Java 實作費波那契數列：陣列迭代法完整範例

費波那契數列定義

F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2) (n≥2)。常見變體為 1,1,2,3,5,8…（省略首項 0）。

迭代陣列實作（O(n) 時間、O(n) 空間）

public class FibonacciDemo {

    public static void main(String[] args) {
        printFibonacci(10); // 列印前 10 項
    }

    public static void printFibonacci(int count) {
        if (count <= 0) return;

        int[] fib = new int[count];
        fib[0] = 1;
        if (count > 1) fib[1] = 1;

        for (int i = 2; i < count; i++) {
            fib[i] = fib[i - 1] + fib[i - 2];
        }

        for (int n : fib) {
            System.out.print(n + " ");
        }
        System.out.println();
    }
}

執行結果

1 1 2 3 5 8 13 21 34 55

進階優化方向

滾動變數 O(1) 空間版本

public static void printFibonacciO1(int count) {
    if (count <= 0) return;
    int a = 1, b = 1;
    System.out.print(a + " ");
    if (count == 1) return;
    System.out.print(b + " ");
    for (int i = 2; i < count; i++) {
        int c = a + b;
        System.out.print(c + " ");
        a = b;
        b = c;
    }
    System.out.println();
}

大數處理提示

第 47 項起超過 int 上限，第 93 項超過 long，實務上請改用 BigInteger：

BigInteger a = BigInteger.ONE, b = BigInteger.ONE;
for (int i = 2; i < count; i++) {
    BigInteger c = a.add(b);
    a = b; b = c;
}