How to use a Threadpool with recursive jobs?

I have a simple usecase - I want to perform some operation on each file in a directory. For example, let's just say I want to print the file name. A very simple single threaded option for this is below -

Single threaded implementation

use std::{env, fs, path::Path, rc::Rc};fn main() {    let args = env::args().collect::<Vec<String>>();    let process: ProcessFunc = Rc::new(|p| println!("{p}"));    process_file_path(String::from("/playground/target/release/deps"), Rc::clone(&process));}type ProcessFunc = Rc<dyn Fn(String) + Send +'static>;fn process_file_path(source: String, f: ProcessFunc) {    let source_path = Path::new(&source)        .canonicalize()        .expect("invalid source path");    let source_path_str = source_path.as_path().to_str().unwrap().to_string();    f(source_path_str);    if source_path.is_dir() {        for child in fs::read_dir(source_path).unwrap() {            let child = child.unwrap();            process_file_path(                child.path().as_path().to_str().unwrap().to_string(),                Rc::clone(&f),            )        }    }}   

Since no file has dependency on any other file, I want to make it concurrent. To do that I am planning to use a thread-pool where each thread would wait on a channel to receive file paths and then perform the processing function on it.

The part I am not able to figure out is the termination of threads. The complexity is because of the fact that each job, i.e. path, itself can enqueue more jobs, i.e. one for path of each child of current path. So the question is how would threads know when to stop?

I can think of two approaches -

1. Add timeout to threads waiting for jobs - not fully reliable and can cause extra wait time for program.
2. Close thread when it processes a job that doesn't result in more jobs - this will cause close of almost all threads once they process a leaf node in the hierarchy of directories., thus not completing the rest of the jobs.

I tried to use two channels so that the part of deciding whether more jobs are there can be delegated to a dedicated single thread (main thread) but realized soon that the problem remains the same, i.e. how do we know that all jobs are complete.

Multi threaded implementation (Has only threadpool implementation with job and result channels but no usage in main function as I am not able to figure out).

struct ThreadPool<T> {    job_sender: Option<Sender<Box<dyn FnOnce() -> T + Send +'static>>>,    handles: Vec<JoinHandle<()>>,}impl<T> ThreadPool<T>where    T: Send +'static,{    fn new(cap: usize) -> (Self, Receiver<T>) {        assert_ne!(cap, 0);        let (job_sender, job_receiver) = channel::<Box<dyn FnOnce() -> T + Send +'static>>();        let (result_sender, result_receiver) = channel::<T>();        let result_sender = Arc::new(Mutex::new(result_sender));        let job_receiver = Arc::new(Mutex::new(job_receiver));        let mut handles = vec![];        for _i in 0..cap {            let job_receiver = Arc::clone(&job_receiver);            let result_sender = Arc::clone(&result_sender);            handles.push(thread::spawn(move || {                while let Ok(job) = job_receiver.lock().unwrap().recv() {                    result_sender.lock().unwrap().send(job()).unwrap();                }            }));        }        (            ThreadPool {                handles,                job_sender: Some(job_sender),            },            result_receiver,        )    }    fn add(&self, job: Box<dyn FnOnce() -> T + Send +'static>) {        self.job_sender.as_ref().unwrap().send(job).unwrap();    }}impl<T> Drop for ThreadPool<T> {    fn drop(&mut self) {        self.job_sender = None;        while let Some(handle) = self.handles.pop() {            handle.join().unwrap();        }    }}