/-
Copyright (c) 2023 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
module

prelude
public import Init.Data.Range.Polymorphic.Nat
public import Init.Data.Range.Polymorphic.Iterators

public section

namespace Array

/-!
This module contains utility functions involving Arrays that are useful in a few places
of the lean code base, but too specialized to live in `Init.Data.Array`, which arguably
is part of the public, user-facing standard library.
-/

/--
Compares each element of an array with all later elements using `f`. For each comparison, `f`
determines whether to keep both of its arguments. If `f` returns `false` for an argument, that
argument is removed from the array and does not participate in subsequent comparisons. Those
elements that were not discarded are returned.

This can be used to remove elements from an array where a “better” element, in some partial order,
exists in the array.

Example:
```lean example
#eval #["a", "r", "red", "x", "r"].filterPairsM fun x y =>
  pure (!(x.isPrefixOf y), true)
```
```output
#["a", "red", "x", "r"]
```
-/
def filterPairsM {m} [Monad m] {α} (a : Array α) (f : α → α → m (Bool × Bool)) :
    m (Array α) := do
  let mut removed := Array.replicate a.size false
  let mut numRemoved := 0
  for h1 : i in *...a.size do for h2 : j in (i+1)...a.size do
    unless removed[i]! || removed[j]! do
      let xi := a[i]
      let xj := a[j]
      let (keepi, keepj) ← f xi xj
      unless keepi do
        numRemoved := numRemoved + 1
        removed := removed.set! i true
      unless keepj do
        numRemoved := numRemoved + 1
        removed := removed.set! j true
  let mut a' := Array.mkEmpty numRemoved
  for h : i in *...a.size do
    unless removed[i]! do
      a' := a'.push a[i]
  return a'

end Array