Prefix Computation

Given the binary, associative operator $\otimes$ and x₁ .. x_k, compute .

Let
$\;\;\;\;\;$[i,j] = ,
$\;\;\;\;\;$[i,k] = [i,j] $\otimes$ [j+1,k], and
$\;\;\;\;\;$[i,i] = x_i.

We can use pointer jumping to change [i,i] to [1,i].