chore(i18n,curriculum): update translations (#43661)

This commit is contained in:
camperbot
2021-10-03 12:24:27 -07:00
committed by GitHub
parent 3f79710779
commit 504ed3a917
535 changed files with 2158 additions and 116 deletions

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@ -8,30 +8,34 @@ dashedName: problem-137-fibonacci-golden-nuggets
# --description-- # --description--
Consider the infinite polynomial series AF(x) = xF1 + x2F2 + x3F3 + ..., where Fk is the kth term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ... ; that is, Fk = Fk1 + Fk2, F1 = 1 and F2 = 1. 考慮無窮級數 $A_{F}(x) = xF_1 + x^2F_2 + x^3F_3 + \ldots$,其中 $F_k$ 是斐波那契數列 $1, 1, 2, 3, 5, 8, \ldots$ 的第 $k$ 項;即 $F_k = F_{k 1} + F_{k 2}, F_1 = 1$$F_2 = 1$。
For this problem we shall be interested in values of x for which AF(x) is a positive integer. 在這個問題中,我們關注的是那些使得 $A_{F}(x)$ 爲正整數的 $x$ 的值。
Surprisingly AF(1/2) 令人驚訝的是:
= $$\begin{align} A_F(\frac{1}{2}) & = (\frac{1}{2}) × 1 + {(\frac{1}{2})}^2 × 1 + {(\frac{1}{2})}^3 × 2 + {(\frac{1}{2})}^4 × 3 + {(\frac{1}{2})}^5 × 5 + \cdots \\\\ & = \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \cdots \\\\ & = 2 \end{align}$$
(1/2).1 + (1/2)2.1 + (1/2)3.2 + (1/2)4.3 + (1/2)5.5 + ... 前五個對應的自然數 $x$ 如下。
= 1/2 + 1/4 + 2/8 + 3/16 + 5/32 + ... | $x$ | $A_F(x)$ |
| --------------------------- | -------- |
| $\sqrt{2} 1$ | $1$ |
| $\frac{1}{2}$ | $2$ |
| $\frac{\sqrt{13} 2}{3}$ | $3$ |
| $\frac{\sqrt{89} 5}{8}$ | $4$ |
| $\frac{\sqrt{34} 3}{5}$ | $5$ |
= 2 The corresponding values of x for the first five natural numbers are shown below. 當 $x$ 是有理數時,我們稱 $A_F(x)$ 是一個金磚,因爲這樣的數字逐漸變得稀少;例如,第 10 個金磚是 74049690。
xAF(x) √211 1/22 (√132)/33 (√895)/84 (√343)/55 請求出第 15 個金磚。
We shall call AF(x) a golden nugget if x is rational, because they become increasingly rarer; for example, the 10th golden nugget is 74049690. Find the 15th golden nugget.
# --hints-- # --hints--
`euler137()` should return 1120149658760. `goldenNugget()` 應該返回 `1120149658760`
```js ```js
assert.strictEqual(euler137(), 1120149658760); assert.strictEqual(goldenNugget(), 1120149658760);
``` ```
# --seed-- # --seed--
@ -39,12 +43,12 @@ assert.strictEqual(euler137(), 1120149658760);
## --seed-contents-- ## --seed-contents--
```js ```js
function euler137() { function goldenNugget() {
return true; return true;
} }
euler137(); goldenNugget();
``` ```
# --solutions-- # --solutions--

View File

@ -1,6 +1,6 @@
--- ---
id: 5900f37a1000cf542c50fe8d id: 5900f37a1000cf542c50fe8d
title: 'Problem 14: Longest Collatz sequence' title: '問題 14最長考拉茲序列'
challengeType: 5 challengeType: 5
forumTopicId: 301768 forumTopicId: 301768
dashedName: problem-14-longest-collatz-sequence dashedName: problem-14-longest-collatz-sequence
@ -8,61 +8,61 @@ dashedName: problem-14-longest-collatz-sequence
# --description-- # --description--
The following iterative sequence is defined for the set of positive integers: 對正整數集定義如下迭代序列:
<div style='padding-left: 4em;'><var>n</var><var>n</var>/2 (<var>n</var> is even)</div> <div style='padding-left: 4em;'><var>n</var><var>n</var> / 2<var>n</var> 爲偶數)</div>
<div style='padding-left: 4em;'><var>n</var> → 3<var>n</var> + 1 (<var>n</var> is odd)</div> <div style='padding-left: 4em;'><var>n</var> → 3<var>n</var> + 1<var>n</var> 爲奇數)</div>
Using the rule above and starting with 13, we generate the following sequence: 從 13 開始使用上述規則,我們可以得到如下序列:
<div style='text-align: center;'>13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1</div> <div style='text-align: center;'>13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1</div>
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1. 可以看出,該序列(從 13 開始到 1 結束)共包含 10 項。 雖然考拉茲猜想尚未得到證明,但是該猜想認爲以任意數字開始,序列均到 1 結束。
Which starting number, under the given `limit`, produces the longest chain? 求出在小於 `limit` 的數中,哪個可以產生最長的考拉茲序列?
**Note:** Once the chain starts the terms are allowed to go above one million. **注意:** 序列中數字的個數允許超過一百萬。
# --hints-- # --hints--
`longestCollatzSequence(14)` should return a number. `longestCollatzSequence(14)` 應該返回一個數字。
```js ```js
assert(typeof longestCollatzSequence(14) === 'number'); assert(typeof longestCollatzSequence(14) === 'number');
``` ```
`longestCollatzSequence(14)` should return 9. `longestCollatzSequence(14)` 應該返回 9
```js ```js
assert.strictEqual(longestCollatzSequence(14), 9); assert.strictEqual(longestCollatzSequence(14), 9);
``` ```
`longestCollatzSequence(5847)` should return 3711. `longestCollatzSequence(5847)` 應該返回 3711
```js ```js
assert.strictEqual(longestCollatzSequence(5847), 3711); assert.strictEqual(longestCollatzSequence(5847), 3711);
``` ```
`longestCollatzSequence(46500)` should return 35655. `longestCollatzSequence(46500)` 應該返回 35655
```js ```js
assert.strictEqual(longestCollatzSequence(46500), 35655); assert.strictEqual(longestCollatzSequence(46500), 35655);
``` ```
`longestCollatzSequence(54512)` should return 52527. `longestCollatzSequence(54512)` 應該返回 52527
```js ```js
assert.strictEqual(longestCollatzSequence(54512), 52527); assert.strictEqual(longestCollatzSequence(54512), 52527);
``` ```
`longestCollatzSequence(100000)` should return 77031. `longestCollatzSequence(100000)` 應該返回 77031
```js ```js
assert.strictEqual(longestCollatzSequence(100000), 77031); assert.strictEqual(longestCollatzSequence(100000), 77031);
``` ```
`longestCollatzSequence(1000000)` should return 837799. `longestCollatzSequence(1000000)` 應該返回 837799
```js ```js
assert.strictEqual(longestCollatzSequence(1000000), 837799); assert.strictEqual(longestCollatzSequence(1000000), 837799);

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