Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this Dart DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.dart 
class Node {
  Node(this.value, [this.left, this.right]);
  final int value;
  Node? left;
  Node? right;
}
String render(Node? node) {
  if (node == null) return "_";
  if (node.left == null && node.right == null) return node.value.toString();
  return "${node.value}(${render(node.left)},${render(node.right)})";
}
Node sampleTree() => Node(4, Node(2, Node(1), Node(3)), Node(6, Node(5), Node(7)));
String listString(List<int> values) => "[${values.join(", ")}]";
Node insert(Node? root, int value) { if (root == null) return Node(value); if (value < root.value) { root.left = insert(root.left, value); } else { root.right = insert(root.right, value); } return root; }
void main() { Node? root; for (final value in [4, 2, 6, 1, 3, 5, 7]) { root = insert(root, value); } print(render(root)); }

Complexity

  • Time: O(h) per insert
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.
binary search tree Values smaller than a node go left; larger values go right.