chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f50c1000cf542c51001e
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title: 问题415:泰坦尼克号集
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title: 'Problem 415: Titanic sets'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 302084
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dashedName: problem-415-titanic-sets
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---
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# --description--
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如果存在一条直线恰好经过S中的两个点,则一组晶格点S称为钛酸组。
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A set of lattice points S is called a titanic set if there exists a line passing through exactly two points in S.
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泰坦尼克集的示例是S = {(0,0),(0,1),(0,2),(1,1),(2,0),(1,0)},其中 通过(0,1)和(2,0)的通道不会通过S中的任何其他点。
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An example of a titanic set is S = {(0, 0), (0, 1), (0, 2), (1, 1), (2, 0), (1, 0)}, where the line passing through (0, 1) and (2, 0) does not pass through any other point in S.
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另一方面,集合{(0,0),(1,1),(2,2),(4,4)}不是泰坦尼克号集合,因为穿过集合中任意两点的线也经过 通过其他两个。
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On the other hand, the set {(0, 0), (1, 1), (2, 2), (4, 4)} is not a titanic set since the line passing through any two points in the set also passes through the other two.
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对于任何正整数N,令T(N)为每个点(x,y)都满足0≤x,y≤N的钛酸集合S的数量。 可以验证T(1)= 11,T(2)= 494,T(4)= 33554178,T(111)mod 108 = 13500401和T(105)mod 108 = 63259062。
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For any positive integer N, let T(N) be the number of titanic sets S whose every point (x, y) satisfies 0 ≤ x, y ≤ N. It can be verified that T(1) = 11, T(2) = 494, T(4) = 33554178, T(111) mod 108 = 13500401 and T(105) mod 108 = 63259062.
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找出T(1011)mod 108。
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Find T(1011) mod 108.
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# --hints--
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`euler415()`应该返回55859742。
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`euler415()` should return 55859742.
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```js
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assert.strictEqual(euler415(), 55859742);
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