Question

Assume that we have multiple arrays of integers. You can consider each array as a level. We try to find a sequence of elements, exactly one element from each array, and proceed to the next array with the same predicate. For example, we have v1, v2, v3 as the arrays:

v1  | v2  | v3
-----------------
1   | 4   | 16
2   | 5   | 81
3   | 16  | 100
4   | 64  | 121

I could say that the predicate is: next_element == previous_element^2
A valid sequence from the above example is: 2 -> 4 -> 16
Actually, in this example there isn’t another valid sequence.
I could write three loops to brute-force the mentioned example, but what if the number of arrays is variable, but with know order of course, how would you solve this problem?

Hints, or references to design patters are very appreciated. I shall do it in C++, but I just need the idea.

Thanks,

Answer 1

If you order your arrays beforehand, the search can be done much faster. You could start on your smaller array, then binary-search for expected numbers on each of them. This would be O(nklogM), n being the size of the smallest array, k being the numbers of arrays, M being the size of larger array

This could be done even faster if you use Hashmaps instead of arrays. This would let you search in O(n*k).

If using reverse functions (to search in earlier arrays) is not an option, then you should start on first array, and n = size of first array.

For simplicity, I’ll start from first array

//note the 1-based arrays
for (i : 1 until allArrays[1].size()) {
  baseNumber = allArrays[1][i];
  for (j: 2 until allArrays.size()) {
    expectedNumber = function(baseNumber);
    if (!find(expectedNumber, allArrays[j]))
        break;
    baseNumber = expectedNumber;
  }
}

You can probably do some null checks and add some booleans in there to know if the sequence exist or not