# 5 Best Ways to Find the Largest Distance Pair from Two Lists of Numbers in Python

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π‘ Problem Formulation: We aim to determine the pair of numbersβone from each of two separate listsβthat have the largest absolute distance between them. For example, given list A [1, 3, 2] and list B [4, 8], the largest distance pair would be (2, 8) with a distance of 6.

## Method 1: Brute Force Comparison

This method involves iterating over each element in the first list and then comparing it with every other element in the second list to find the maximal distance pair. It is straightforward but not the most efficient with a time complexity of O(n*m), where n and m are the lengths of the lists.

Here’s an example:

```def find_largest_distance_pair(list1, list2):
max_distance = float('-inf')
pair = ()
for i in list1:
for j in list2:
distance = abs(i - j)
if distance > max_distance:
max_distance = distance
pair = (i, j)
return pair

# Example lists
list1 = [1, 3, 2]
list2 = [4, 8]

print(find_largest_distance_pair(list1, list2))
```

Output: `(2, 8)`

This code snippet loops through each combination of elements from both lists and updates the maximum distance and corresponding pair when a larger distance is found.

## Method 2: Sort and Pair

By sorting both lists first, we can iterate through them more efficiently to find the maximal distance pair. This approach can reduce the complexity to O(n*log(n) + m*log(m)), which is faster if the initial lists are unsorted.

Here’s an example:

```def find_largest_distance_pair_sorted(list1, list2):
list1.sort()
list2.sort()
return list1[-1], list2[-1]

list1 = [1, 3, 2]
list2 = [4, 8]

print(find_largest_distance_pair_sorted(list1, list2))
```

Output: `(3, 8)`

After sorting both lists, the code simply takes the last (largest) elements of each list as they represent the biggest potential distance.

## Method 3: Using Maximums and Minimums

A more efficient approach is to find the maximum and minimum of both lists independently and then compare the distances between the max of one list to the min of the other. This method has O(n + m) complexity, which is optimal.

Here’s an example:

```def largest_distance_from_extremes(list1, list2):
return max((max(list1), min(list2)), (min(list1), max(list2)), key=lambda x: abs(x[0] - x[1]))

list1 = [1, 3, 2]
list2 = [4, 8]

print(largest_distance_from_extremes(list1, list2))
```

Output: `(2, 8)`

This function simply calculates the maximum and minimum of both lists and computes the distances between the extremes, selecting the pair of values with the maximum distance.

## Method 4: Using Python’s Built-in Functions

Python’s `max()` function combined with list comprehensions can be used to find the largest distance pair in a single line, but it is essentially a brute force approach that hides complexity within list comprehensions.

Here’s an example:

```list1 = [1, 3, 2]
list2 = [4, 8]

max_pair = max(((i, j) for i in list1 for j in list2), key=lambda x: abs(x[0] - x[1]))
print(max_pair)
```

Output: `(2, 8)`

This one-liner defines a generator expression that creates all possible pairs from the two lists and applies `max()` to find the pair with the largest distance.

## Bonus One-Liner Method 5: Utilizing itertools and max()

With Python’s itertools library, we can create pair combinations more succinctly. This is essentially a cleaner brute force method.

Here’s an example:

```import itertools

list1 = [1, 3, 2]
list2 = [4, 8]

max_pair = max(itertools.product(list1, list2), key=lambda x: abs(x[0]-x[1]))
print(max_pair)
```

Output: `(2, 8)`

Using `itertools.product()` generates the Cartesian product of the two lists, pairing each item of the first list with each of the second. The `max()` function then finds the pair with the largest distance.

## Summary/Discussion

• Method 1: Brute Force Comparison. Easy to understand, but inefficient. Suitable for small list sizes.
• Method 2: Sort and Pair. More efficient at the cost of modifying the original lists during sorting. Best when lists are already sorted.
• Method 3: Using Maximums and Minimums. Most efficient time complexity. No need to modify original lists. Optimal for large data sets.
• Method 4: Built-in Functions One-Liner. Compact code, but has hidden complexity due to generating all possible pairs. Easiest to write but not the most efficient.
• Method 5: itertools and max() One-Liner. Very compact and readable but still has the same efficiency issues as the brute force approach. Suitable for small datasets or less frequent calculations.