Given 2 arrays A and B of size m and n respectively. The array A is extended by concatenating n copies of A to itself and array B is extended by concatenating m copies of B to itself, thus the new size of each array is m*n. Find the sum abs(A[i]-B[i]) for i from 0 to m*n-1.
Constraints :-
A[i], B[i] <= 50 and Length of the arrays A, B < 1e5
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It is pretty clear that if $$$n = m$$$, you just add $$$n \cdot |A_{i} - B_{i}|$$$. If you've tried writing the operations down on paper, then, the other case should also be fairly obvious. Assume WLOG $$$m \lt n$$$, then, for each element in $$$A$$$, you must add $$$\sum_{j=1}^{m}|A_{i} - B_{j}|$$$. You can optimize the sum by using prefix sums.
Here I have assumed $$$n$$$ to be the size of array $$$A$$$, and $$$m$$$ for $$$B$$$
How are you using prefix sum here exactly? As we require sum of differences of absolute values, won't the prefix sums be different for each $$$A_{i}$$$
For each element in $$$A$$$, you can find the set of indices it ,matches to in $$$B$$$. This set will be same for all $$$A_i$$$ where $$$i = k . gcd(n,m)$$$ and disjoint from other indices. Then you just sort and use prefix sums + binary search for the value at each index of $$$A$$$.