fibonacci-number

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Algorithms

The Fibonacci numbers, commonly denoted <code>F(n)</code> form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from <code>0</code> and <code>1</code>. That is,

<pre>
F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n &gt; 1.
</pre>

Given <code>n</code>, calculate <code>F(n)</code>.

&nbsp;
Example 1:

<pre>
Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
</pre>

Example 2:

<pre>
Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
</pre>

Example 3:

<pre>
Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>0 &lt;= n &lt;= 30</code></li>
</ul>

Fibonacci Number

Climbing Stairs

climbing-stairs

爬楼梯

Split Array into Fibonacci Sequence

split-array-into-fibonacci-sequence

将数组拆分成斐波那契序列

Length of Longest Fibonacci Subsequence

length-of-longest-fibonacci-subsequence

最长的斐波那契子序列的长度

N-th Tribonacci Number

n-th-tribonacci-number

第 N 个泰波那契数

Recursion

Memoization

Math

Dynamic Programming

斐波那契数&nbsp;（通常用&nbsp;<code>F(n)</code> 表示）形成的序列称为 斐波那契数列 。该数列由&nbsp;<code>0</code> 和 <code>1</code> 开始，后面的每一项数字都是前面两项数字的和。也就是：

<pre>
F(0) = 0，F(1)&nbsp;= 1
F(n) = F(n - 1) + F(n - 2)，其中 n &gt; 1
</pre>

给定&nbsp;<code>n</code> ，请计算 <code>F(n)</code> 。

&nbsp;

示例 1：

<pre>
输入：n = 2
输出：1
解释：F(2) = F(1) + F(0) = 1 + 0 = 1
</pre>

示例 2：

<pre>
输入：n = 3
输出：2
解释：F(3) = F(2) + F(1) = 1 + 1 = 2
</pre>

示例 3：

<pre>
输入：n = 4
输出：3
解释：F(4) = F(3) + F(2) = 2 + 1 = 3
</pre>

&nbsp;

提示：

<ul>
	<li><code>0 &lt;= n &lt;= 30</code></li>
</ul>