fibonacci number & fibonacci sequence All In One

fibonacci number & fibonacci sequence All In One

斐波那契数 / 斐波那契数列

https://www.mathsisfun.com/numbers/fibonacci-sequence.html

http://www.shuxuele.com/numbers/fibonacci-sequence.html

best practice / 最佳实践

在 ES6 规范中，有一个尾调用优化，可以实现高效的尾递归方案。

ES6 的尾调用优化只在严格模式下开启，正常模式是无效的。

// 在 ES6 规范中，有一个尾调用优化，可以实现`高效`的`尾递归`方案。
// ES6 的尾调用优化只在`严格模式`下开启，正常模式是无效的。
      

'use strict'
function fib(n, current = 0, next = 1) {
    if(n == 0) return 0;
    if(n == 1) return next;
    return fib(n - 1, next, current + next);
}

fib(32)
2178309
fib(64)
10610209857723
fib(100)
354224848179262000000

function f(num) {
  let n1 = 0;
  let n2 = 1;
  while (num) {
    // swap
    [
      n1,
      n2,
    ] = [
      n2,
      (n1 + n2),
    ];
    // const temp = n1 + n2;
    // n1 = n2;
    // n2 = temp;
    num -= 1;
  }
  return n2;
}


f(100);
573147844013817200000

https://www.cnblogs.com/xgqfrms/p/14116628.html

Fibonacci Sequence

300 : 222232244629420445529739893461909967206666939096499764990979600

https://r-knott.surrey.ac.uk/Fibonacci/fibtable.html

https://www.rapidtables.com/math/number/fibonacci.html

fibonacci sequence with cache

"use strict";

/**
 *
 * @author xgqfrms
 * @license MIT
 * @copyright xgqfrms
 * @created 2020-05-17
 * @modified
 *
 * @description  fibonacci 算法缓存优化 javascript
 * @augments
 * @example
 * @link https://en.wikipedia.org/wiki/Fibonacci_number
 *
 */


/*

  for n = 0 and n = 1, Fn = F(n)

  F0 = 0
  F1 = 1

  for n > 1, Fn = F(n - 1) + F(n - 2);

  F2 = F1 + F0 = 1
  F3 = F2 + F1 = 2
  F4 = F3 + F2 = 3
  F5 = F4 + F3 = 5
  ...

  The beginning of the fibonacci sequence is thus:

  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

*/

const log = console.log;


const fib = (n) => {
  const caches = [0, 1];
  if(n > 1 && typeof caches[n] === "undefined") {
    const temp = fib(n - 2) + fib(n - 1);
    caches[n] = temp;
  }
  // log(`caches[n]`, n, caches[n])
  return caches[n];
}

// const fib = (n) => {
//   const caches = [0, 1];
//   if(n === 0 || n === 1) {
//     return caches[n];
//   } else {
//     if(typeof caches[n] === "undefined") {
//       const temp = fib(n - 2) + fib(n - 1);
//       caches[n] = temp;
//     }
//     // log(`caches[n]`, n, caches[n])
//     return caches[n];
//   }
// }

// const fib = (n) => {
//   const caches = [0, 1];
//   if(n === 0 || n === 1) {
//       return caches[n];
//   } else {
//     // log(`caches[n]`, n, caches[n])
//     if(typeof caches[n] !== "undefined") {
//       return caches[n];
//     } else {
//       const temp = fib(n- 2) + fib(n- 1);
//       caches[n] = temp;
//       return temp;
//     }
//   }
// }

const v0 = fib(0)
log(`fib0`, v0)

const v1 = fib(1)
log(`fib1`, v1)

const v3 = fib(3)
log(`fib3`, v3)

const v5 = fib(5)
log(`fib5`, v5)

Fibonacci memory 缓存优化

// USING MEMOIZATION
function fibonacci(n,memo) {
  memo = memo || {}
  if (memo[n]) {
      return memo[n]
  }
  if (n <= 1) {
      return 1
  }
  return memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)
}

Fibonacci languages race rank sorter

https://9wlnh.csb.app/

hackster

https://www.hackster.io/users/preferences?show_welcome=true

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