I said the same a few days ago in codechef.The blogs that have been written so far in codeforces or topcoder does not make the topic crystal clear.I would really like someone to write a beautiful blog on this.

I guess its as i say :

We have an array $$$a$$$ of $$$n$$$ integers, we want to calculate $$$\sum\limits_{1 \le i < j \le n} a_i \cdot a_j$$$.

My approach is that lets calculate array $$$sl$$$ of length $$$n$$$ such that $$$sl_k = \sum\limits_{1 \le i < j \le k} a_i \cdot a_j$$$ and $$$sl_1 = 0$$$ by definition, then $$$sl_i$$$ can be calculated using $$$sl_{i-1}$$$, its a DP form of scanline, you can instead of storing array $$$sl$$$, just remember the previous one. For some cases its useful to not to store them, for example when we calculate LIS using monotonically increasing stack.

I'm not sure, correct me if i'm not.

You should contact the MAME team. It uses scanlines to emulate the Arcade screen.

https://www.youtube.com/watch?v=lFBpH_Mt_LI&t=412s

It's an algorithm used to find the resultant array after performing several queries on an array of the form : add a number to each element of the array in a particular range. Formally, given an array a[] and several queries of the form (l, r, val) add val to each element of subarray a[l...r] and finally output the array a[] after performing all the queries.

Algorithm: For each query (l, r, val) add val to a[l] and -val to a[r+1] and finally take the prefix sum array. That would give you the resultant array.

Most likely you have used this algo without realising that it has a fancy name.

Most of the time "scanline" means "sweep line" (something about processing events in some order),so there is a terminology problem in the community.

I think its similiar like diffrence array tecqnique

https://youtu.be/96RG7EBF8LI?si=KmVhQMO1mP-87gLS