AK: Fix RedBlackTree::find_smallest_not_below_iterator

Before this was incorrectly assuming that if the current node `n` was at
least the key and the left child of `n` was below the key that `n` was
always correct.
However, the right child(ren) of the left child of `n` could still be
at least the key.

Also added some tests which produced the wrong results before this.

AK/RedBlackTree.h

@@ -133,16 +133,19 @@ protected:
 
     static Node* find_smallest_not_below(Node* node, K key)
     {
+        Node* candidate = nullptr;
         while (node) {
-            if (node->key >= key && (!node->left_child || node->left_child->key < key))
+            if (node->key == key)
                 return node;
 
-            if (node->key <= key)
+            if (node->key <= key) {
                 node = node->right_child;
-            else
+            } else {
+                candidate = node;
                 node = node->left_child;
+            }
         }
-        return node;
+        return candidate;
     }
 
     void insert(Node* node)

Tests/AK/TestRedBlackTree.cpp

@@ -86,3 +86,45 @@ TEST_CASE(clear)
     test.clear();
     EXPECT_EQ(test.size(), 0u);
 }
+
+TEST_CASE(find_smallest_not_below_iterator)
+{
+    RedBlackTree<size_t, size_t> test;
+
+    for (size_t i = 0; i < 8; i++) {
+        auto above_all = test.find_smallest_not_below_iterator(i);
+        EXPECT(above_all.is_end());
+
+        test.insert(i, i);
+
+        auto only_just_added_i_is_not_below = test.find_smallest_not_below_iterator(i);
+        EXPECT(!only_just_added_i_is_not_below.is_end());
+        EXPECT_EQ(only_just_added_i_is_not_below.key(), i);
+    }
+
+    {
+        auto smallest_not_below_two = test.find_smallest_not_below_iterator(2);
+        EXPECT(!smallest_not_below_two.is_end());
+        EXPECT_EQ(smallest_not_below_two.key(), 2u);
+    }
+
+    test.remove(2);
+
+    {
+        auto smallest_not_below_two_without_two = test.find_smallest_not_below_iterator(2);
+        EXPECT(!smallest_not_below_two_without_two.is_end());
+        EXPECT_EQ(smallest_not_below_two_without_two.key(), 3u);
+    }
+
+    {
+        auto smallest_not_below_one = test.find_smallest_not_below_iterator(1);
+        EXPECT(!smallest_not_below_one.is_end());
+        EXPECT_EQ(smallest_not_below_one.key(), 1u);
+    }
+
+    {
+        auto smallest_not_below_three = test.find_smallest_not_below_iterator(3);
+        EXPECT(!smallest_not_below_three.is_end());
+        EXPECT_EQ(smallest_not_below_three.key(), 3u);
+    }
+}