Here is an update example:
!<{margin-right: 20px; auto;display:block;}blog/square-root-trick?image01.png!

In $update(6, 5)$ we have to change $A[6]$ to 5 which results in changing the value of $S[1]$ to keep $S$ up to date.

In $update(6, 5)$ we have to change A[6] to 5 which results in changing the value of $S[1]$ to keep $S$ up to date.

!<{margin-right: 20px; auto;display:block;}blog/square-root-trick?image00.png!