126 lines
4.3 KiB
Text
126 lines
4.3 KiB
Text
def StateT (m : Type → Type) (σ : Type) (α : Type) := (Unit × σ) → m (α × σ)
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namespace StateT
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variable {m : Type → Type} [Monad m] {σ : Type} {α β : Type}
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@[inline] protected def pure (a : α) : StateT m σ α := λ ⟨_, s⟩, pure (a, s)
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@[inline] protected def bind (x : StateT m σ α) (f : α → StateT m σ β) : StateT m σ β := λ p, do (a, s') ← x p, f a ((), s')
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@[inline] def read : StateT m σ σ := λ ⟨_, s⟩, pure (s, s)
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@[inline] def write (s' : σ) : StateT m σ Unit := λ ⟨_, s⟩, pure ((), s')
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@[inline] def updt (f : σ → σ) : StateT m σ Unit := λ ⟨_, s⟩, pure ((), f s)
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instance : Monad (StateT m σ) :=
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{pure := @StateT.pure _ _ _, bind := @StateT.bind _ _ _}
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end StateT
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def ExceptT (m : Type → Type) (ε : Type) (α : Type) := m (Except ε α)
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namespace ExceptT
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variable {m : Type → Type} [Monad m] {ε : Type} {α β : Type}
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@[inline] protected def pure (a : α) : ExceptT m ε α := (pure (Except.ok a) : m (Except ε α))
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@[inline] protected def bind (x : ExceptT m ε α) (f : α → ExceptT m ε β) : ExceptT m ε β :=
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(do { v ← x, match v with
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| Except.error e := pure (Except.error e)
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| Except.ok a := f a } : m (Except ε β))
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@[inline] def error (e : ε) : ExceptT m ε α := (pure (Except.error e) : m (Except ε α))
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@[inline] def lift (x : m α) : ExceptT m ε α := (do {a ← x, pure (Except.ok a) } : m (Except ε α))
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instance : Monad (ExceptT m ε) :=
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{pure := @ExceptT.pure _ _ _, bind := @ExceptT.bind _ _ _}
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end ExceptT
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abbreviation Node := Nat
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structure nodeData :=
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(find : Node) (rank : Nat := 0)
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abbreviation ufData := Array nodeData
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abbreviation M (α : Type) := ExceptT (StateT id ufData) String α
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@[inline] def read : M ufData := ExceptT.lift StateT.read
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@[inline] def write (s : ufData) : M Unit := ExceptT.lift (StateT.write s)
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@[inline] def updt (f : ufData → ufData) : M Unit := ExceptT.lift (StateT.updt f)
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def error {α : Type} (e : String) : M α := ExceptT.error e
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def run {α : Type} (x : M α) (s : ufData := Array.nil) : Except String α × ufData :=
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x ((), s)
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def capacity : M Nat :=
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do d ← read, pure d.size
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def findEntryAux : Nat → Node → M nodeData
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| 0 n := error "out of fuel"
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| (i+1) n :=
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do s ← read,
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if h : n < s.size then
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do { let e := s.read ⟨n, h⟩,
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if e.find = n then pure e
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else do e₁ ← findEntryAux i e.find,
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updt (λ s, s.write' n e₁),
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pure e₁ }
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else error "invalid Node"
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def findEntry (n : Node) : M nodeData :=
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do c ← capacity,
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findEntryAux c n
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def find (n : Node) : M Node :=
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do e ← findEntry n, pure e.find
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def mk : M Node :=
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do n ← capacity,
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updt $ λ s, s.push {find := n, rank := 1},
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pure n
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def union (n₁ n₂ : Node) : M Unit :=
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do r₁ ← findEntry n₁,
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r₂ ← findEntry n₂,
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if r₁.find = r₂.find then pure ()
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else updt $ λ s,
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if r₁.rank < r₂.rank then s.write' r₁.find { find := r₂.find }
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else if r₁.rank = r₂.rank then
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let s₁ := s.write' r₁.find { find := r₂.find } in
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s₁.write' r₂.find { rank := r₂.rank + 1, .. r₂}
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else s.write' r₂.find { find := r₁.find }
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def mkNodes : Nat → M Unit
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| 0 := pure ()
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| (n+1) := mk *> mkNodes n
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def checkEq (n₁ n₂ : Node) : M Unit :=
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do r₁ ← find n₁, r₂ ← find n₂,
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unless (r₁ = r₂) $ error "nodes are not equal"
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def mergePackAux : Nat → Nat → Nat → M Unit
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| 0 _ _ := pure ()
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| (i+1) n d :=
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do c ← capacity,
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if (n+d) < c
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then union n (n+d) *> mergePackAux i (n+1) d
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else pure ()
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def mergePack (d : Nat) : M Unit :=
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do c ← capacity, mergePackAux c 0 d
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def numEqsAux : Nat → Node → Nat → M Nat
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| 0 _ r := pure r
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| (i+1) n r :=
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do c ← capacity,
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if n < c
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then do { n₁ ← find n, numEqsAux i (n+1) (if n = n₁ then r else r+1) }
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else pure r
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def numEqs : M Nat :=
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do c ← capacity,
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numEqsAux c 0 0
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def test (n : Nat) : M Nat :=
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if n < 2 then error "input must be greater than 1"
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else do
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mkNodes n,
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mergePack 50000,
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mergePack 10000,
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mergePack 5000,
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mergePack 1000,
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numEqs
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def main (xs : List String) : IO UInt32 :=
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let n := xs.head.toNat in
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match run (test n) with
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| (Except.ok v, s) := IO.println ("ok " ++ toString v) *> pure 0
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| (Except.error e, s) := IO.println ("Error : " ++ e) *> pure 1
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