#### Max Difference Pair

```def max_difference(a: list[int]) -> tuple[int, int]:
"""
We are given an array A[1..n] of integers, n >= 1. We want to
find a pair of indices (i, j) such that
1 <= i <= j <= n and A[j] - A[i] is as large as possible.

Explanation:
https://www.geeksforgeeks.org/maximum-difference-between-two-elements/

>>> max_difference([5, 11, 2, 1, 7, 9, 0, 7])
(1, 9)
"""
# base case
if len(a) == 1:
return a, a
else:
# split A into half.
first = a[: len(a) // 2]
second = a[len(a) // 2 :]

# 2 sub problems, 1/2 of original size.
small1, big1 = max_difference(first)
small2, big2 = max_difference(second)

# get min of first and max of second
# linear time
min_first = min(first)
max_second = max(second)

# 3 cases, either (small1, big1),
# (min_first, max_second), (small2, big2)
# constant comparisons
if big2 - small2 > max_second - min_first and big2 - small2 > big1 - small1:
return small2, big2
elif big1 - small1 > max_second - min_first:
return small1, big1
else:
return min_first, max_second

if __name__ == "__main__":
import doctest

doctest.testmod()
```  