I love the fact that you based this on a question from Answers! I kind of wanted to link back to it, but I can see that you might not want people to see your answer.
This is a short coded solution but it is not efficient. A solution that involves sorting the vector, A, uses less memory and is faster but take a couple more lines of code.
Find the sum of the elements in the "second" diagonal
What is the distance from point P(x,y) to the line Ax + By + C = 0?
Flag largest magnitude swings as they occur
Basic arrays operations.
compress sequence into intervals
Dispatch and collect
Find the distance between runs
Find similar sequences
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