lca.js

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": []
            }
          ]
        }
      ]
    }
  ]
}

// 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

function getLowestCommonAncestor(root, id1, id2) {
  const { id, children } = root;
  const isLeaf = children.length === 0;

  // node doesn't have a value
  if ( id === null ) return null;

  // node is a leaf and doesn't match
  if ( isLeaf && id !== id1 && id !== id2 ) return null;
  
  // node matches
  if ( id === id1 || id === id2 ) return id;

  const leftNode = getLowestCommonAncestor(children[0], id1, id2);
  const rightNode = getLowestCommonAncestor(children[1], id1, id2);

  if ( leftNode && rightNode ) return id;
  if ( !leftNode && !rightNode ) return null;

  return leftNode ? leftNode : rightNode;
}