斐波那契数列（滚动变量方法）-优快云博客

本文介绍了使用滚动变量方法优化斐波那契数列的计算，对比了其与递归解法在时间复杂度上的优势。

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斐波那契数列的小技巧

滚动变量方法：

原理图

public class Fibonacci {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        long a = 0,b = 1;
        while (n - 1 > 0){
            long c = a + b;
            a = b;
            b = c;
            n--;
        }
        System.out.println(a);
    }
}

与递归的时间比较

public class CompareFibonacci {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int m = scanner.nextInt();
        Fib1 fib1 = new Fib1();
        fib1.caleTime(m);
        System.out.println(fib1.code(m));
        Fib fib = new Fib();
        fib.caleTime(m);
        System.out.println(fib.code(m));

    }
}

abstract class TimeTest{
    abstract long code(int n);
    public void caleTime(int n){
        long start = System.currentTimeMillis();
        code(n);
        long end = System.currentTimeMillis();
        System.out.println("耗费时间： " + (end - start) + "ms");
    }
}

class Fib extends TimeTest{

    @Override
    long code(int n) {
        if(n == 1){
           return 0;
        }
        if(n == 2 || n == 3){
            return 1;
        }
        return code(n - 1) + code(n - 2);
    }
}

class Fib1 extends TimeTest{

    @Override
    long code(int n) {
        long a = 0, b = 1;
        while(n - 1 > 0){
            long c = a + b;
            a = b;
            b = c;
            n--;
        }
        return a;
    }
}