chore(i8n,learn): processed translations
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Mrugesh Mohapatra
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---
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id: 5900f51a1000cf542c51002d
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title: 问题430:范围翻转
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title: 'Problem 430: Range flips'
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challengeType: 5
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videoUrl: ''
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forumTopicId: 302101
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dashedName: problem-430-range-flips
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---
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# --description--
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N个磁盘连续放置,从左到右从1到N索引。
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N disks are placed in a row, indexed 1 to N from left to right.
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每个磁盘都有黑色和白色的一面。 最初,所有磁盘都显示白色的一面。
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Each disk has a black side and white side. Initially all disks show their white side.
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在每一回合,随机地均匀地选择介于1和N(含)之间的两个整数A和B(不一定是不同的)。 索引从A到B(包括B)的所有磁盘均被翻转。
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At each turn, two, not necessarily distinct, integers A and B between 1 and N (inclusive) are chosen uniformly at random. All disks with an index from A to B (inclusive) are flipped.
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以下示例显示了N = 8的情况。在第一圈A = 5且B = 2,在第二圈A = 4且B = 6。
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The following example shows the case N = 8. At the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6.
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令E(N,M)为M圈后显示白色面的预期磁盘数量。 我们可以验证E(3,1)= 10/9,E(3,2)= 5/3,E(10,4)≈5,157和E(100,10)≈51,893。
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Let E(N, M) be the expected number of disks that show their white side after M turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.
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找出E(1010,4000)。 将答案四舍五入到小数点后两位。
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Find E(1010, 4000). Give your answer rounded to 2 decimal places behind the decimal point.
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# --hints--
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`euler430()`应该返回5000624921.38。
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`euler430()` should return 5000624921.38.
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```js
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assert.strictEqual(euler430(), 5000624921.38);
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