Use Apply[] when f has 2 or more functions?

Questions
1

Consider the following line of code that operates on a list of lists.

This code finds the Maximum element in each list of lists.

In[1]:=  Apply[Max, {{1, 2, 3}, {4, 5}, {6, 7, 8, 9}}, 1]
Out[1]:= {3, 5, 9}

This code finds the Minimum element in each list of lists.

In[2]:=  Apply[Min, {{1, 2, 3}, {4, 5}, {6, 7, 8, 9}}, 1]
Out[2]:= {1, 4, 6}

But how do I find Max - Min for each list in the “list of lists” using Apply[] only?

2

Is this what you want?

 (Max[#] - Min[#]) & /@ {{1, 2, 3}, {4, 5}, {6, 7, 8, 9}}
3

Yes. But, how do i use Apply[] function that can apply on more than 1 function in its arguments?

4

The solution offered by Okkes will not work if you use Apply. the reason is that both Max and Min use only the first argument (the # sign), so if you try (@@ is the shortcut for Apply and @@@ for Apply at level 1)

 (Max[#] - Min[#]) @@@ {{1, 2, 3}, {4, 5}, {6, 7, 8, 9}}

you will get {0,0,0} as the answer

So, you need to take care that both Max and Min will enclose all the arguments and for that you need to use ## (SlotSequence stand for “all arguments”, see documentation). So

 (Max[##] - Min[##]) & @@@ {{1, 2, 3}, {4, 5}, {6, 7, 8, 9}}

returns {2,1,3} as expected, and probably this is what you are looking for

yehuda

5

Yes, this is perfect. Thank you so much for explaining about the ## SoltSequence sign

6

Comment,
The Apply needs to be at level 1, that is, use @@@ as its shortcut. I edited my previous answer above

best