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 Swift DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.swift 
final class Node {
    let value: Int
    var left: Node?
    var right: Node?
    init(_ value: Int, _ left: Node? = nil, _ right: Node? = nil) { self.value = value; self.left = left; self.right = right }
}
func render(_ node: Node?) -> String {
    guard let node = node else { return "_" }
    if node.left == nil && node.right == nil { return String(node.value) }
    return "\(node.value)(\(render(node.left)),\(render(node.right)))"
}
func sampleTree() -> Node {
    return Node(4, Node(2, Node(1), Node(3)), Node(6, Node(5), Node(7)))
}
func listString(_ values: [Int]) -> String { return "[" + values.map(String.init).joined(separator: ", ") + "]" }
func insert(_ root: Node?, _ value: Int) -> Node { guard let root = root else { return Node(value) }; if value < root.value { root.left = insert(root.left, value) } else { root.right = insert(root.right, value) }; return root }
var root: Node? = nil
for 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.