Given an input representing a filesystem, and two files, find the closest folder containing both files.

Boilerplate

function findParent(root, a, b) {
  //implement this function
}

class FileNode {
	children: Array<FileNode>
	name: string
	
	constructor(name) {
    this.children = [];
    this.name = name;
  }

  addChild(file: FileNode) {
    this.children.push(file)
  }
}

/*
Example

root ->
  a ->
    c
    d
  b    
*/

const root = new FileNode('root')
const [a,b,c,d] = ['abcd'].split('').map(char => new FileNode(char))      

root.addChild(a)
root.addChild(b)
a.addChild(c)
a.addChild(d)

findParent(root, a, b)
//-> root

findParent(root, c, d)
//-> a

We expect you to:

1. Provide an elegant and performant implementation of this function
2. An explanation of the algorithm used and a correct implementation

Tips:

1. You can solve this challenge in any language of your choosing
2. Create more test cases to ensure correctness beyond the example in the boilerplate
3. Feel free to accommodate the input and format to your convenience - we care about the function implementation the most