Closest Pair in Python - python

I am having a hard time modifying this code, I'm really new to python and I am trying to find the closest pair among the 10 input integers from a user. Here's my code so far and there is a syntax error...
a = [0,1,2,3,4,5,6,7,8,9]
a[0]=input()
a[1]=input()
a[2]=input()
a[3]=input()
a[4]=input()
a[5]=input()
a[6]=input()
a[7]=input()
a[8]=input()
a[9]=input()
a.sort()
b=sorted(set(a))
for item in enumerate(a):
for item1 in enumerate(b):
c = item - enumerate(b)
if c = item-1:
print item
print c
Thank,
Ai

Your code is causing exceptions because you're not handling the output of enumerate properly. Your item values are going to be (value, index) pairs, not single values, so there's no way to subtract them directly.
Here's another implementation, which may be something like what you were aiming for:
import itertools
def find_nearest_pair(lst):
min_pair = None
min_distance = float("inf")
for a, b in itertools.combinations(lst, 2): # generates all (a,b) pairs
distance = abs(a-b) # abs makes distance always non-negative
if distance < min_distance:
min_pair = (a,b)
min_distance = distance
return min_pair # you could return min_distance here too (or instead)
You could even compress it down further using the min function:
nearest_pair = min(itertools.combinations(lst, 2),
key=lambda item: abs(item[0]-item[1]))
Or if you just want the value:
nearest_pair_distance = min(abs(a-b) for a, b in itertools.combinations(lst, 2))

What are all these calls for enumerate for? That's for when you want to iterate through a collection and also keep a counter. You should remove all of them - but especially the one in the line c = item - enumerate(b) which makes absolutely no sense.
Once you've got it running, you should see you have a number of logic errors too, but I'll leave you to fix those yourself.

Related

Finding the count of how many elements of list A appear before than in the similar but mixed list B

A=[2,3,4,1] B=[1,2,3,4]
I need to find how many elements of list A appear before than the same element of list B. In this case values 2,3,4 and the expected return would be 3.
def count(a, b):
muuttuja = 0
for i in range(0, len(a)-1):
if a[i] != b[i] and a[i] not in b[:i]:
muuttuja += 1
return muuttuja
I have tried this kind of solution but it is very slow to process lists that have great number of values. I would appreciate some suggestions for alternative methods of doing the same thing but more efficiently. Thank you!
If both the lists have unique elements you can make a map of element (as key) and index (as value). This can be achieved using dictionary in python. Since, dictionary uses only O(1) time for lookup. This code will give a time complexity of O(n)
A=[2,3,4,1]
B=[1,2,3,4]
d = {}
count = 0
for i,ele in enumerate(A) :
d[ele] = i
for i,ele in enumerate(B) :
if i > d[ele] :
count+=1
Use a set of already seen B-values.
def count(A, B):
result = 0
seen = set()
for a, b in zip(A, B):
seen.add(b)
if a not in seen:
result += 1
return result
This only works if the values in your lists are immutable.
Your method is slow because it has a time complexity of O(N²): checking if an element exists in a list of length N is O(N), and you do this N times. We can do better by using up some more memory instead of time.
First, iterate over b and create a dictionary mapping the values to the first index that value occurs at:
b_map = {}
for index, value in enumerate(b):
if value not in b_map:
b_map[value] = index
b_map is now {1: 0, 2: 1, 3: 2, 4: 3}
Next, iterate over a, counting how many elements have an index less than that element's value in the dictionary we just created:
result = 0
for index, value in enumerate(a):
if index < b_map.get(value, -1):
result += 1
Which gives the expected result of 3.
b_map.get(value, -1) is used to protect against the situation when a value in a doesn't occur in b, and you don't want to count it towards the total: .get returns the default value of -1, which is guaranteed to be less than any index. If you do want to count it, you can replace the -1 with len(a).
The second snippet can be replaced by a single call to sum:
result = sum(index < b_map.get(value, -1)
for index, value in enumerate(a))
You can make a prefix-count of A, which is an array where for each index you keep track of the number of occurrences of each element before the index.
You can use this to efficiently look-up the prefix-counts when looping over B:
import collections
A=[2,3,4,1]
B=[1,2,3,4]
prefix_count = [collections.defaultdict(int) for _ in range(len(A))]
prefix_count[0][A[0]] += 1
for i, n in enumerate(A[1:], start=1):
prefix_count[i] = collections.defaultdict(int, prefix_count[i-1])
prefix_count[i][n] += 1
prefix_count_b = sum(prefix_count[i][n] for i, n in enumerate(B))
print(prefix_count_b)
This outputs 3.
This still could be O(NN) because of the copy from the previous index when initializing the prefix_count array, if someone knows a better way to do this, please let me know*

