getLowestCommonDenominator challenge

getLowestCommonDenominator.js

// write a function getLowestCommonAncestor(root, id1, id2)
// it should return the lowest common ancestor
// getLowestCommonAncestor(root, 13, 13) === 13
// getLowestCommonAncestor(root, 14, 14) === 14
// getLowestCommonAncestor(root, 13, 14) === 6
// getLowestCommonAncestor(root, 12, 14) === 2
// getLowestCommonAncestor(root, 7, 14) === 0

const root = {
  id: 0,
  children: [
    {
      id: 1,
      children: [
        {
          id: 3,
          children: [
            {
              id: 7,
              children: [],
            },
            {
              id: 8,
              children: [],
            },
          ],
        },
        {
          id: 4,
          children: [
            {
              id: 9,
              children: [],
            },
            {
              id: 10,
              children: [],
            },
          ],
        },
      ],
    },
    {
      id: 2,
      children: [
        {
          id: 5,
          children: [
            {
              id: 11,
              children: [],
            },
            {
              id: 12,
              children: [],
            },
          ],
        },
        {
          id: 6,
          children: [
            {
              id: 13,
              children: [],
            },
            {
              id: 14,
              children: [],
            },
          ],
        },
      ],
    },
  ],
}

const getPaths = (paths, node, currentPath) => ({
  ...paths,
  [node.id]: currentPath,
  ...node.children.reduce(
    (acc, val) => ({
      ...acc,
      ...getPaths(acc, val, [...currentPath, val.id]),
    }),
    {}
  ),
})

const getLowestCommonAncestor = (root, id1, id2) => {
  const paths = getPaths({}, root, [root.id])
  const path1 = paths[id1]
  const path2 = paths[id2]
  return path1.reverse().find(a => path2.includes(a))
}

console.log([
  getLowestCommonAncestor(root, 13, 13) === 13,
  getLowestCommonAncestor(root, 14, 14) === 14,
  getLowestCommonAncestor(root, 13, 14) === 6,
  getLowestCommonAncestor(root, 12, 14) === 2,
  getLowestCommonAncestor(root, 7, 14) === 0,
])

// This solution would ideally involve a cache 
// of some sort so that `paths` isn't calculated 
// on every call