Given an array of infinite length and two integers M and N which are co-primes, the task is to find the number of positions that cannot be visited starting from the first position when in a single move from arr[i], either arr[i + M] or arr[i + N] can be reached. Note that the result is always finite.
Input: M = 2, N = 5
From index 0, the indices that can be visited are
0 + 2 = 2
0 + 2 + 2 = 4
0 + 5 = 5
0 + 2 + 2 + 2 = 6
0 + 2 + 5 = 7
0 + 2 + 2 + 2 + 2 = 8
0 + 2 + 2 + 5 = 9
0 + 5 + 5 = 10
1 and 3 are the only indices that cannot be visited.
Input: M = 5, N = 6
- Find the largest index that can’t be obtained using any combination of M & N using Frobenius number say X = (M * N) – M – N .
- Since, X is the largest index than cannot be visited so every index greater than it doesn’t need to be checked.
- Now, for the indices smaller than X, if X is unvisited then Y = X – M and Z = X – N are also unrechable and same goes Y – M and Z – N and so on.. until the indices are greater than 0.
Below is the implementation of the above approach:
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