2018-10-10 18:03:03 -04:00
|
|
|
|
---
|
|
|
|
|
id: 5900f4531000cf542c50ff65
|
2020-12-16 00:37:30 -07:00
|
|
|
|
title: 问题230:斐波纳契语
|
2018-10-10 18:03:03 -04:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
2021-01-13 03:31:00 +01:00
|
|
|
|
dashedName: problem-230-fibonacci-words
|
2018-10-10 18:03:03 -04:00
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
# --description--
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
对于任何两个数字串A和B,我们将FA,B定义为序列(A,B,AB,BAB,ABBAB,...),其中每个术语是前两个术语的串联。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
此外,我们将DA,B(n)定义为FA的第一项中的第n个数字,B包含至少n个数字。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
例:
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
设A = 1415926535,B = 8979323846。我们希望找到DA,B(35)。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
FA,B的前几个术语是:1415926535 8979323846 14159265358979323846 897932384614159265358979323846 14159265358979323846897932384614159265358979323846
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
然后DA,B(35)是第五项中的第35位,即9。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
现在我们使用A小数点后面的前100位数字:14159265358979323846264338327950288419716939937510 58209749445923078164062862089986280348253421170679
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
对于B下一百个数字:
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
82148086513282306647093844609550582231725359408128 48111745028410270193852110555964462294895493038196。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
求Σn= 0,1,...,17 10n×DA,B((127 + 19n)×7n)。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
# --hints--
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
`euler230()`应返回850481152593119200。
|
2018-10-10 18:03:03 -04:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 00:37:30 -07:00
|
|
|
|
assert.strictEqual(euler230(), 850481152593119200);
|
2018-10-10 18:03:03 -04:00
|
|
|
|
```
|
2020-08-13 17:24:35 +02:00
|
|
|
|
|
2021-01-13 03:31:00 +01:00
|
|
|
|
# --seed--
|
|
|
|
|
|
|
|
|
|
## --seed-contents--
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function euler230() {
|
|
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
euler230();
|
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 00:37:30 -07:00
|
|
|
|
# --solutions--
|
|
|
|
|
|
2021-01-13 03:31:00 +01:00
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|