fibonacci all in one
fibonacci sequence
https://www.mathsisfun.com/numbers/fibonacci-sequence.html
fibonacci number
https://en.wikipedia.org/wiki/Fibonacci_number
"use strict";
/**
*
* @author xgqfrms
* @license MIT
* @copyright xgqfrms
* @created 2020-09-30
* @modified
*
* @description fibonacci all in one
* @difficulty Easy
* @complexity O(n)
* @augments
* @example
* @link https://www.cnblogs.com/xgqfrms/p/13757617.html
* @link https://www.freecodecamp.org/learn/ fibo
* @link https://www.freecodecamp.org/learn/coding-interview-prep/project-euler/problem-2-even-fibonacci-numbers
* @solutions
*
* @best_solutions
*
*/
const log = console.log;
// 1. 递归
// 2. 迭代
// 3. 性能优化 cache
1. 递归
fibonacci 递归
// 1. 递归
function fibonacci(n) {
if(n > 0) {
if (n === 1 || n === 2) {
return 1;
} else {
return fibonacci(n - 1) + fibonacci(n - 2);
}
} else {
throw new Error(`N must bigger than 0!`);
}
}
``
## 2. 迭代
> fibonacci 迭代
```js
// 2. 迭代
function fibonacci(n) {
if (n === 1 || n === 2) {
return 1;
} else {
let sum = 2;
let temp1 = 1;
let temp2 = 1;
while(n > 2) {
sum = temp1 + temp2;
// swap
temp1 = temp2;
temp2 = sum;
n--;
}
return sum;
}
}
3. 性能优化 cache
fibonacci memory 缓存优化
// 性能优化 cache
function fibonacci(n, memo) {
if(n < 0) {
throw new Error(`N must bigger than 0!`);
}
var memo = memo || {}
// ReferenceError: Cannot access 'memo' before initialization
// let memo = memo || {}
if (memo[n]) {
return memo[n];
}
if (n <= 2) {
return 1;
}
// if (n <= 1) {
// return 1;
// }
return memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo);
}
fibonacci sequence vs 杨辉三角
https://zh.wikipedia.org/wiki/杨辉三角形
杨辉三角形，又称帕斯卡三角形、贾宪三角形、海亚姆三角形、巴斯卡三角形，是二项式系数的一种写法，形似三角形;
在中国首现于南宋杨辉的《详解九章算法》得名，书中杨辉说明是引自贾宪的《释锁算书》，故又名贾宪三角形。前 9 行写出来如下：
１
１ １
１ ２ １
１ ３ ３ １
１ ４ ６ ４ １
１ ５ 10 10 ５ １
１ ６ 15 20 15 ６ １
１ ７ 21 35 35 21 ７ １
１ ８ 28 56 70 56 28 ８ １
refs
https://www.cnblogs.com/xgqfrms/p/12909516.html
©xgqfrms 2012-2020
www.cnblogs.com 发布文章使用：只允许注册用户才可以访问！