js-simple-trees.js

const baseTree = {
  id: 'root',
  children: [
    {
      id: 'child0',
      children: [
        {
          id: 'child0-0',
          children: [
            {
              id: 'child0-0-0',
              children: [
                {
                  id: 'child0-0-0-0',
                  children: [
                    {
                      id: 'child0-0-0-0',
                      children: null,
                    },
                  ],
                },
              ],
            },
            {
              id: 'child0-0-1',
              children: null,
            },
          ],
        },
      ],
    },
    {
      id: 'child1',
      children: [
        {
          id: 'child1-0',
          children: null,
        },
      ],
    },
  ],
};

const iterationDfsGetIds = (tree) => {
  const stack = [tree];
  const result = [];
  while (stack.length > 0) {
    const { id, children } = stack.pop();
    result.push(id);
    if (children) {
      stack.push(...children);
    }
  }
  return result;
};

/*
Don't use this. Really. :) JavaScript does not perform tail recursion optimization, 
so if your recursion is too deep, you may get a call stack overflow. 
*/
const recursionDfsGetIds = (tree) => {
  const result = [tree.id];
  if (tree.children) {
    result.push(...tree.children.map((node) => recursionDfsGetIds(node)).flat());
  }
  return result;
};

const iterationBfsGetIds = (tree) => {
  const queue = [tree];
  const result = [];
  while (queue.length > 0) {
    const { id, children } = queue.shift();
    result.push(id);
    if (children) {
      queue.push(...children);
    }
  }
  return result;
};

const addParentIds = (tree) => {
  const newTree = JSON.parse(JSON.stringify(tree));
  // root node
  newTree.parentId = null;

  const queue = [newTree];

  while (queue.length > 0) {
    const node = queue.shift();

    if (node.children) {
      queue.push(
        ...node.children.map((child) => {
          // mutating the reference here intentionally
          child.parentId = node.id;
          return child;
        }),
      );
    }
  }
  return newTree;
};

console.log('iterationDfsGetIds', iterationDfsGetIds(baseTree));
console.log('recursionDfsGetIds', recursionDfsGetIds(baseTree));
console.log('iterationBfsGetIds', iterationBfsGetIds(baseTree));
console.log('addParentIds', JSON.stringify(addParentIds(baseTree), null, 2));