What's the pattern that will match a head anywhere in an expression

Question

I'm looking for the pattern patt[head] that will match any expression expr in which head occurs as a head anywhere within expr. (Ideally, the matching would stop as soon as a matching subexpression is found.)

For example,

Cases[{f, f[0], h[f[e[d[c[a]]]]], p[q[r[f]]], f[2][3][4], x[y[z[0,f[5][6],1,2]]]},
      patt[f]]

should evaluate to

{f[0], h[f[e[d[c[a]]]]], f[2][3][4], x[y[z[0,f[5][6],1,2]]]}

The answers given to a less general question produce the result

{f[0], f[2][3][4]}

I can't figure out how to adapt those answers to this more general problem.

Answer 1

FirstCase[{f, f[0], h[f[e[d[c[a]]]]], p[q[r[f]]], f[2][3][4], x[y[z[0, f[5][6], 1, 2]]]},
   _?(! FreeQ[#, f[___]] &)]

(* f[0] *)