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Asked: 2026-05-12T08:41:45+00:00

let’s say I have a matrix (array) like this example, but much larger: 0

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let’s say I have a matrix (array) like this example, but much larger:

0 0 5 0 3 6 6 4 0 3 0 8 0 1 1
9 4 0 6 0 0 0 4 1 0 6 0 7 0 0
3 1 6 1 5 0 8 0 8 0 3 2 6 4 8
1 0 2 2 8 5 8 1 8 7 4 1 0 3 0
6 3 8 1 0 0 4 0 0 3 1 5 2 0 0
0 0 5 0 3 6 6 4 0 3 0 8 0 1 1
9 4 0 6 0 0 0 4 1 0 6 0 7 0 0
3 1 6 1 5 0 8 0 8 0 3 2 6 4 8
1 0 2 2 8 5 8 1 8 7 4 1 0 3 0
6 3 8 1 0 0 4 0 9 4 1 5 2 0 0

I’m trying to determine the position of two equal numbers with greatest distance between them in the array in a diagonal, horizontal or vertical straight line, with the distance calculated as the count of numbers between them (distance d >= 0).

Other Constraints:

  • The straight line as described above may not contain the same number that is marking its beginning and end, so you can’t have 6 0 4 5 6 1 7 3 5 6 and say distance 6..6 is 8 as there is a 6 in the sequence.
  • The numbers to look for are not given but must be determined dynamically.

In the example the result (considering the array as a regular X|Y coord system with 0, 0 in the lower left) it should determine P1(0, 8), P2(8, 0) with d = 7 (number: 9).

Any good ideas on how to do this efficiently? I’m using C# but examples/ideas in other languages are appreciated too.

In case you wonder where this question comes from, I’ve been thinking about various math related challenges that I believe are tough to solve (for myself) and hope to get a better handle on such problems by seeing how others solve such issues. Thank you!

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1 Answer

  1. Editorial Team

    Algorithm:

    Simplify the problem. It is equivalent to solving the 1-dimensional version (find largest gap between equal values in a list) once per row, column and diagonal then returning the maximum.

    Simplify more. The 1-dimensional version is pretty easy. You just build a Dictionary which maps values to a list of their positions, solve the trivial problem of ‘what is the largest delta in this list of positions’ for each value, and return the maximum.

    Analysis:

    The trivial problem takes linear time in the size of the position list (because the list is sorted [by the natural insertion order]). Therefore the 1-dim gap problem takes linear time in the size of the value list (because there is one position per value). Therefore the 2-dim gap problem takes linear time in the size of the matrix (because each value is included in exactly four 1-dim sub-problems).

    So if the matrix is nm, the solution will take O(nm) time. It requires O(n+m) space (to store the value->positions dictionary during each 1-dim phase). I really doubt you’ll do better (the time is clearly optimal, not so sure about the size).

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