module

public import Std
public import Init.Data.Iterators.Lemmas.Basic
open Std

public section

def frequencies (xs : List Nat) : TreeMap Nat Nat (fun a b => compare b a) :=
  xs.foldl (init := ∅) (fun freq (x : Nat) => freq.alter x (fun v? => some (v?.getD 0 + 1)))

def search (xs : List Nat) : Int :=
  let frequencies := frequencies xs
  let kv := frequencies.iter
    |>.filter (fun (k, v) => 0 < k ∧ k ≤ v)
    |>.map (fun (k, _) => k)
    |>.first?
  kv.getD (-1)

/-! ## Tests -/

example : search [5, 5, 5, 5, 1] = 1 := by cbv
example : search [4, 1, 4, 1, 4, 4] = 4 := by cbv
example : search [3, 3] = -1 := by cbv
example : search [8, 8, 8, 8, 8, 8, 8, 8] = 8 := by cbv
example : search [2, 3, 3, 2, 2] = 2 := by cbv
example : search [2, 7, 8, 8, 4, 8, 7, 3, 9, 6, 5, 10, 4, 3, 6, 7, 1, 7, 4, 10, 8, 1] = 1 := by cbv
example : search [3, 2, 8, 2] = 2 := by cbv
example : search [6, 7, 1, 8, 8, 10, 5, 8, 5, 3, 10] = 1 := by cbv
example : search [8, 8, 3, 6, 5, 6, 4] = -1 := by cbv
example : search [6, 9, 6, 7, 1, 4, 7, 1, 8, 8, 9, 8, 10, 10, 8, 4, 10, 4, 10, 1, 2, 9, 5, 7, 9] = 1 := by cbv
example : search [1, 9, 10, 1, 3] = 1 := by cbv
example : search [6, 9, 7, 5, 8, 7, 5, 3, 7, 5, 10, 10, 3, 6, 10, 2, 8, 6, 5, 4, 9, 5, 3, 10] = 5 := by cbv
example : search [1] = 1 := by cbv
example : search [8, 8, 10, 6, 4, 3, 5, 8, 2, 4, 2, 8, 4, 6, 10, 4, 2, 1, 10, 2, 1, 1, 5] = 4 := by cbv
example : search [2, 10, 4, 8, 2, 10, 5, 1, 2, 9, 5, 5, 6, 3, 8, 6, 4, 10] = 2 := by cbv
example : search [1, 6, 10, 1, 6, 9, 10, 8, 6, 8, 7, 3] = 1 := by cbv
example : search [9, 2, 4, 1, 5, 1, 5, 2, 5, 7, 7, 7, 3, 10, 1, 5, 4, 2, 8, 4, 1, 9, 10, 7, 10, 2, 8, 10, 9, 4] = 4 := by cbv
example : search [2, 6, 4, 2, 8, 7, 5, 6, 4, 10, 4, 6, 3, 7, 8, 8, 3, 1, 4, 2, 2, 10, 7] = 4 := by cbv
example : search [9, 8, 6, 10, 2, 6, 10, 2, 7, 8, 10, 3, 8, 2, 6, 2, 3, 1] = 2 := by cbv
example : search [5, 5, 3, 9, 5, 6, 3, 2, 8, 5, 6, 10, 10, 6, 8, 4, 10, 7, 7, 10, 8] = -1 := by cbv
example : search [10] = -1 := by cbv
example : search [9, 7, 7, 2, 4, 7, 2, 10, 9, 7, 5, 7, 2] = 2 := by cbv
example : search [5, 4, 10, 2, 1, 1, 10, 3, 6, 1, 8] = 1 := by cbv
example : search [7, 9, 9, 9, 3, 4, 1, 5, 9, 1, 2, 1, 1, 10, 7, 5, 6, 7, 6, 7, 7, 6] = 1 := by cbv
example : search [3, 10, 10, 9, 2] = -1 := by cbv