Here is an update example:
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In $update(2, 5)$ we have to change $A[2]$ 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!