斐波那契数列 PHP

用外行的语言来说，斐波那契数列就是通过将前两个元素相加形成下一个元素，直到得到所需的数列大小而形成或获得的一系列元素。我们通常从 0 和 1 开始斐波那契数列。

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系列一旦形成，如下：

0, 1, 1, 2 ,3, 5, 8, 13, 21, 34

如上所述，下一个数字是前两个数字相加而成的。

• 上述序列中第 4 个 位置（第 n^第 位置）上的“2”是通过将其前面的两个数字相加获得的[ [n-1]和 n-2]), 1.
• ‘3’是通过将其前面的两个数字 2 相加得到的。
• ‘5’是通过将其前面的两个数字 3 相加得到的。
• 等等。

PHP 中的斐波那契系列及其逻辑

在这里，我们将看到在 PHP 环境中工作时具体获取斐波那契数列。区别在于我们编码的格式，即使用 PHP 脚本的起始标签及其结束标签。

<?php …;
…;
…;
?>

这将帮助您理解和学习如何在 PHP 中使用迭代方式和递归方式两种方法生成斐波那契数列。

当给我们一个数字，即“n”（系列大小）时，我们将尝试找到不超过给定数字的斐波那契系列。

例如，如果我们需要为 n=5 创建斐波那契，我们将显示元素直到第 5 项。

示例#1

• 输入：n = 9
• 输出：0 1 1 2 3 5 8 13 21

示例 #2

• 输入：n=13
• 输出： 0 1 1 2 3 5 8 13 21 34 55 89 144

PHP 中的逻辑

逻辑与上述相同。这里我们给定 n=10，即我们需要找到直到第 n 项的元素。因此，我们将继续遵循我们的逻辑，直到我们的系列中有 n 个术语。

让我们看一下上面给出的示例之一。

在上面的一个示例中，我们有 n=9，逻辑表示：

• 将第一个数字初始化为 0。
• 将第二个数字初始化为 1。
• 打印第一个和第二个数字。
• 循环从这里开始。
• 对于系列中的下一个元素，即第 3^rd 元素 [n^th 元素]，我们将添加其紧邻的前两个数字 [(n-1) 和 (n- 2)] 获取该系列中的下一个数字，如下所示，0 + 1 = 1。

对于 n=3

• n – 1 = 3 – 1 = 系列的第二个元素 = 1
• n – 2 = 3 – 2 = 系列的第一个元素 = 0 3^rd 元素 = (n-1) + (n-2) = 1 + 0 = 1

因此，级数中的第三个元素是 1。

• 类似地，根据逻辑，要获得该系列的第 4^第 元素 [n]，我们需要添加其前面的数字 e。 (n-1) 和 (n-2) 元素。

此时，‘n’等于‘4’：

• n – 1 = 4 – 1 = 系列的第 3 个元素 = 1
• n – 2 = 4 – 2 = 系列中的第 2 个元素 = 1 4^第 元素 = (n-1) + (n-2) = 1 + 1 = 2

因此，我们得到第 4 个^第 元素为 2。

因此，对于“n”等于 9，按照与上面解释相同的逻辑，我们得到序列为，斐波那契序列是 0 1 1 2 3 5 8 13 21

使用两种方法进行斐波那契打印的 PHP 系列

关于如何用 PHP 编写程序来打印斐波那契数列，基本上有两个著名的版本：

• 没有递归
• 使用递归

像 PHP 中一样，我们将使用“echo”语句来打印输出。

1.非递归方式

也称为使用迭代。在这种方法中，我们将从 0 和 1 开始序列。之后我们将打印第一个和第二个数字。接下来我们将使用循环开始迭代，这里我们使用 while 循环。

用于打印前 10 个斐波那契数列元素的 PHP 脚本。

代码：

<?php function Fibonacci($n)
{
$num1= 0;
$num2= 1;
$counter= 0; while($counter < $n)
{
echo ' '.$num1;
$num3= $num2 + $num1;
$num1= $num2;
$num2= $num3;
$counter= $counter+1;
}
}
//for a pre defined number for Fibonacci.
$n=10; Fibonacci($n);
?>

