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

Basic Implementation

basic.js 
class Node {
  constructor(value, left = null, right = null) {
    this.value = value;
    this.left = left;
    this.right = right;
  }
}
function render(node) {
  if (node === null) return "_";
  if (node.left === null && node.right === null) return String(node.value);
  return `${node.value}(${render(node.left)},${render(node.right)})`;
}
function sampleTree() {
  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));
}

function insert(root, value) { if (root === null) return new Node(value); if (value < root.value) root.left = insert(root.left, value); else root.right = insert(root.right, value); return root; }
let root = null;
for (const value of [4, 2, 6, 1, 3, 5, 7]) root = insert(root, value);
console.log(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.