5a52c229f5
* fix: clean-up Project Euler 181-200 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
58 lines
1.7 KiB
Markdown
58 lines
1.7 KiB
Markdown
---
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id: 5900f4281000cf542c50ff39
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title: 'Problem 186: Connectedness of a network'
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challengeType: 5
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forumTopicId: 301822
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dashedName: problem-186-connectedness-of-a-network
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---
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# --description--
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Here are the records from a busy telephone system with one million users:
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| RecNr | Caller | Called |
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|-------|--------|--------|
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| 1 | 200007 | 100053 |
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| 2 | 600183 | 500439 |
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| 3 | 600863 | 701497 |
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| ... | ... | ... |
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The telephone number of the caller and the called number in record $n$ are $Caller(n) = S_{2n - 1}$ and $Called(n) = S_{2n}$ where ${S}_{1,2,3,\ldots}$ come from the "Lagged Fibonacci Generator":
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For $1 ≤ k ≤ 55$, $S_k = [100003 - 200003k + 300007{k}^3]\\;(\text{modulo}\\;1000000)$
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For $56 ≤ k$, $S_k = [S_{k - 24} + S_{k - 55}]\\;(\text{modulo}\\;1000000)$
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If $Caller(n) = Called(n)$ then the user is assumed to have misdialled and the call fails; otherwise the call is successful.
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From the start of the records, we say that any pair of users $X$ and $Y$ are friends if $X$ calls $Y$ or vice-versa. Similarly, $X$ is a friend of a friend of $Z$ if $X$ is a friend of $Y$ and $Y$ is a friend of $Z$; and so on for longer chains.
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The Prime Minister's phone number is 524287. After how many successful calls, not counting misdials, will 99% of the users (including the PM) be a friend, or a friend of a friend etc., of the Prime Minister?
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# --hints--
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`connectednessOfANetwork()` should return `2325629`.
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```js
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assert.strictEqual(connectednessOfANetwork(), 2325629);
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```
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# --seed--
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## --seed-contents--
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```js
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function connectednessOfANetwork() {
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return true;
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}
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connectednessOfANetwork();
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```
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# --solutions--
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```js
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// solution required
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```
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