Optimizations for UnionFind (#1334)

Implements ranks & path compression for union find.

---------

Co-authored-by: Alexander McCord <[email protected]>

EqSat/include/Luau/UnionFind.h

@@ -13,10 +13,15 @@ struct UnionFind final
 {
     Id makeSet();
     Id find(Id id) const;
+    Id find(Id id);
     void merge(Id a, Id b);
 
 private:
     std::vector<Id> parents;
+    std::vector<int> ranks;
+
+private:
+    Id canonicalize(Id id) const;
 };
 
 } // namespace Luau::EqSat

EqSat/src/UnionFind.cpp

@@ -10,26 +10,59 @@ Id UnionFind::makeSet()
 {
     Id id{parents.size()};
     parents.push_back(id);
+    ranks.push_back(0);
+
     return id;
 }
 
 Id UnionFind::find(Id id) const
 {
-    LUAU_ASSERT(size_t(id) < parents.size());
+    return canonicalize(id);
+}
+
+Id UnionFind::find(Id id)
+{
+    Id set = canonicalize(id);
 
     // An e-class id 𝑎 is canonical iff find(𝑎) = 𝑎.
     while (id != parents[size_t(id)])
-        id = parents[size_t(id)];
-
-    return id;
+    {
+        // Note: we don't update the ranks here since a rank
+        // represents the upper bound on the maximum depth of a tree
+        Id parent = parents[size_t(id)];
+        parents[size_t(id)] = set;
+        id = parent;
+    }
+
+    return set;
 }
 
 void UnionFind::merge(Id a, Id b)
 {
-    LUAU_ASSERT(size_t(a) < parents.size());
-    LUAU_ASSERT(size_t(b) < parents.size());
+    Id aSet = find(a);
+    Id bSet = find(b);
+    if (aSet == bSet)
+        return;
 
-    parents[size_t(b)] = a;
+    // Ensure that the rank of set A is greater than the rank of set B
+    if (ranks[size_t(aSet)] < ranks[size_t(bSet)])
+        std::swap(aSet, bSet);
+
+    parents[size_t(bSet)] = aSet;
+
+    if (ranks[size_t(aSet)] == ranks[size_t(bSet)])
+        ranks[size_t(aSet)]++;
+}
+
+Id UnionFind::canonicalize(Id id) const
+{
+    LUAU_ASSERT(size_t(id) < parents.size());
+
+    // An e-class id 𝑎 is canonical iff find(𝑎) = 𝑎.
+    while (id != parents[size_t(id)])
+        id = parents[size_t(id)];
+
+    return id;
 }
 
 } // namespace Luau::EqSat