Given a large number, n (having number digits up to 10^6) and various queries of the below form :
Query(l, r) : find if the sub-string between the indices l and r (Both inclusive) are divisible by 11.
Input: n = 122164154695 Queries: l = 0 r = 3, l = 1 r = 2, l = 5 r = 9, l = 0 r = 11 Output: True False False True Explanation: In the first query, 1221 is divisible by 11 In the second query, 22 is divisible by 11 and so on.
We know that any number is divisible by 11 if the difference between sum of odd indexed digits and the sum of even indexed digits is divisible by 11, i.e.,
Sum(digits at odd places) – Sum(digits at even places) should be divisible by 11.
Hence the idea is to pre-process an auxiliary array that would store sum of digits at odd and even places.
To evaluate a query we can use the auxiliary array to answer it in O(1).
1 1 0 1
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