Java 中使用递归和循环程序实现斐波那契数列

在算术中，Wythoff 数组是由斐波那契数列生成的无限矩阵。

The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

使用 For 循环的 Java 斐波那契数列程序

//Using  For Loop
public class FibonacciExample {
	public static void main(String[] args) 
	{
		// Set it to the number of elements you want in the Fibonacci Series
		 int maxNumber = 10; 
		 int previousNumber = 0;
		 int nextNumber = 1;
	        System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
	        for (int i = 1; i <= maxNumber; ++i)
	        {
	            System.out.print(previousNumber+" ");
	            /* On each iteration, we are assigning second number
	             * to the first number and assigning the sum of last two
	             * numbers to the second number
	             */
 
	      
	            int sum = previousNumber + nextNumber;
	            previousNumber = nextNumber;
	            nextNumber = sum;
	        }
	}
}

输出

Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34

程序逻辑

• previousNumber 初始化为 0，nextNumber 初始化为 1
• 斐波那契 For 循环迭代 maxNumber
• 显示 previousNumber
• 计算 previousNumber 和 nextNumber 的总和
• 更新 previousNumber 和 nextNumber 的新值

使用 While 循环的 Java 斐波那契数列程序

您还可以使用 Java 中的 While 循环生成 Java 斐波那契数列

//Using  While Loop
public class FibonacciWhileExample {
	public static void main(String[] args) 
	{
		 int maxNumber = 10, previousNumber = 0, nextNumber = 1;
	        System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
 
	        int i=1;
	        while(i <= maxNumber)
	        {
	            System.out.print(previousNumber+" ");
	            int sum = previousNumber + nextNumber;
	            previousNumber = nextNumber;
	            nextNumber = sum;
	            i++;
	        }
 
	}
 
}

输出

Fibonacci Series of 10 numbers:0 1 1 2 3 5 8 13 21 34

程序逻辑的唯一区别在于使用 WHILE 循环打印斐波那契数

基于用户输入的斐波那契数列

//fibonacci series based on the user input
import java.util.Scanner;
public class FibonacciExample {
 
	public static void main(String[] args) 
	{
	
		 int maxNumber = 0; 
		 int previousNumber = 0;
		 int nextNumber = 1;
		 
		    System.out.println("How many numbers you want in Fibonacci:");
	        Scanner scanner = new Scanner(System.in);
	        maxNumber = scanner.nextInt();
	        System.out.print("Fibonacci Series of "+maxNumber+" numbers:");
 
	        for (int i = 1; i <= maxNumber; ++i)
	        {
	            System.out.print(previousNumber+" ");
	            /* On each iteration, we are assigning second number
	             * to the first number and assigning the sum of last two
	             * numbers to the second number
	             */
 
	      
	            int sum = previousNumber + nextNumber;
	            previousNumber = nextNumber;
	            nextNumber = sum;
	        }
 
	}
 
}

程序逻辑
逻辑与之前相同。与硬编码要显示在 Java 斐波那契数列中的元素数量相反，用户被要求输入数字。

Java 中使用递归的斐波那契数列

下面是一个使用递归的 Java 斐波那契数列程序

//Using Recursion
public class FibonacciCalc{
	public static int fibonacciRecursion(int n){
	if(n == 0){
		return 0;
	}
	if(n == 1 || n == 2){
			return 1;
		}
	return fibonacciRecursion(n-2) + fibonacciRecursion(n-1);
	}
    public static void main(String args[]) {
	int maxNumber = 10;
	System.out.print("Fibonacci Series of "+maxNumber+" numbers: ");
	for(int i = 0; i < maxNumber; i++){
			System.out.print(fibonacciRecursion(i) +" ");
		}
	}
}

输出

Fibonacci Series of 10 numbers: 0 1 1 2 3 5 8 13 21 34

程序逻辑

递归函数是能够调用自身的函数。

fibonacciRecursion()

1. Java 斐波那契递归函数接收一个输入数字。检查 0、1、2 并相应地返回 0、1、1，因为 Java 中的斐波那契数列以 0、1、1 开始。
2. 当输入 n 大于等于 3 时，该函数将递归调用自身。该调用执行两次。让我们以输入 4 为例，看看 Java 递归斐波那契数列。

fibonacciRecursion (4)  
	It will recursively call fibonacciRecursion function for values 2 and 3
		fibonacciRecursion (2) \\ call for value 0 and 1
			fibonacciRecursion (0) = 0
			fibonacciRecursion (1) = 1
		fibonacciRecursion (3) \\ It will call for 1 and 2
			fibonacciRecursion (1) = 1
			fibonacciRecursion (2) \\ It will call for 0 and 1
				fibonacciRecursion (0) = 0
				fibonacciRecursion (1) = 1

现在结果为 0+1+1+0+1=3

此代码可编辑。点击“运行”进行编译+执行