We chose to test drive a maths problem during Tuesday's Extreme Wednesday session (don't ask) mostly as an exercise in playing with Ruby Idioms and Emacs. The problem was calculating the maximum number that could be obtained by summing consequtive numbers in a list. It's clearer with examples: For [1,2,3] the answer is 6 [1,2,-2,1] the answer is 3 [3,3,-1,3,3,-20,8] the answer is 11 We could only think of a brute force answer: sum all possible combinations. Afterwards Anthony tried a solution in a paper he had on that subject which was something like (in Ruby)

def max_consecutive_sequence_in_array(arr)
 result = sequence_sum = 0
 arr.each do |x|
     sequence_sum = [0, sequence_sum + x].max
     result = [result, sequence_sum].max
 end
 return result
end

That passed all the tests, but we could not figure out why it works. Bothered by this I fired up Excel on the train this morning to see the algorithm in action; I got the whole thing working in a minute or so and was staring at the numbers wondering how this was going to help when suddenly the solution made sense. So what am I getting at? Making the spreadsheet did not directly lead me to the solution, yet somehow making the algorithm more explicit by tackling it in a different way. It reminded me of the "Team Therapy" workshop with Dave Hover and Tim Bacon at XP 2005. One of my stories was of a team attempting XP but being foiled by one very obstructive team member; let's call him Andrew(not his real name). I had reflected on those events previously, and thought I could understand Andrew's point of view. It wasn't until the second telling of the story during the workshop that I realised just how shoddily he had been treated around the time of the team's formation and how, as a team, we had failed him. I already knew all the facts but I did not fully understand their implications until I told Andrew's story to other people.

Thursday, September 15, 2005 | Permalink | 0 Comments