Factorial
n! is the product 1 × 2 × … × n, with 0! defined as 1.
ابدأ بهذا النموذج الذهني
n! is the product 1 × 2 × … × n, with 0! defined as 1.
كيف يعمل، بلا مصطلحات زائدة
It appears in permutations, combinations and probability formulas.
An iterative implementation avoids recursion overhead; large n quickly exceeds JavaScript Number precision.
اقرأ الخوارزمية كسلسلة من القرارات
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;
}لا تحفظ الصياغة. تتبع الحالة التي تتغير في كل سطر واربطها بالثابت الموضح أعلاه.
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Do not quote this complexity mechanically.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.
مناسب لـ
- Use the direct mathematical property when it removes unnecessary brute force.
ما الذي يسوء عادةً
- Ignoring floating-point precision or integer range.
- Using a formula outside its valid assumptions.
صيغة إجابة احترافية
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.
ماذا يجب أن أذكر عن التعقيد؟
Its typical cost here is O(n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
ما الخطأ الأكثر شيوعاً؟
Ignoring floating-point precision or integer range.