Add entriesTail method to RBTree

src/RBTree.mo

@@ -72,6 +72,12 @@ module {
     /// iterator is persistent, like the tree itself
     public func entriesRev() : I.Iter<(X, Y)> { iter(tree, #bwd) };
 
+
+    /// An iterator for the key-value entries of the map, in ascending key order
+    /// over the keys greater than or equal to x.
+    ///
+    /// iterator is persistent, like the tree itself
+    public func entriesTail(x : X) : I.Iter<(X, Y)> { iterTail(tree, x, compareTo) };
   };
 
 
@@ -108,6 +114,47 @@ module {
     }
   };
 
+  /// An iterator for the entries of the map, in ascending order over the keys
+  /// greater than or equal to x.
+  public func iterTail<X, Y>(t : Tree<X, Y>, x : X, compareTo : (X, X) -> O.Order)
+    : I.Iter<(X, Y)> {
+    object {
+      var trees : IterRep<X, Y> = ?(#tr(t), null);
+      public func next() : ?(X, Y) {
+        switch trees {
+          case null { null };
+          case (?(#tr(#leaf), ts)) { 
+            trees := ts; 
+            next() 
+          };
+          case (?(#xy(xy), ts)) { 
+            trees := ts; 
+            switch (xy.1) { 
+              case null { next() };
+              case (?y) { ?(xy.0, y) } 
+            } 
+          };
+          case (?(#tr(#node(_, l, xy, r)), ts)) { 
+            switch (compareTo(x, xy.0)) {
+              case (#less) {
+                trees := ?(#tr(l), ?(#xy(xy), ?(#tr(r), ts)));
+                next() 
+              };
+              case (#equal) {
+                trees := ?(#xy(xy), ?(#tr(r), ts));
+                next() 
+              };
+              case (#greater) {
+                trees := ?(#tr(r), ts);
+                next() 
+              };
+            }
+          };
+        }
+      };
+    }
+  };
+
   /// Remove the value associated with a given key.
   func removeRec<X, Y>(x : X, compareTo : (X, X) -> O.Order, t : Tree<X, Y>)
     : (?Y, Tree<X, Y>) {

test/RBTreeTest.mo

@@ -1,6 +1,6 @@
 import Debug "mo:base/Debug";
 import Nat "mo:base/Nat";
-import I "mo:base/Iter";
+import Iter "mo:base/Iter";
 import List "mo:base/List";
 import RBT "mo:base/RBTree";
 
@@ -56,6 +56,20 @@ for ((num, lab) in t.entriesRev()) {
 
 assert RBT.size(t.share()) == 9;
 
+do { var i = 4;
+for ((num, lab) in t.entriesTail(4)) {
+  assert(num == i);
+  i += 1;
+}};
+
+do { var i = 1;
+for ((num, lab) in t.entriesTail(0)) {
+  assert(num == i);
+  i += 1;
+}};
+
+assert Iter.size(t.entriesTail(10)) == 0;
+
 t.delete(5);
 
 assert RBT.size(t.share()) == 8;