Factorial
n! is the product 1 × 2 × … × n, with 0! defined as 1.
Start with this mental model
n! is the product 1 × 2 × … × n, with 0! defined as 1.
How it works, without unnecessary jargon
It appears in permutations, combinations and probability formulas.
An iterative implementation avoids recursion overhead; large n quickly exceeds JavaScript Number precision.
Read the algorithm as a sequence of decisions
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;
}Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.
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Do not quote this complexity mechanically.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.
Good fit
- Use the direct mathematical property when it removes unnecessary brute force.
What usually goes wrong
- Ignoring floating-point precision or integer range.
- Using a formula outside its valid assumptions.
A professional answer shape
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.
What should I mention about complexity?
Its typical cost here is O(n), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
What is the most common mistake?
Ignoring floating-point precision or integer range.