How to find the longest sequence in a 2d array?











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Given a 2d grid, with the below constraints, I want to find the longest sub-sequence :




  1. allowed to move up, right, left, down, diagonally

  2. difference between the current value and the next value should be greater than or equal to 3 (i.e absolute difference).

  3. visited cells should not be repeated

  4. grid could be maximum 10 x 10

  5. not allowed to do 4 -> 9 in the below example


Example:



824

061

379


The length of the longest path for the above input is 8, with the sequence 9,1,6,2,8,0,7,3



I tired to approach using multiple for loops, but it would be highly inefficient. I want to know how do I approach using Dynamic Programming. Any help would be appreciated.






algorithm recursion data-structures dynamic-programming







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  • if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
    – mangusta
    Nov 21 at 3:46










  • Pham, I've edited the question. It's actually greater than or equal to 3.
    – Ramesh
    Nov 21 at 3:56






  • 2




    This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
    – SaiBot
    Nov 21 at 7:05










  • Why not do a depth first search instead of dynamic programming?
    – vivek_23
    Nov 21 at 7:11










  • apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
    – mangusta
    Nov 21 at 7:15















up vote
0
down vote

favorite












Given a 2d grid, with the below constraints, I want to find the longest sub-sequence :




  1. allowed to move up, right, left, down, diagonally

  2. difference between the current value and the next value should be greater than or equal to 3 (i.e absolute difference).

  3. visited cells should not be repeated

  4. grid could be maximum 10 x 10

  5. not allowed to do 4 -> 9 in the below example


Example:



824

061

379


The length of the longest path for the above input is 8, with the sequence 9,1,6,2,8,0,7,3



I tired to approach using multiple for loops, but it would be highly inefficient. I want to know how do I approach using Dynamic Programming. Any help would be appreciated.






algorithm recursion data-structures dynamic-programming







share|improve this question









New contributor




Ramesh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
    – mangusta
    Nov 21 at 3:46










  • Pham, I've edited the question. It's actually greater than or equal to 3.
    – Ramesh
    Nov 21 at 3:56






  • 2




    This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
    – SaiBot
    Nov 21 at 7:05










  • Why not do a depth first search instead of dynamic programming?
    – vivek_23
    Nov 21 at 7:11










  • apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
    – mangusta
    Nov 21 at 7:15













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given a 2d grid, with the below constraints, I want to find the longest sub-sequence :




  1. allowed to move up, right, left, down, diagonally

  2. difference between the current value and the next value should be greater than or equal to 3 (i.e absolute difference).

  3. visited cells should not be repeated

  4. grid could be maximum 10 x 10

  5. not allowed to do 4 -> 9 in the below example


Example:



824

061

379


The length of the longest path for the above input is 8, with the sequence 9,1,6,2,8,0,7,3



I tired to approach using multiple for loops, but it would be highly inefficient. I want to know how do I approach using Dynamic Programming. Any help would be appreciated.






algorithm recursion data-structures dynamic-programming







share|improve this question









New contributor




Ramesh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Given a 2d grid, with the below constraints, I want to find the longest sub-sequence :




  1. allowed to move up, right, left, down, diagonally

  2. difference between the current value and the next value should be greater than or equal to 3 (i.e absolute difference).

  3. visited cells should not be repeated

  4. grid could be maximum 10 x 10

  5. not allowed to do 4 -> 9 in the below example


Example:



824

061

379


The length of the longest path for the above input is 8, with the sequence 9,1,6,2,8,0,7,3



I tired to approach using multiple for loops, but it would be highly inefficient. I want to know how do I approach using Dynamic Programming. Any help would be appreciated.






algorithm recursion data-structures dynamic-programming




algorithm recursion data-structures dynamic-programming






share|improve this question









New contributor




Ramesh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









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Ramesh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




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edited Nov 21 at 3:53





















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asked Nov 21 at 3:30









Ramesh

11




11




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Ramesh is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Check out our Code of Conduct.












  • if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
    – mangusta
    Nov 21 at 3:46










  • Pham, I've edited the question. It's actually greater than or equal to 3.
    – Ramesh
    Nov 21 at 3:56






  • 2




    This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
    – SaiBot
    Nov 21 at 7:05










  • Why not do a depth first search instead of dynamic programming?
    – vivek_23
    Nov 21 at 7:11










  • apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
    – mangusta
    Nov 21 at 7:15


















  • if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
    – mangusta
    Nov 21 at 3:46










  • Pham, I've edited the question. It's actually greater than or equal to 3.
    – Ramesh
    Nov 21 at 3:56






  • 2




    This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
    – SaiBot
    Nov 21 at 7:05










  • Why not do a depth first search instead of dynamic programming?
    – vivek_23
    Nov 21 at 7:11










  • apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
    – mangusta
    Nov 21 at 7:15
















if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
– mangusta
Nov 21 at 3:46




if you want to use dynamic programming you need to define a recurrence relation with base case first. that shouldn't be very hard since you already got a feeling that the same subproblems are called multiple times
– mangusta
Nov 21 at 3:46












Pham, I've edited the question. It's actually greater than or equal to 3.
– Ramesh
Nov 21 at 3:56




Pham, I've edited the question. It's actually greater than or equal to 3.
– Ramesh
Nov 21 at 3:56




2




2




This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
– SaiBot
Nov 21 at 7:05




This looks like a variation of the en.wikipedia.org/wiki/Longest_path_problem to me. So there might be no efficient solution.
– SaiBot
Nov 21 at 7:05












Why not do a depth first search instead of dynamic programming?
– vivek_23
Nov 21 at 7:11




Why not do a depth first search instead of dynamic programming?
– vivek_23
Nov 21 at 7:11












apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
– mangusta
Nov 21 at 7:15




apparently I think it cannot be solved by means of dynamic programming, because all subproblems are distinct from each other. for example, we would like to find sequences starting with 2 and 7. at first glance it seems that going one step down for 2 and one step up for 7 will call the same subproblem i.e. start with 6, but it is actually not the same subproblem because if we go from 2, then 2 is visited so we can't pick 2 anymore, and if we go from 7 then 7 is visited and we can't pick 7 anymore
– mangusta
Nov 21 at 7:15












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Just run bfs (Breadth-first search) from every possible source in the grid by following the constraints. For example, in your given sample input the number of possible source is 9. Then, save the paths in some suitable data structure. After saving the paths, check which path is longest and that's your answer.






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    Just run bfs (Breadth-first search) from every possible source in the grid by following the constraints. For example, in your given sample input the number of possible source is 9. Then, save the paths in some suitable data structure. After saving the paths, check which path is longest and that's your answer.






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      Just run bfs (Breadth-first search) from every possible source in the grid by following the constraints. For example, in your given sample input the number of possible source is 9. Then, save the paths in some suitable data structure. After saving the paths, check which path is longest and that's your answer.






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        up vote
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        down vote









        Just run bfs (Breadth-first search) from every possible source in the grid by following the constraints. For example, in your given sample input the number of possible source is 9. Then, save the paths in some suitable data structure. After saving the paths, check which path is longest and that's your answer.






        share|improve this answer












        Just run bfs (Breadth-first search) from every possible source in the grid by following the constraints. For example, in your given sample input the number of possible source is 9. Then, save the paths in some suitable data structure. After saving the paths, check which path is longest and that's your answer.







        share|improve this answer












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        answered Nov 22 at 13:39









        Golam Rahman Tushar

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