sum(1)(2)(3) Complexity and Optimization

sum(1)(2)(3) Complexity and Optimization

Time Complexity

O(n) where n is the number of chained calls. Each call creates a new function and performs one addition.

Space Complexity

O(n) where n is the number of chained calls. Each call creates a new closure. However, since each call returns a new function and the old one is no longer referenced, the GC can free the old closures. In practice, the space is O(1) (only the current closure is alive).

Tail Call Optimization

In theory, return sum(a + b) is a tail call. If the JS engine supported tail call optimization (TCO), the space would be O(1). However, most JS engines (V8, SpiderMonkey) do not implement TCO. So the call stack grows.

Stack Overflow

For a very long chain (e.g., 10,000 calls), the call stack may overflow. In practice, this is not an issue because nobody chains 10,000 calls.

Optimization

If performance is critical (it usually is not for this question), use a loop instead:

function sum(...nums) {
  return nums.reduce((a, b) => a + b, 0);
}
sum(1, 2, 3); // 6 (not curried, but O(n) with no closure overhead)

The Takeaway

Time: O(n). Space: O(n) (call stack) or O(1) (if GC frees old closures). TCO is not available in most JS engines. Stack overflow is possible for very long chains but impractical. If performance matters, use a non-curried reduce.