Construct hierarchy tree from flat list with parent field?

function treeify(list, idAttr, parentAttr, childrenAttr) {
    if (!idAttr) idAttr = 'id';
    if (!parentAttr) parentAttr = 'parent';
    if (!childrenAttr) childrenAttr = 'children';

    var treeList = [];
    var lookup = {};
    list.forEach(function(obj) {
        lookup[obj[idAttr]] = obj;
        obj[childrenAttr] = [];
    });
    list.forEach(function(obj) {
        if (obj[parentAttr] != null) {
            if (lookup[obj[parentAttr]] !== undefined) {
                lookup[obj[parentAttr]][childrenAttr].push(obj);
            } else {
                 //console.log('Missing Parent Data: ' + obj[parentAttr]);
                 treeList.push(obj);
            }               
        } else {
            treeList.push(obj);
        }
    });
    return treeList;
};

Fiddle

The accepted answer was very helpful in my research, but, I had to mentally parse the id params which I understand make the function more flexible, but perhaps a bit harder to reason about for someone new to the algorithm.

In case someone else is has this difficulty, here's essentially the same code, but maybe easier to grok:

const treeify = (arr, pid) => {
  const tree = [];
  const lookup = {};
  // Initialize lookup table with each array item's id as key and 
  // its children initialized to an empty array 
  arr.forEach((o) => {
    lookup[o.id] = o;
    lookup[o.id].children = [];
  });
  arr.forEach((o) => {
    // If the item has a parent we do following:
    // 1. access it in constant time now that we have a lookup table
    // 2. since children is preconfigured, we simply push the item
    if (o.parent !== null) {
      lookup[o.parent].children.push(o);
    } else {
      // no o.parent so this is a "root at the top level of our tree
      tree.push(o);
    }
  });
  return tree;
};

It's the same code as accepted answer with some comments to explain what's going on. Here is a use case for this which will result in a list of divs rendered to page with inline marginLeft indentation based on the level:

const arr = [
  {id: 1, title: 'All', parent: null},
  {id: 2, title: 'Products', parent: 1},
  {id: 3, title: 'Photoshop', parent: 2},
  {id: 4, title: 'Illustrator', parent: 2},
  {id: 4, title: 'Plugins', parent: 3},
  {id: 5, title: 'Services', parent: 1},
  {id: 6, title: 'Branding', parent: 5},
  {id: 7, title: 'Websites', parent: 5},
  {id: 8, title: 'Pen Testing', parent: 7}];
const render = (item, parent, level) => {
  const div = document.createElement('div');
  div.textContent = item.title;
  div.style.marginLeft = level * 8 + 'px';
  parent.appendChild(div);
  if (item.children.length) {
    item.children.forEach(child => render(child, div, ++level));
  }
  return parent;
}
const fragment = document.createDocumentFragment();
treeify(arr)
  .map(item => render(item, fragment, 1))
  .map(frag => document.body.appendChild(frag))

Codepen if you'd like to run it: https://codepen.io/roblevin/pen/gVRowd?editors=0010

To my mind, the interesting part about this solution is that the lookup table remains flat using the IDs of the items as keys, and only the root object(s) get pushed into the resulting tree list. However, due to the referential nature of JavaScript objects, the root has its children, and children their children, and so on, but it's essentially connected from the root and hence tree-like.