Guidance on removing a nested for loop from function

I'm trying to write the fastest algorithm possible to return the number of "magic triples" (i.e. x, y, z where z is a multiple of y and y is a multiple of x) in a list of 3-2000 integers.
(Note: I believe the list was expected to be sorted and unique but one of the test examples given was [1,1,1] with the expected result of 1 - that is a mistake in the challenge itself though because the definition of a magic triple was explicitly noted as x < y < z, which [1,1,1] isn't. In any case, I was trying to optimise an algorithm for sorted lists of unique integers.)
I haven't been able to work out a solution that doesn't include having three consecutive loops and therefore being O(n^3). I've seen one online that is O(n^2) but I can't get my head around what it's doing, so it doesn't feel right to submit it.
My code is:
def solution(l):
if len(l) < 3:
return 0
elif l == [1,1,1]:
return 1
else:
halfway = int(l[-1]/2)
quarterway = int(halfway/2)
quarterIndex = 0
halfIndex = 0
for i in range(len(l)):
if l[i] >= quarterway:
quarterIndex = i
break
for i in range(len(l)):
if l[i] >= halfway:
halfIndex = i
break
triples = 0
for i in l[:quarterIndex+1]:
for j in l[:halfIndex+1]:
if j != i and j % i == 0:
multiple = 2
while (j * multiple) <= l[-1]:
if j * multiple in l:
triples += 1
multiple += 1
return triples
I've spent quite a lot of time going through examples manually and removing loops through unnecessary sections of the lists but this still completes a list of 2,000 integers in about a second where the O(n^2) solution I found completes the same list in 0.6 seconds - it seems like such a small difference but obviously it means mine takes 60% longer.
Am I missing a really obvious way of removing one of the loops?
Also, I saw mention of making a directed graph and I see the promise in that. I can make the list of first nodes from the original list with a built-in function, so in principle I presume that means I can make the overall graph with two for loops and then return the length of the third node list, but I hit a wall with that too. I just can't seem to make progress without that third loop!!
from array import array
def num_triples(l):
n = len(l)
pairs = set()
lower_counts = array("I", (0 for _ in range(n)))
upper_counts = lower_counts[:]
for i in range(n - 1):
lower = l[i]
for j in range(i + 1, n):
upper = l[j]
if upper % lower == 0:
lower_counts[i] += 1
upper_counts[j] += 1
return sum(nx * nz for nz, nx in zip(lower_counts, upper_counts))
Here, lower_counts[i] is the number of pairs of which the ith number is the y, and z is the other number in the pair (i.e. the number of different z values for this y).
Similarly, upper_counts[i] is the number of pairs of which the ith number is the y, and x is the other number in the pair (i.e. the number of different x values for this y).
So the number of triples in which the ith number is the y value is just the product of those two numbers.
The use of an array here for storing the counts is for scalability of access time. Tests show that up to n=2000 it makes negligible difference in practice, and even up to n=20000 it only made about a 1% difference to the run time (compared to using a list), but it could in principle be the fastest growing term for very large n.
How about using itertools.combinations instead of nested for loops? Combined with list comprehension, it's cleaner and much faster. Let's say l = [your list of integers] and let's assume it's already sorted.
from itertools import combinations
def div(i,j,k): # this function has the logic
return l[k]%l[j]==l[j]%l[i]==0
r = sum([div(i,j,k) for i,j,k in combinations(range(len(l)),3) if i<j<k])
#alaniwi provided a very smart iterative solution.
Here is a recursive solution.
def find_magicals(lst, nplet):
"""Find the number of magical n-plets in a given lst"""
res = 0
for i, base in enumerate(lst):
# find all the multiples of current base
multiples = [num for num in lst[i + 1:] if not num % base]
res += len(multiples) if nplet <= 2 else find_magicals(multiples, nplet - 1)
return res
def solution(lst):
return find_magicals(lst, 3)
The problem can be divided into selecting any number in the original list as the base (i.e x), how many du-plets we can find among the numbers bigger than the base. Since the method to find all du-plets is the same as finding tri-plets, we can solve the problem recursively.
From my testing, this recursive solution is comparable to, if not more performant than, the iterative solution.
This answer was the first suggestion by #alaniwi and is the one I've found to be the fastest (at 0.59 seconds for a 2,000 integer list).
def solution(l):
n = len(l)
lower_counts = dict((val, 0) for val in l)
upper_counts = lower_counts.copy()
for i in range(n - 1):
lower = l[i]
for j in range(i + 1, n):
upper = l[j]
if upper % lower == 0:
lower_counts[lower] += 1
upper_counts[upper] += 1
return sum((lower_counts[y] * upper_counts[y] for y in l))
I think I've managed to get my head around it. What it is essentially doing is comparing each number in the list with every other number to see if the smaller is divisible by the larger and makes two dictionaries:
One with the number of times a number is divisible by a larger
number,
One with the number of times it has a smaller number divisible by
it.
You compare the two dictionaries and multiply the values for each key because the key having a 0 in either essentially means it is not the second number in a triple.
Example:
l = [1,2,3,4,5,6]
lower_counts = {1:5, 2:2, 3:1, 4:0, 5:0, 6:0}
upper_counts = {1:0, 2:1, 3:1, 4:2, 5:1, 6:3}
triple_tuple = ([1,2,4], [1,2,6], [1,3,6])

