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Try to calculate bh #31

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Try to calculate bh #31

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149 changes: 107 additions & 42 deletions src/PersistentOrderedSet.mo
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Original file line number Diff line number Diff line change
Expand Up @@ -178,12 +178,24 @@ module {
/// Space: `O(m * log(n/m + 1))`, where `m` and `n` denote the number of elements
/// in the sets, and `m <= n`.
public func union(rbSet1 : Set<T>, rbSet2 : Set<T>) : Set<T> {
func f ((bh1, s1) : (Nat, Set<T>), (bh2, s2) : (Nat, Set<T>)) : (Nat, Set<T>) {
switch (s1, s2) {
case (#leaf, rbSet) { (bh2, rbSet) };
case (rbSet, #leaf) { (bh1, rbSet) };
case (#node (_, l1, x, r1), _) {
let (l2, _, r2) = Internal.split(x, (bh2, s2), compare);
Internal.join(f(Internal.bhFromParent(bh1, l1), l2), x, f(Internal.bhFromParent(bh1, r1), r2))
};
};
};
switch (rbSet1, rbSet2) {
case (#leaf, rbSet) { rbSet };
case (rbSet, #leaf) { rbSet };
case (#node (_, l1, x, r1), _) {
let (l2, _, r2) = Internal.split(x, rbSet2, compare);
Internal.join(union(l1, l2), x, union(r1, r2))
case _ {
let bh1 = Internal.blackHeight rbSet1;
let bh2 = Internal.blackHeight rbSet2;
let (_, set) = f ((bh1, rbSet1), (bh2, rbSet2));
set
};
};
};
Expand All @@ -209,15 +221,27 @@ module {
/// Space: `O(m * log(n/m + 1))`, where `m` and `n` denote the number of elements
/// in the sets, and `m <= n`.
public func intersect(rbSet1 : Set<T>, rbSet2 : Set<T>) : Set<T> {
func f ((bh1, s1) : (Nat, Set<T>), (bh2, s2) : (Nat, Set<T>)) : (Nat, Set<T>) {
switch (s1, s2) {
case (#leaf, _) { (0, #leaf) };
case (_, #leaf) { (0, #leaf) };
case (#node (_, l1, x, r1), _) {
let (l2, b2, r2) = Internal.split(x, (bh2, s2), compare);
let l = f(Internal.bhFromParent(bh1, l1), l2);
let r = f(Internal.bhFromParent(bh1, r1), r2);
if b2 { Internal.join (l, x, r) }
else { Internal.join2(l, r) };
};
};
};
switch (rbSet1, rbSet2) {
case (#leaf, _) { #leaf };
case (_, #leaf) { #leaf };
case (#node (_, l1, x, r1), _) {
let (l2, b2, r2) = Internal.split(x, rbSet2, compare);
let l = intersect(l1, l2);
let r = intersect(r1, r2);
if b2 { Internal.join (l, x, r) }
else { Internal.join2(l, r) };
case _ {
let bh1 = Internal.blackHeight rbSet1;
let bh2 = Internal.blackHeight rbSet2;
let (_, set) = f((bh1, rbSet1), (bh2, rbSet2));
set
};
};
};
Expand All @@ -243,12 +267,24 @@ module {
/// Space: `O(m * log(n/m + 1))`, where `m` and `n` denote the number of elements
/// in the sets, and `m <= n`.
public func diff(rbSet1 : Set<T>, rbSet2 : Set<T>) : Set<T> {
func f ((bh1, s1) : (Nat, Set<T>), (bh2, s2) : (Nat, Set<T>)) : (Nat, Set<T>) {
switch (s1, s2) {
case (#leaf, _) { (0, #leaf) };
case (rbSet, #leaf) { (bh1, rbSet) };
case (_, (#node(_, l2, x, r2))) {
let (l1, _, r1) = Internal.split(x, (bh1, s1), compare);
Internal.join2(f(l1, Internal.bhFromParent(bh2, l2)), f(r1, Internal.bhFromParent(bh2, r2)));
}
}
};
switch (rbSet1, rbSet2) {
case (#leaf, _) { #leaf };
case (rbSet, #leaf) { rbSet };
case (_, (#node(_, l2, x, r2))) {
let (l1, _, r1) = Internal.split(x, rbSet1, compare);
Internal.join2(diff(l1, l2), diff(r1, r2));
case _ {
let bh1 = Internal.blackHeight rbSet1;
let bh2 = Internal.blackHeight rbSet2;
let (_, set) = f((bh1, rbSet1), (bh2, rbSet2));
set
}
}
};
Expand Down Expand Up @@ -866,7 +902,6 @@ module {
};
};

