[Algorithm] Tree Width with Level Width

// --- Directions
// Given the root node of a tree, return
// an array where each element is the width
// of the tree at each level.
// --- Example
// Given:
//
//   / |  \
// 1   2   3
// |       |
// 4       5
// Answer: [1, 3, 2]

function levelWidth(root) {
  let counts = [0];
  let levels = [root, "$end$"];
  // [1, 3, 2]
  // ["e"]

  while (levels.length > 1) {
    const current = levels.shift();
    if (current === "$end$") {
      counts[counts.length] = 0;
      levels.push("$end$");
    } else {
      const { children } = current;
      for (let node of children) {
        levels.push(node);
      }
      counts[counts.length - 1]++;
    }
  }

  return counts;
}

module.exports = levelWidth;

Test:

const Node = require('./node');
const levelWidth = require('./index');

test('levelWidth is a function', () => {
  expect(typeof levelWidth).toEqual('function');
});

test('levelWidth returns number of nodes at widest point', () => {
  const root = new Node(0);
  root.add(1);
  root.add(2);
  root.add(3);
  root.children[0].add(4);
  root.children[2].add(5);

  expect(levelWidth(root)).toEqual([1, 3, 2]);
});

test('levelWidth returns number of nodes at widest point', () => {
  const root = new Node(0);
  root.add(1);
  root.children[0].add(2);
  root.children[0].add(3);
  root.children[0].children[0].add(4);

  expect(levelWidth(root)).toEqual([1, 1, 2, 1]);
});