I'm getting a 'Memory Error' when running my code [ Python ] - Time Complexity

I'm trying to write a script that counts the number of 'distinct' (or unique) pairs in my array that have a difference equal to a value K . For example, let's say that I have a list that's [a,a,b,c]. My distinct pairs will be then: (a,b) and (a,c) and (b,c) (Distinct is true if at least one element of a pair isn't in another pair of numbers.)
For the difference, my pair, (a,b) for example, is valid only if a+K = b .
I wrote the two following codes but I'm not sure about the time complexity of the first one and for the second one, I just couldn't think of something less memory-taking.
Thank you!
1st:
def count(arr, k):
a = set(arr)
return sum(x+k in a for x in a)
2nd:
def pairs(k, arr):
setA = set(arr)
count = 0
for x in list(setA):
if (x-k) in setA:
count = count +1
return (count)

How to check if sum of 3 integers in list matches another integer? (python)

Here's my issue:
I have a large integer (anywhere between 0 and 2^32-1). Let's call this number X.
I also have a list of integers, unsorted currently. They are all unique numbers, greater than 0 and less than X. Assume that there is a large amount of items in this list, let's say over 100,000 items.
I need to find up to 3 numbers in this list (let's call them A, B and C) that add up to X.
A, B and C all need to be inside of the list, and they can be repeated (for example, if X is 4, I can have A=1, B=1 and C=2 even though 1 would only appear once in the list).
There can be multiple solutions for A, B and C but I just need to find one possible solution for each the quickest way possible.
I've tried creating a for loop structure like this:
For A in itemlist:
For B in itemlist:
For C in itemlist:
if A + B + C == X:
exit("Done")
But since my list of integers contains over 100,000 items, this uses too much memory and would take far too long.
Is there any way to find a solution for A, B and C without using an insane amount of memory or taking an insane amount of time? Thanks in advance.
you can reduce the running time from n^3 to n^2 by using set something like that
s = set(itemlist)
for A in itemlist:
for B in itemlist:
if X-(A+B) in s:
print A,B,X-(A+B)
break
you can also sort the list and use binary search if you want to save memory
import itertools
nums = collections.Counter(itemlist)
target = t # the target sum
for i in range(len(itemlist)):
if itemlist[i] > target: continue
for j in range(i+1, len(itemlist)):
if itemlist[i]+itemlist[j] > target: continue
if target - (itemlist[i]+itemlist[j]) in nums - collections.Counter([itemlist[i], itemlist[j]]):
print("Found", itemlist[i], itemlist[j], target - (itemlist[i]+itemlist[j]))
Borrowing from #inspectorG4dget's code, this has two modifications:
If C < B then we can short-circuit the loop.
Use bisect_left() instead of collections.Counter().
This seems to run more quickly.
from random import randint
from bisect import bisect_left
X = randint(0, 2**32 - 1)
itemset = set(randint(0,X) for _ in range(100000))
itemlist = sorted(list(itemset)) # sort the list for binary search
l = len(itemlist)
for i,A in enumerate(itemlist):
for j in range(i+1, l): # use numbers above A
B = itemlist[j]
C = X - A - B # calculate C
if C <= B: continue
# see https://docs.python.org/2/library/bisect.html#searching-sorted-lists
i = bisect_left(itemlist, C)
if i != l and itemlist[i] == C:
print("Found", A, B, C)
To reduce the number of comparisons, we enforce A < B < C.

Using recursion to create a list combination

I'm in trouble creating a combination of elements from list.
What i would like to do is to create a recursive function in Python which returns a combination of elements for example list a = [1,2,3,4,5,6,7,8] and a result will be combinations [1,2,3,4],[1,3,4,5],[1,4,5,6],[1,2,4,5] etc. For 8 elements it should return 70 combinations (if i did my math right). Although the best option would be that the combinations don't repeat.
I tried to code it, but what i get is only [1,2,3,4],[1,3,4,5] etc but not combination [1,5,7,8]
I know there is a special function but i'd like to do it recursively. Any suggestions?
nimed = ["A","B","C","D","E","F","G","H"]
def kombinatsioonid(listike,popitav):
if len(listike) < 4:
return
tyhi = []
for c in range(len(listike)):
tyhi.append(listike[c])
listike.pop(popitav)
print(tyhi)
kombinatsioonid(listike,popitav)
kombinatsioonid(nimed,1)
This can be done in this way :
def combination(l,n, mylist=[]):
if not n: print(mylist)
for i in range(len(l)):
mylist.append(l[i])
combination(l[i+1:], n-1, mylist)
mylist.pop()
l = ["A","B","C","D","E","F","G","H"]
n=4
combination(l, n)
For each element x in a, generate all k-1 combinations from the elements right to it, and prepend x to each one. If k==0, simply return one empty combination, thus exiting the recursion:
def combs(a, k):
if k == 0:
return [[]]
r = []
for i, x in enumerate(a):
for c in combs(a[i+1:], k - 1):
r.append([x] + c)
#print '\t' * k, k, 'of', a, '=', r
return r
Uncomment the "print" line to see what's going on.
As a side note, it's better to use English variable and function names, just for the sake of interoperability (your very question being an example).

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