Modulo Congurence

This is helpful in solving problems like rotation of arrays.

Given k , which represents number of rotations that needs to be made on an array, we can use modulo congurence to achieve it

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Normalization

Here are the single-line reasons for each:

1. Normalization: It prevents "Out of Bounds" errors and eliminates redundant full-circle movements by reducing any shift $k$ to its effective value within the range of the array size $n$.

2. Double Modulo: It forces Java's remainder-based % operator to return a mathematically correct positive index, even when $k$ is negative (Left Shift).

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Task	Formula for k
Normalize Right Shift	k = (k % n + n) % n;
Normalize Left Shift	k = ((-k) % n + n) % n;
Find Target Index (Right)	(oldIndex + k) % n (after normalizing $k$)
Find Target Index (Left)	(oldIndex - k + n) % n (after normalizing $k$)