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Here's my solution for the Leet Code's Two Sum problem -- would love feedback on (1) code efficiency and (2) style/formatting.

Problem:

Given an array of integers, return indices of the two numbers such that they add up to a specific target.

You may assume that each input would have exactly one solution, and you may not use the same element twice.

Example:

Given nums = [2, 7, 11, 15], target = 9,

Because nums[0] + nums[1] = 2 + 7 = 9, return [0, 1].

My solution:

def twoSum(nums, target):
    """
    :type nums: List[int]
    :type target: int
    :rtype: List[int]
    """

    num_lst = list(range(len(nums)))

    for indx, num in enumerate(num_lst):
        for num_other in num_lst[indx+1:]:
            if nums[num] + nums[num_other] == target:
                return [num, num_other]
            else: 
                continue
    return None
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  • 2
    \$\begingroup\$ Would any of the lists contain negative numbers? \$\endgroup\$ – MSeifert Jan 26 at 14:00
  • \$\begingroup\$ @MSeifert I don't know, but feel free to assume yes \$\endgroup\$ – zthomas.nc Jan 27 at 18:06
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Code Style

  • Your code contains a few lines that accomplish nothing and obfuscate your intent:

        else: 
            continue
    

    If the conditional is false, you'll automatically continue on to the next iteration without having to tell the program to do that.

        return None
    

    All Python functions implicitly return None. While PEP 8 appears to endorse this practice ("explicit is better than implicit"), it seems noisy to me.

  • num_lst = list(range(len(nums))) effectively generates a list of all the indices in the nums input list. Then, you immediately enumerate this list, which produces pairs of identical indices indx, num. If all you're attempting to do is iterate, this is significant obfuscation; simply call enumerate directly on nums to produce index-element tuples:

    def twoSum(self, nums, target):
        for i, num in enumerate(nums):
            for j in range(i + 1, len(nums)):
                if num + nums[j] == target:
                    return [i, j]
    

    This makes the intent much clearer: there are no duplicate variables with different names representing the same thing. It also saves unnecessary space and overhead associated with creating a list from a range.

  • Following on the previous item, indx, num and num_lst are confusing variable names, especially when they're all actually indices (which are technically numbers).

Efficiency

  • This code is inefficient, running in quadratic time, or \$\mathcal{O}(n^2)\$. Leetcode is generous to let this pass (but won't be so forgiving in the future!). The reason for this is the nested loop; for every element in your list, you iterate over every other element to draw comparisons. A linear solution should finish in ~65 ms, while this takes ~4400 ms.

    Here is an efficient solution that runs in \$\mathcal{O}(n)\$ time:

    hist = {}
    
    for i, n in enumerate(nums):
        if target - n in hist:
            return [hist[target-n], i]
        hist[n] = i
    

    How does this work? The magic of hashing. The dictionary hist offers constant \$\mathcal{O}(1)\$ lookup time. Whenever we visit a new element in nums, we check to see if its sum complement is in the dictionary; else, we store it in the dictionary as a num => index pair.

    This is the classic time-space tradeoff: the quadratic solution is slow but space efficient, while this solution takes more space but gains a huge boost in speed. In almost every case, choose speed over space.

    For completeness, even if you were in a space-constrained environment, there is a fast solution that uses \$\mathcal{O}(1)\$ space and \$\mathcal{O}(n\log{}n)\$ time. This solution is worth knowing about for the practicality of the technique and the fact that it's a common interview follow-up. The way it works is:

    1. Sort nums.
    2. Create two pointers representing an index at 0 and an index at len(nums) - 1.
    3. Sum the elements at the pointers.
      • If they produce the desired sum, return the pointer indices.
      • Otherwise, if the sum is less than the target, increment the left pointer
      • Otherwise, decrement the right pointer.
    4. Go back to step 3 unless the pointers are pointing to the same element, in which case return failure.
  • Be wary of list slicing; it's often a hidden linear performance hit. Removing this slice as the nested loop code above illustrates doesn't improve the quadratic time complexity, but it does reduce overhead.

Now you're ready to try 3 Sum!

