Calculating complexity of js alghortim

Question

I'm trying to caluclate complexity of below method in Big O notation

function algorithm(n,m){
    let result = [];

    for (let i = 0; i < n.length; i++) {
      const total = m.filter((x) => x === n[i]).length;
  
      if (PrimalityTest(total)) {
        result.push(n[i]);
      }
    }
    return result;
  };


function PrimalityTest(c){
    if (c <= 1) {
        return false;
      } else if (c === 2) {
        return true;
      } else {
        for (let i = 2; i * i <= c; i++) {
          if (c % i === 0) {
            return false;
          }
        }
        return true;
      }
}

So, firstly there is loop which have O(n) and then there is nested loop and primality test function so that means complexity of all is O(n * m * sqrt(c))?

Can you please confirm If my understanding is correct?

Answer 1

The loop for (let i = 0; i < n.length; i++) is executed n times. The function m.filter((x) => x === n[i]).length checks every element in m, so executes m-times. So we have an execution time of O(n*m).

Considering

if (PrimalityTest(total)) {
      result.push(n[i]);
}

is executed n times because it is in the same loop as above. So at worst it is O(n*sqrt(c))

To sum it up: It is O(n*m)+O(n*sqrt(c)). Because O(n*m) surpasses O(n*sqrt(c)) we get as result: O(n*m).

Your solution would mean that the filter function integrates the PrimalityTest method.