Factorial
n! is the product 1 × 2 × … × n, with 0! defined as 1.
이 멘탈 모델부터 시작하세요
n! is the product 1 × 2 × … × n, with 0! defined as 1.
불필요한 전문용어 없이 동작 방식 이해하기
It appears in permutations, combinations and probability formulas.
An iterative implementation avoids recursion overhead; large n quickly exceeds JavaScript Number precision.
알고리즘을 연속된 의사결정으로 읽기
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;
}문법을 외우지 마세요. 각 줄에서 바뀌는 상태를 따라가고 위에서 설명한 불변식과 연결하세요.
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Do not quote this complexity mechanically.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.
적합한 경우
- Use the direct mathematical property when it removes unnecessary brute force.
보통 어디에서 문제가 생기는가
- Ignoring floating-point precision or integer range.
- Using a formula outside its valid assumptions.
전문적인 답변 구조
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.
복잡도에 대해 무엇을 언급해야 하나요?
Its typical cost here is O(n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
가장 흔한 실수는 무엇인가요?
Ignoring floating-point precision or integer range.