2018-10-10 18:03:03 -04:00
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---
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id: 5900f4b01000cf542c50ffc2
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2020-12-16 00:37:30 -07:00
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title: 问题323:对随机整数进行按位或运算
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2018-10-10 18:03:03 -04:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 03:31:00 +01:00
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dashedName: problem-323-bitwise-or-operations-on-random-integers
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2018-10-10 18:03:03 -04:00
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---
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2020-12-16 00:37:30 -07:00
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# --description--
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2020-02-18 01:40:55 +09:00
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2020-12-16 00:37:30 -07:00
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令y0,y1,y2,...是随机无符号32位整数的序列
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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(即0≤yi <232,每个值的可能性均等)。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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对于序列xi,给出以下递归:x0 = 0且
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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xi = xi-1 | yi-1,对于i>0。(|是按位或运算符)
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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可以看出,对于所有i≥N,最终将存在一个索引N,使得xi = 232 -1(所有比特的位模式)。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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找到N的期望值。 将答案四舍五入到小数点后10位。
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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# --hints--
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2018-10-10 18:03:03 -04:00
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2020-12-16 00:37:30 -07:00
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`euler323()`应该返回6.3551758451。
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2018-10-10 18:03:03 -04:00
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```js
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2020-12-16 00:37:30 -07:00
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assert.strictEqual(euler323(), 6.3551758451);
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2018-10-10 18:03:03 -04:00
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```
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2021-01-13 03:31:00 +01:00
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# --seed--
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## --seed-contents--
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```js
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function euler323() {
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return true;
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}
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euler323();
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```
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2020-12-16 00:37:30 -07:00
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# --solutions--
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2020-08-13 17:24:35 +02:00
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2021-01-13 03:31:00 +01:00
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```js
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// solution required
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```
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