Current Code Challenges
Your function is facing two main challenges. Firstly, there is unreachable code present:
function isPrime(...) {
if (...) {
return false
} else if (...) {
return true
} else {
return isPrime(...)
}
// The code after this point cannot be accessed as the function has already returned a value in a previous block.
}
Secondly, while you have included base cases, the function does not progress towards them:
function isPrime(number, divisor) {
if (number == 1) { // Base case for 'number'
return false;
} else if (number == 2) { // Base case for 'number'
return true;
} else {
return isPrime(number, ++divisor); // Recursive case where 'number' remains unchanged
}
// Even if this section was reachable, it faces the same issue of lack of progression.
}
In order for recursion to effectively work, each recursive call must lead towards a base case. If there is no clear progression towards the base case with each call, it becomes uncertain whether the program can complete successfully.
The Choice between Recursion and Iteration
A fundamental question arises – why opt for recursion in this scenario? Is it primarily for educational purposes, such as homework or personal study? While both recursion and iteration are powerful tools, the decision often hinges on the suitability of the data structure involved. For instance, when dealing with tree structures, recursion usually offers a cleaner solution. Conversely, for processing linear lists, either recursion or iteration may be more efficient.
In the current problem of identifying divisors, stopping at the first occurrence, a simple iterative approach suffices: checking divisibility by consecutive numbers until a factor is found. Recursion does not inherently provide a clearer or more elegant solution in this context.
(An important performance improvement tip is to halt once the square root of the target number is surpassed since any factors must be smaller than the square root.)
An Alternative Recursive Solution
Nevertheless, recursion can still be employed for implementation. Here is a possible recursive approach:
const isPrime = (n, d = 2) =>
d * d > n
? true
: n % d == 0
? false
: isPrime (n, d + 1)
console .log (isPrime (40)) //=> false
console .log (isPrime (41)) //=> true
Alternatively, following the style of your existing code:
function isPrime(n, d = 2) {
if (d * d > n) {
return true;
} else if (n % d == 0) {
return false;
} else {
return isPrime(n , d + 1)
}
}
Although we could also express it as:
const isPrime = (n, d = 2) =>
d * d > n || (n % d !== 0 && isPrime (n, d + 1))
This condensed form might obscure the understanding of the recursive process.
A More Suited Practice Problem for Recursion
If the goal is to enhance understanding of recursion, a related problem emphasizing its utility might be solving for all prime factors of n:
primeFactors(17) //=> [17]
primeFactors(18) //=> [2, 3, 3]
primeFactors(19) //=> [19]
primeFactors(20) //=> [2, 2, 5]
primeFactors(55440) //=> [2, 2, 2, 2, 3, 3, 5, 7, 11]
While this task can be tackled iteratively or recursively, recursive solutions often yield more elegant code.