I'm confused! Two successful solutions have been submitted, but I would swear that the test suite answers for problems 6 and 15 are incorrect. In problem 15, it is easy to see that there is no way to get a production rate higher than 43; yet the answer given is 44.
To clarify, here is a possible breakdown for Test Case 15: [34 goods can flow along path 1-2-10-11] + [2 goods can flow along path 1-3-4-8-11] + [8 goods can flow along path 1-3-7-9-11] = 34 + 2 + 8 = 44. Take note that we can flow 34 goods from Point 10 to Point 11.
This solution can be improved if line 6 becomes: a(P(j,1),P(j,2)) = a(P(j,1),P(j,2)) + P(j,3); I'm sorry for the confusion. You see, there can be more than 1 path between two points.
What is the distance from point P(x,y) to the line Ax + By + C = 0?
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