Fibonacci Number
The Fibonacci sequence starts from base values and each next number is the sum of the previous two.
ابدأ بهذا النموذج الذهني
The Fibonacci sequence starts from base values and each next number is the sum of the previous two.
كيف يعمل، بلا مصطلحات زائدة
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.
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 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;
}لا تحفظ الصياغة. تتبع الحالة التي تتغير في كل سطر واربطها بالثابت الموضح أعلاه.
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Do not quote this complexity mechanically.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.
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
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.
ماذا يجب أن أذكر عن التعقيد؟
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.
ما الخطأ الأكثر شيوعاً؟
Ignoring floating-point precision or integer range.