Factorial
n! is the product 1 × 2 × … × n, with 0! defined as 1.
Beginne mit diesem mentalen Modell
n! is the product 1 × 2 × … × n, with 0! defined as 1.
So funktioniert es – ohne unnötigen Jargon
It appears in permutations, combinations and probability formulas.
An iterative implementation avoids recursion overhead; large n quickly exceeds JavaScript Number precision.
Lies den Algorithmus als Folge von Entscheidungen
State the mathematical identity/property.
Choose numeric representation and constraints.
Translate the property into an iterative/recursive computation and analyze precision.
Read a tiny input by hand and write down the state after every important operation. For Factorial, the goal is to make the invariant visible rather than to memorize code.
function factorial(n) {
if (!Number.isInteger(n) || n < 0) throw new Error("n must be a non-negative integer");
let result = 1;
for (let i = 2; i <= n; i++) result *= i;
return result;
}Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.
O(n)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Gut geeignet
- Use the direct mathematical property when it removes unnecessary brute force.
Was typischerweise schiefgeht
- Ignoring floating-point precision or integer range.
- Using a formula outside its valid assumptions.
Struktur einer professionellen Antwort
State the base case and complexity O(n). If constraints are large, mention overflow/precision rather than treating numeric range as unlimited.
What problem does Factorial solve?
n! is the product 1 × 2 × … × n, with 0! defined as 1.
Was sollte ich zur Komplexität erwähnen?
Its typical cost here is O(n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
Was ist der häufigste Fehler?
Ignoring floating-point precision or integer range.