49 lines
1.4 KiB
Markdown
49 lines
1.4 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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RecNrCallerCalled120000710005326001835004393600863701497......... The telephone number of the caller and the called number in record n are Caller(n) = S2n-1 and Called(n) = S2n where S1,2,3,... come from the "Lagged Fibonacci Generator":
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For 1 ≤ k ≤ 55, Sk = \[100003 - 200003k + 300007k3] (modulo 1000000) For 56 ≤ k, Sk = \[Sk-24 + Sk-55] (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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`euler186()` should return 2325629.
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```js
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assert.strictEqual(euler186(), 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 euler186() {
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return true;
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}
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euler186();
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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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