// TODO: Instead, consider storing the black height in the node constructor
public func blackHeight<T> (rbSet : Set<T>) : Nat {
func f (node : Set<T>, acc : Nat) : Nat {
switch node {
Expand All @@ -878,23 +913,51 @@ module {
f (rbSet, 0)
};

public func joinL<T>(l : Set<T>, x : T, r : Set<T>) : Set<T> {
if (blackHeight r <= blackHeight l) { (#node (#R, l, x, r)) }
public func bhFromParent<T> (parentBH : Nat, rbSet : Set<T>) : (Nat, Set<T>) {
if (parentBH == 0) { return (0, rbSet) };
switch rbSet {
case (#node (#B, _, _, _)) { (parentBH - 1 : Nat, rbSet) };
case (#leaf) { (0, #leaf) };
case _ { (parentBH, rbSet) };
}
};

public func bhFromChild<T> (childBH : Nat, rbSet : Set<T>) : Nat {
switch rbSet {
case (#node (#R, _, _, _)) { childBH };
case _ { childBH + 1 };
}
};

public func joinL<T>((lbh, l) : (Nat, Set<T>), x : T, (rbh, r) : (Nat, Set<T>)) : (Nat, Set<T>) {
if (rbh <= lbh) { (bhFromChild(rbh, l), (#node (#R, l, x, r))) }
else {
switch r {
case (#node (#R, rl, rx, rr)) { (#node (#R, joinL(l, x, rl) , rx, rr)) };
case (#node (#B, rl, rx, rr)) { balLeft (joinL(l, x, rl), rx, rr) };
case (#node (#R, rl, rx, rr)) {
let (llbh, ll) = joinL((lbh, l), x, bhFromParent(rbh, rl));
(bhFromChild(llbh, ll), (#node (#R, ll , rx, rr)))
};
case (#node (#B, rl, rx, rr)) {
let (llbh, ll) = joinL((lbh, l), x, bhFromParent(rbh, rl));
(bhFromChild(llbh, ll), lbalance (ll, rx, rr))
};
case _ { Debug.trap "joinL" };
}
}
};

public func joinR<T>(l : Set<T>, x : T, r : Set<T>) : Set<T> {
if (blackHeight l <= blackHeight r) { (#node (#R, l, x, r)) }
public func joinR<T>((lbh, l) : (Nat, Set<T>), x : T, (rbh, r) : (Nat, Set<T>)) : (Nat, Set<T>) {
if (lbh <= rbh) { (bhFromChild(lbh, r), (#node (#R, l, x, r))) }
else {
switch l {
case (#node (#R, ll, lx, lr)) { (#node (#R, ll , lx, joinR (lr, x, r))) };
case (#node (#B, ll, lx, lr)) { balRight (ll, lx, joinR (lr, x, r)) };
case (#node (#R, ll, lx, lr)) {
let (rrbh, rr) = joinR (bhFromParent(lbh, lr), x, (rbh, r));
(bhFromChild(rrbh, rr), (#node (#R, ll, lx, rr)))
};
case (#node (#B, ll, lx, lr)) {
let (rrbh, rr) = joinR (bhFromParent(lbh, lr), x, (rbh, r));
(bhFromChild(rrbh, rr), rbalance (ll, lx, rr))
};
case _ { Debug.trap "joinR" };
}
}
Expand All @@ -907,37 +970,39 @@ module {
}
};

