in reply to Highest total sum path problem

> so that the number of moves (summing operations) from x to that position is the minimum possible and the total sum (summarized values) of the path is the maximum possible.

Too fuzzy, as usual.

You have two criteria to optimize, without telling us which one has to be prioritized.

Cheers Rolf
(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery

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Re^2: Highest total sum path problem
by baxy77bax (Deacon) on Mar 04, 2020 at 11:16 UTC
    good catch !! sorry for that :)

    -> the max valued among the shortest path? // WRONG BULLET POINT C/P

    PS

    as usual. -> was directed to me or a general comment :) I can take a critique, don't worry (speak your mind freely on this thread) :)

    UPDATE:

    I copy/past the wrong bullet point. The correct one is

    -> the shortest among the max value path!!

    First i need to figure out which one is the highest and then if many have the same value , pick the shortest

    @Rata , Thnx!

[reply]

      Hello baxy77bax,

      you need to rethink your requirements. If you want to have the minimum number of moves, you only have two possibilities:

      • slide from aa to ba and then to bb
      • slide from aa to ab and then to bb
      any other solution would have a longer path. And calculating the maximum sum for these two paths is rather trivial ...

      HTH, Rata
[reply]
      Can you clarify the problem statement?

      For instance, is it legal to try to do a tour of the matrix, to pick up as many high value cells as possible? If the priority is "max sum", followed by "min terms", then a "rook's tour" of the positive valued cells is in order.

      Another idea, can you revisit a cell? What's to keep you from circling through 4 positive value cells forever?

      Can you go "offline", by taking a longer tour than necessary?

      -QM
      --
      Quantum Mechanics: The dreams stuff is made of

[reply]
        a) It is legal to do a tour of the matrix and pick up as many high value cells as possible. :)

        b) this is not legal... each cell can only be visited once (but if this was associated to some fintech problem where total sum is your account balance, I guess this would be a good way to boost it up :D )

        c)Yes you can go offline if the number of moves is higher that the total sum of the path toward the final value (cell), but this only holds if a path already exists. If it is the initial search then there is no reference and the condition does not hold (at least one path (solution) needs to exist )

        thnx I did not catch those conditions but now that you mentioned it i see how they are crucial for the problem

        by helping you I helped myself. Thank you !!!

[reply]

      What does slide mean? If you slide A->D, skipping B and C, what is the path length?3 or 1? Also, does sliding mean that the points on the squares you slided over are not counted to your sum? Only the final square you landed on is counted?

[reply]
        slide A -> D means skipping B and C and only values on A and D are counted, B and C are not counted and the path length in case you slide A-> D is 2 and when you go A->B->C->D is 4.

        direction in which I am thinking is that maybe I could compute max and min rang query matrix and then from both sides start and end somehow figure out the outer boundaries .... but as QM said i see no way to avoid full all-pair traversal of the matrix ... also i am thinking in direction of maybe starting the taversal from the highest value in the matrix and working my way to reach start and end point but i am not sure if this is a good way to go...

[reply]

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