
# [[0], [1, 2], [3, 4, 5, 6], [7, 8, 9, 10, 11, 12, 13, 14]]
Note that this code is not efficient, but it can be used as a template for writing a better algorithm.
Something like this should solve the problem.
for i in range (0, int(np.sqrt(2*len(a)))):
c = a[i**2:min( (i+1)**2, len(a) )]
b.append(c)
Not very pythonic but does what you want.
def splitList(a, n, inc):
"""
a list to split
n number of sublist
inc ideal difference between the number of elements in two successive sublists
"""
zr = len(a) # remaining number of elements to split into sublists
st = 0 # starting index in the full list of the next sublist
nr = n # remaining number of sublist to construct
nc = 1 # number of elements in the next sublist
#
b=[]
while (zr/nr >= nc and nr>1):
b.append( a[st:st+nc] )
st, zr, nr, nc = st+nc, zr-nc, nr-1, nc+inc
#
nc = int(zr/nr)
for i in range(nr-1):
b.append( a[st:st+nc] )
st = st+nc
#
b.append( a[st:max(st+nc,len(a))] )
return b
# Example of call
# b = splitList(a, 32, 2)
# to split a into 32 sublist, where each list ideally has 2 more element
# than the previous
There's always this.
>>> def log_list(l):
if len(l) == 0:
return [] #If the list is empty, return an empty list
new_l = [] #Initialise new list
new_l.append([l[0]]) #Add first iteration to new list inside of an array
for i in l[1:]: #For each other iteration,
if len(new_l) == len(new_l[-1]):
new_l.append([i]) #Create new array if previous is full
else:
new_l[-1].append(i) #If previous not full, add to it
return new_l
>>> log_list([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
[[1], [2, 3], [4, 5, 6], [7, 8, 9, 10]]
for n in range(1,1000000):
print(n)
result = []
for x in range(1,3000001):
if n%2==0:
x=n/2
else:
x=3*n+ 1
n=x
result.append(n)
if n==1:
break
print(len(result))
n+=1
I want these results to be printed in an array or something like that.I mean like this.
3,1,7,2,5,8,1,..
Then I want to take the highest element and its index.How can I do that?Thank you.
You can use str.join for the first task:
>>> result = [4, 0, 9, 7, 8, 3, 2, 6, 1, 5]
>>> print (', '.join(map(str, result)))
4, 0, 9, 7, 8, 3, 2, 6, 1, 5
And max with enumerate for the second task:
>>> ind, val = max(enumerate(result), key=lambda x:x[1])
>>> ind, val
(2, 9)
If you separate out the loop that does the work into its own function, this becomes much easier.
def collatz_length(n):
result = []
for x in range(1,3000001):
if n%2==0:
x=n/2
else:
x=3*n+ 1
n=x
result.append(n)
if n==1:
break
return len(result)
print(max((collatz_length(i + 1), i) for i in range(1000000)))
Since you're not using result, just its length, you could simplify (and speed up) the function a little by simply counting
You can tidy up the calculation of x by using a ternary expression
def collatz_length(n):
for c in range(1, 3000001):
x = 3 * n + 1 if n % 2 else n / 2
n = x
if n == 1:
return c