How to find min or max in constant time using infinite # processors? Given $ n $ numbers and an infinite number of processors can the min or max be found in constant time? Assume a shared memory architecture (all processors can write to a common shared memory) and the ability to perform concurrent writes

I have tried dividing up the numbers into groups of 2 each and then using $n/2$ processors at the first step and then $n/4$ processors on the output of the first step etc. I can't see how to make use of more than $n/2$ processors given that I have $\infty$ of them
I managed to solve this so hoping it's alright to answer your own question.
Initialize to all elements off, an $n$ bit vector $A$ having a 1:1 mapping with the $n $ numbers. Compare each number against every other number on $n \choose 2$ processors. Each processor switches the bit corresponding to the smaller of its two elements to 1. Assumption is that the processors can do concurrent writes to $A$. The bit in $A$ remaining off denotes the maximum element.

This is $\Theta(1)$ (constant time) as the depth of the computational graph is independent of the number of elements. The work required is however $\mathcal {O(n^{2})}$.