代码说明：

1. Here n is defined as equal to 10, so the logic will run till nth element e. Until we have n=10 elements in the series.
2. First element is initialized to 0 and second element is initialized to 1, e. num1 = 0 and num2 = 1.
3. The two elements i.e. num1 and num2 are printed as the first and second elements of the Fibonacci series.
4. The logic we discussed will be used from here on and our iteration loop starts.
5. According to our logic, to get num3, we need to add num1 and num2. Since currently num1 = 0 and num2 = 1, num3 comes out as 1.
6. Now new number obtained is placed in num2 variable and num2 is saved in num1 variable. Basically simple swapping is taking place so that, now num1 is equal to ‘1’ and num2 = newly obtained num3 i.e. ‘1’.
7. So when the next iteration happens and num3 is obtained by adding current values of num1 and num2, which, according to our PHP script, are as follows:

• • • num1 = 1
    • num2 = 1
    • num3 = num1 + num2 = 1 + 1 = 2

Thus we get our next number in the Fibonacci Series.

8. Similarly, the iteration keeps on till we achieve n = 10, size of the series that was defined in the program itself.

When the above program is executed, we get the output as follows:

2. The Recursion Way

By recursion, we mean the way where the same function is called repeatedly until a base condition is achieved or matched. At this point, recursion is stopped.

The said “function is called repeatedly” phrase points to the section in your code where we will define our logic for the Fibonacci Series.

Below is an example of generating Fibonacci Series in PHP, using If-Else conditions giving way for our recursive approach.

Here is the PHP Scripts for printing the first 15 elements for Fibonacci Series.

<?php function Fibonacci($num)
{
//If-Else IF will generate first two numbers for the series if($num == 0)
return 0;
else if($num == 1) return 1;
// This is where Recursive way comes in.
//recursive call to get the rest of the numbers in the series else
return(Fibonacci($num -1) + Fibonacci( $num -2));
}
//For a given n=15
$num =15;
for($counter = 0; $counter < $num; $counter++)
{
echo Fibonacci($counter).' ';
}
?>

Code Explanation:

This is the recursive way, which means our function that contains our logic is called again and again for generating the next element in the series until our condition for achieving a specific series size is obtained.

In Iterative approaches, the First and Second element is first initialized and printed. Here we allow a For Loop to give us our first and second elements starting with 0 and 1.

1. We are using a For loop having a ‘counter’ variable that starts with 0. The For loop works up till the given ‘n’, size for the series.
2. when loop starts, with the counter variable as 0, we use the recursion approach and call our defined function, Fibonacci ( ).
3. Here code starts, with If and Else IF condition.
4. First IF condition checks if ‘num’ variable holds value as ‘0’, if yes, then the code prints or returns ‘0’ as the element for the series.
5. Similarly, second Else-If condition checks for the value ‘1’, if the ‘num’ variable holds ‘1’ as its value, the program returns it as it is.
6. Next Else condition recursively calls the Fibonacci function for’ num’ values other than ‘0’ and ‘1’, continuing to reading the values from the For loop counter.

This is where our Fibonacci Logic comes into work and the next number in the sequence is obtained by adding its previous two numbers. Because this is the recursive method, we need to give a counter value to count the recursions equal to nth value, which is being handled by our For Loop.

When the above program or code is executed, the following output is displayed.

The Fibonacci Series does not only appear in mathematics or science calculations but in nature too, have you ever noticed Yellow chamomile flower head.

The Fibonacci Series if plotted on a graph, it forms a spiral called Fibonacci Spiral. It is also one of the gems given by Indian soil. It is found in Indian Mathematics as early as 200 BC in the works done by the mathematician, Pingala. Later Fibonacci introduced the sequence to European countries in his book Liber Abacci in 1200s.

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