Lazy allocate root and handle cases with null root

structure/tree/btree.go

@@ -37,7 +37,7 @@ func NewBTree[T constraints.Ordered](maxKeys int) *BTree[T] {
 		panic("Must be >= 3 keys")
 	}
 	return &BTree[T]{
-		root:    NewBTreeNode[T](maxKeys, true),
+		root:    nil,
 		maxKeys: maxKeys,
 	}
 }
@@ -72,6 +72,9 @@ func (node *BTreeNode[T]) Search(key T) bool {
 }
 
 func (tree *BTree[T]) Search(key T) bool {
+	if tree.root == nil {
+		return false;
+	}
 	return tree.root.Search(key)
 }
 
@@ -342,6 +345,9 @@ func (node *BTreeNode[T]) Delete(tree *BTree[T], key T) {
 }
 
 func (tree *BTree[T]) Delete(key T) {
+	if tree.root == nil {
+		return
+	}
 	tree.root.Delete(tree, key)
 	if tree.root.numKeys == 0 {
 		tree.root = tree.root.children[0]

structure/tree/btree_test.go

@@ -12,6 +12,9 @@ func TestBTreeIncreasing(t *testing.T) {
 	for _, maxKeys := range maxKeysCases {
 		for _, size := range sizes {
 			tree := bt.NewBTree[int](maxKeys)
+			if tree.Search(0) {
+					t.Errorf("Tree expected to contain 0")
+			}
 			for i := 0; i < size; i++ {
 				tree.Insert(i)
 			}
@@ -45,6 +48,9 @@ func TestBTreeDecreasing(t *testing.T) {
 	for _, maxKeys := range maxKeysCases {
 		for _, size := range sizes {
 			tree := bt.NewBTree[int](maxKeys)
+			if tree.Search(0) {
+					t.Errorf("Tree expected to contain 0")
+			}
 			for i := size - 1; i >= 0; i-- {
 				tree.Insert(i)
 			}
@@ -80,6 +86,9 @@ func TestBTreeRandom(t *testing.T) {
 			rnd := rand.New(rand.NewSource(0))
 			tree := bt.NewBTree[int](maxKeys)
 			nums := rnd.Perm(size)
+			if tree.Search(0) {
+					t.Errorf("Tree expected to contain 0")
+			}
 			for i := 0; i < size; i++ {
 				tree.Insert(nums[i])
 			}
@@ -103,3 +112,22 @@ func TestBTreeRandom(t *testing.T) {
 		}
 	}
 }
+
+func TestBTreeDeleteEverything(t *testing.T) {
+	tree := bt.NewBTree[int](4)
+	size := 128
+	for i := 0; i < size; i++ {
+		tree.Insert(i)
+	}
+	for i := 0; i < size; i++ {
+		tree.Delete(i)
+	}
+	tree.Delete(-1)
+	tree.Delete(1000)
+
+	for i := 0; i < size; i++ {
+		if tree.Search(i) {
+			t.Errorf("Tree not expected to contain %d", i)
+		}
+	}
+}