public func splitMin<T> (rbSet : Set<T>) : (T, Set<T>) {
public func splitMin<T> ((bh, rbSet) : (Nat, Set<T>)) : (T, (Nat, Set<T>)) {
switch rbSet {
case (#leaf) { Debug.trap "splitMin" };
case (#node(_, #leaf, x, r)) { (x, r) };
case (#node(_, #leaf, x, r)) { (x, (bhFromParent(bh, r))) };
case (#node(_, l, x, r)) {
let (m, l2) = splitMin l;
(m, join(l2, x, r))
let (m, l2) = splitMin (bhFromParent(bh, l));
(m, join(l2, x, bhFromParent(bh, r)))
};
}
};

// Joins an element and two trees.
// See Tobias Nipkow's "Functional Data Structures and Algorithms", 117
public func join<T>(l : Set<T>, x : T, r : Set<T>) : Set<T> {
if (Internal.blackHeight r < Internal.blackHeight l) {
return Internal.paint(#B, Internal.joinR(l, x, r))
public func join<T>((lbh, l) : (Nat, Set<T>), x : T, (rbh, r) : (Nat, Set<T>)) : (Nat, Set<T>) {
if (rbh < lbh) {
let (bh, set) = Internal.joinR((lbh, l), x, (rbh, r));
return (bh, Internal.paint(#B, set))
};
if (Internal.blackHeight l < Internal.blackHeight r) {
return Internal.paint(#B, Internal.joinL(l, x, r))
if (lbh < rbh) {
let (bh, set) = Internal.joinL((lbh, l), x, (rbh, r));
return (bh, Internal.paint(#B, set))
};
return (#node (#B, l, x, r))
return (bhFromChild(lbh, l), (#node (#B, l, x, r)))
};

// Joins two trees.
// See Tobias Nipkow's "Functional Data Structures and Algorithms", 117
public func join2<T>(l : Set<T>, r : Set<T>) : Set<T> {
public func join2<T>((lbh, l) : (Nat, Set<T>), (rbh, r) : (Nat, Set<T>)) : (Nat, Set<T>) {
switch r {
case (#leaf) { l };
case (#leaf) { (lbh, l) };
case _ {
let (m, r2) = Internal.splitMin r;
join(l, m, r2)
let (m, r2) = Internal.splitMin ((rbh, r));
join((lbh, l), m, r2)
};
}
};
Expand All @@ -946,19 +1011,19 @@ module {
// such that `l` contains the elements less than `x`, `r` contains the elements greater than `x`
// and `b` is `true` if `x` was in the `rbSet`.
// See Tobias Nipkow's "Functional Data Structures and Algorithms", 117
public func split<T>(x : T, rbSet : Set<T>, compare : (T, T) -> O.Order) : (Set<T>, Bool, Set<T>) {
public func split<T>(x : T, (bh, rbSet) : (Nat, Set<T>), compare : (T, T) -> O.Order) : ((Nat, Set<T>), Bool, (Nat, Set<T>)) {
switch rbSet {
case (#leaf) { (#leaf, false, #leaf)};
case (#leaf) { ((0, #leaf), false, (0, #leaf))};
case (#node (_, l, x1, r)) {
switch (compare(x, x1)) {
case (#less) {
let (l1, b, l2) = split(x, l, compare);
(l1, b, join(l2, x1, r))
let (l1, b, l2) = split(x, bhFromParent(bh, l), compare);
(l1, b, join(l2, x1, bhFromParent(bh, r)))
};
case (#equal) { (l, true, r) };
case (#equal) { (bhFromParent(bh, l), true, bhFromParent(bh, r)) };
case (#greater) {
let (r1, b, r2) = split(x, r, compare);
(join(l, x1, r1), b, r2)
let (r1, b, r2) = split(x, (bh, r), compare);
(join(bhFromParent(bh, l), x1, r1), b, r2)
};
};
};
Expand Down