Big O & problem solving

When describing asymptotic growth, keep the term that grows fastest. 7n² + 3n + 12 is O(n²): the n² term eventually outweighs the linear and constant terms.

This simplification makes it easier to compare algorithms across machines and implementations.

Write down the iteration count for each loop or recursive branch, combine sequential work by addition and nested work by multiplication, then keep the dominant term. Record stack space separately from the function's other extra memory.

An auxiliary map or array often reduces repeated work. State both sides of the trade: for example, a frequency map can turn repeated scans from O(n²) time into O(n) time while using O(n) extra space.

String methods return new strings instead of changing the original. Repeated concatenation in a loop can copy an ever-growing prefix each time. For a large sequence, collect parts in an array and join once.

function joinChars(chars: string[]): string {
  const parts: string[] = [];
  for (const char of chars) parts.push(char);
  return parts.join("");
}

As you work, say what invariant your code maintains, why each pointer or map changes, and what the largest input implies for complexity. If you get stuck, draw a small input and trace the state by hand.

You do not need to guess the intended pattern immediately. A clear path from contract to baseline to optimization is a reliable way to discover it.