Choose a data shape and follow the work it creates

First, build a mental model

A collection organizes data for particular questions. An algorithm is a repeatable procedure over that data. Complexity asks how its work or memory grows when the input grows, not how impressive its syntax looks.

1. An array preserves positions and order. A map connects keys to values. A set answers membership and uniqueness questions.
2. A linear scan may inspect n items. Two full nested scans can inspect n × n pairs; a suitable keyed lookup can avoid repeated scans, subject to its actual implementation and cost.
3. Recursion solves a smaller instance of the same problem. It needs a reachable base case and progress toward it.
4. Each unfinished recursive call retains work on the call stack. This simple sum uses O(n) time and O(n) stack space; an iterative sum can avoid that growing stack.
5. Big-O describes scaling, not exact milliseconds. Measure realistic input sizes and account for constants and runtime limits.

function sum(items, index = 0) {
  if (index >= items.length) return 0;
  return items[index] + sum(items, index + 1);
}
console.log(sum([2, 3, 4]));

1. Call 0

   Keep 2 pending and ask for the sum beginning at index 1.

2. Calls 1 and 2

   Keep 3, then 4 pending while index moves toward the array length.

3. Base case

   At index 3, return 0. Unwind: 4 + 0, then 3 + 4, then 2 + 7 = 9.