Trees

Build a Binary Tree

Create a fixed seven-node binary tree and render its shape.

Algorithm

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

node links A node stores one value plus references to its left and right children.

Basic Implementation

basic.ts
Replay: real traced execution (multi-file project)
class Node {
  value: number;
  left: Node | null;
  right: Node | null;
  constructor(value: number, left: Node | null = null, right: Node | null = null) {
    this.value = value;
    this.left = left;
    this.right = right;
  }
}
function render(node: Node | null): string {
  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(): Node {
  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));
}

const root = sampleTree();
console.log(render(root));

  1. node ← 1, tree ← 1

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step1node1tree

  2. node ← 3, tree ← 1, 3

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step3node1, 3tree

  3. node ← 2, tree ← 2(1,3)

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step2node2(1,3)tree

  4. node ← 5, tree ← 2(1,3), 5

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step5node2(1,3), 5tree

  5. node ← 7, tree ← 2(1,3), 5, 7

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step7node2(1,3), 5, 7tree

  6. node ← 6, tree ← 2(1,3), 6(5,7)

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step6node2(1,3), 6(5,7)tree

  7. node ← 4, tree ← 4(2(1,3),6(5,7))

    16function sampleTree(): Node {17  return new Node(4, new Node(2, new Node(1), new Node(3)), new Node(6, new Node(5), new Node(7)));18}
    values this step4node4(2(1,3),6(5,7))tree

  8. stdout ← 4(2(1,3),6(5,7))

    1class Node {2  value: number;
    values this step4(2(1,3),6(5,7))stdout4(2(1,3),6(5,7))tree

Complexity

  • Time: O(n)
  • Space: O(n)

Implementation notes

  • Node is a TypeScript class with value: number, left: Node | null, and right: Node | null fields. The constructor defaults both child references to null, so leaves can be created with just new Node(value).
  • sampleTree(): Node wires the tree with nested constructor calls: node 2 receives 1 and 3, node 6 receives 5 and 7, and root 4 receives those two subtree objects.
  • The replay shows allocation bottom-up: create 1, create 3, create 2(1,3), create 5, create 7, create 6(5,7), then create 4(2(1,3),6(5,7)).
  • render(node: Node | null): string handles null as _, returns String(node.value) for leaves, and recursively formats internal nodes with their left and right renderings.
  • console.log(render(root)) prints 4(2(1,3),6(5,7)). Visible allocation is the seven Node objects and render/output strings; after construction the tree is not mutated.