def Array.merge {α : Type u_1} (lt : α → α → Bool) (xs ys : Array α) : Array α

O(|xs| + |ys|). Merge arrays xs and ys. If the arrays are sorted according to lt, then the result is sorted as well. If two (or more) elements are equal according to lt, they are preserved.

Equations

• Array.merge lt xs ys = Array.merge.go✝ lt xs ys (Array.mkEmpty (xs.size + ys.size)) 0 0

def Array.mergeDedupWith {α : Type u_1} [ord : Ord α] (xs ys : Array α) (merge : α → α → α) : Array α

O(|xs| + |ys|). Merge arrays xs and ys, which must be sorted according to compare and must not contain duplicates. Equal elements are merged using merge. If merge respects the order (i.e. for all x, y, y', z, if x < y < z and x < y' < z then x < merge y y' < z) then the resulting array is again sorted.

Equations

• xs.mergeDedupWith ys merge = Array.mergeDedupWith.go✝ xs ys merge (Array.mkEmpty (xs.size + ys.size)) 0 0

@[inline]

def Array.mergeDedup {α : Type u_1} [ord : Ord α] (xs ys : Array α) : Array α

O(|xs| + |ys|). Merge arrays xs and ys, which must be sorted according to compare and must not contain duplicates. If an element appears in both xs and ys, only one copy is kept.

Equations

• xs.mergeDedup ys = xs.mergeDedupWith ys fun (x x_1 : α) => x

def Array.mergeUnsortedDedup {α : Type u_1} [eq : BEq α] (xs ys : Array α) : Array α

O(|xs| * |ys|). Merge xs and ys, which do not need to be sorted. Elements which occur in both xs and ys are only added once. If xs and ys do not contain duplicates, then neither does the result.

Equations

• xs.mergeUnsortedDedup ys = if xs.size < ys.size then Array.mergeUnsortedDedup.go✝ ys xs else Array.mergeUnsortedDedup.go✝ xs ys

def Array.mergeAdjacentDups {α : Type u_1} [eq : BEq α] (f : α → α → α) (xs : Array α) : Array α

O(|xs|). Replace each run [x₁, ⋯, xₙ] of equal elements in xs with f ⋯ (f (f x₁ x₂) x₃) ⋯ xₙ.

Equations

• Array.mergeAdjacentDups f xs = if h : 0 < xs.size then Array.mergeAdjacentDups.go✝ f xs (Array.mkEmpty xs.size) 1 xs[0] xs[0] else xs

def Array.dedupSorted {α : Type u_1} [eq : BEq α] (xs : Array α) : Array α

O(|xs|). Deduplicate a sorted array. The array must be sorted with to an order which agrees with ==, i.e. whenever x == y then compare x y == .eq.

Equations

• xs.dedupSorted = Array.mergeAdjacentDups (fun (x x_1 : α) => x) xs

def Array.sortDedup {α : Type u_1} [ord : Ord α] (xs : Array α) : Array α

O(|xs| log |xs|). Sort and deduplicate an array.

Equations

• xs.sortDedup = (xs.qsort fun (x1 x2 : α) => (compare x1 x2).isLT).dedupSorted