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48 lines
1.1 KiB
Markdown
48 lines
1.1 KiB
Markdown
---
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id: 5900f4b01000cf542c50ffc2
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title: 'Problem 323: Bitwise-OR operations on random integers'
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challengeType: 5
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forumTopicId: 301980
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dashedName: problem-323-bitwise-or-operations-on-random-integers
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---
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# --description--
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Let $y_0, y_1, y_2, \ldots$ be a sequence of random unsigned 32 bit integers (i.e. $0 ≤ y_i < 2^{32}$, every value equally likely).
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For the sequence $x_i$ the following recursion is given:
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- $x_0 = 0$ and
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- $x_i = x_{i - 1} \mathbf{|} y_{i - 1}$, for $i > 0$. ($\mathbf{|}$ is the bitwise-OR operator)
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It can be seen that eventually there will be an index $N$ such that $x_i = 2^{32} - 1$ (a bit-pattern of all ones) for all $i ≥ N$.
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Find the expected value of $N$. Give your answer rounded to 10 digits after the decimal point.
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# --hints--
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`bitwiseOrOnRandomIntegers()` should return `6.3551758451`.
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```js
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assert.strictEqual(bitwiseOrOnRandomIntegers(), 6.3551758451);
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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 bitwiseOrOnRandomIntegers() {
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return true;
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}
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bitwiseOrOnRandomIntegers();
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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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