Efficiency of the way comparator works

Question

I am trying to use a comparator to help sort a list of objects. I have a question about how exactly the comparator works and what it would be doing exactly in the following

Answer 1

Basically, you want to compare students by comparing some values that each maps to. This is usually done by

    static Comparator comparator()
    {
        return Comparator.comparing( Foo::complexOperation );
    }

However, since the function complexOperation is too expensive, we want to cache its results. We can have a general purpose utility method Function cache(Function)

    static Comparator comparator()
    {
        return Comparator.comparing( cache(Foo::complexOperation) );
    }

In general, it is better that the caller can supply a Map as the cache

public static  Function cache(Function f, Map cache)
{
    return k->cache.computeIfAbsent(k, f);
}

We can use IdentityHashMap as the default cache

public static  Function cache(Function f)
{
    return cache(f, new IdentityHashMap<>());
}