Fibonacci Number
The Fibonacci sequence starts from base values and each next number is the sum of the previous two.
Beginne mit diesem mentalen Modell
The Fibonacci sequence starts from base values and each next number is the sum of the previous two.
So funktioniert es – ohne unnötigen Jargon
Naive recursion recomputes the same subproblems and grows exponentially.
An iterative solution keeps only the previous two numbers, giving O(n) time and O(1) extra space.
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 Fibonacci Number, the goal is to make the invariant visible rather than to memorize code.
function fibonacci(n) {
let a = 0, b = 1;
for (let i = 0; i < n; i++) {
[a, b] = [b, a + b];
}
return a;
}Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.
O(n) iterative / O(2ⁿ) naive recursion
Do not quote this complexity mechanically.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
Use Fibonacci to explain overlapping subproblems, memoization and the difference between elegant-looking recursion and efficient recursion.
What problem does Fibonacci Number solve?
The Fibonacci sequence starts from base values and each next number is the sum of the previous two.
Was sollte ich zur Komplexität erwähnen?
Its typical cost here is O(n) iterative / O(2ⁿ) naive recursion, 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.