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  • 2
    \$\begingroup\$ As for returning None, see the relevant section of PEP 8. \$\endgroup\$ – Solomon Ucko Jan 26 at 1:48
  • \$\begingroup\$ That's true, Python does say "explicit is better than implicit". I can amend my recommendation to be "at least be aware that Python statements implicitly return None". Maybe Python should also put else: continue at the end of every loop, just to be explicit :-) \$\endgroup\$ – ggorlen Jan 26 at 1:58
  • \$\begingroup\$ Python should, but doesn't know not to copy the entire thing. It has no such optimisation. \$\endgroup\$ – wizzwizz4 Jan 26 at 16:44
  • \$\begingroup\$ @wizzwizz4 No lazy copying? E.g. return a pointer in O(1) to the slice element and then wait for mutation to perform a copy? I'd like to update if incorrect here. \$\endgroup\$ – ggorlen Jan 26 at 17:20
  • \$\begingroup\$ @ggorlen Apparently not. Try it online! Rule of thumb: Python performs no optimisations at all. \$\endgroup\$ – wizzwizz4 Jan 26 at 17:54
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num_lst = list(range(len(nums)))

for indx, num in enumerate(num_lst):

I'm not sure if I'm missing something, but I think not. I ran this code

nums = [2,5,7,9]
num_lst = list(range(len(nums)))
list(enumerate(num_lst))

output : [(0, 0), (1, 1), (2, 2), (3, 3)]

So why do you create the list and then enumerate it? Maybe what you want to do is simply : enumerate(nums) then enumerate(nums[index+1:]) on your other loop? A simpler way would be to only use the ranges, as I'll show below.

Also, given your input, there's a possibility that a single number would be higher than the target, in this case you shouldn't make the second iteration.

You also don't need the else: continue , as it's going to continue either way.

I'd end up with :

def twoSum(nums, target):
    """
    :type nums: List[int]
    :type target: int
    :rtype: List[int]
    """

    for i1 in range(len(nums)):
        if nums[i1] > target:
            continue

        for i2 in range(i1 + 1, len(nums)):
            if nums[i1] + nums[i2] == target:
                return [i1, i2]

    return None

Without knowing the expected input size, it's hard to focus on performance improvements. The main goal of my review was to remove what seemed like a misunderstanding in your code and in my opinion the code is clearer now.

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  • 1
    \$\begingroup\$ Your code is still O(n**2), so I wouldn't say it offers any significant performance boost. \$\endgroup\$ – Eric Duminil Jan 26 at 15:12
  • \$\begingroup\$ Also, your code has a few bugs. It doesn't work with negative numbers, it doesn't even work with 0 reliably (twoSum([2,0], 2)) and it uses the same number twice (twoSum([1, 1], 2)). :-/ \$\endgroup\$ – Eric Duminil Jan 26 at 15:16
  • \$\begingroup\$ @EricDuminil The latter is fine; number != element. \$\endgroup\$ – wizzwizz4 Jan 26 at 16:46
  • 1
    \$\begingroup\$ @wizzwizz4: Thanks for the comment. You're right. I meant to write twoSum([1], 2), which should return None, not [0, 0]. The bug is here, my description was incorrect. \$\endgroup\$ – Eric Duminil Jan 26 at 16:53
  • \$\begingroup\$ @EricDuminil I mainly wanted to focus on some of the bloat to simplify it, went fast and introduced bugs, lol. And without the expected size of input it's hard to tell if there's a real performance value to my answer (and to any other one at that, if we always expect 4 numbers, performance isn't really an issue). I also wrongfully assumed that we dealt with positive non-zero integers. \$\endgroup\$ – IEatBagels Jan 29 at 19:23
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You can use itertools.combinations for a more readable (and likely faster) for loop. As long as returning a list isn't a requirement, I would consider it better style to return a tuple instead. (Especially since it allows you to convey the list length.) Also, as long as the current name isn't a requirement, it is preferable to use snake_case for function and variable names.

from itertools import combinations


def twoSum(nums, target):
    """
    :type nums: List[int]
    :type target: int
    :rtype: List[int]
    """

    for (i, first), (j, second) in combinations(enumerate(nums), 2):
        if first + second == target:
            return [i, j]

    return None
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  • 1
    \$\begingroup\$ You don't need to create num_list anymore. Also, combinations requires (at least in Python 3.6) a second argument r which specifies the length of the combinations. Here, r should be 2. \$\endgroup\$ – Schmuddi Jan 26 at 9:31

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