98 lines
2.8 KiB
Markdown
98 lines
2.8 KiB
Markdown
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---
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id: 5e4ce2f5ac708cc68c1df261
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title: Linear congruential generator
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challengeType: 5
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forumTopicId: 385266
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dashedName: linear-congruential-generator
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---
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# --description--
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The [linear congruential generator](https://en.wikipedia.org/wiki/linear congruential generator) is a very simple example of a [random number generator](http://rosettacode.org/wiki/random number generator). All linear congruential generators use this formula:
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$$r_{n + 1} = (a \times r_n + c) \bmod m$$
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Where:
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<ul>
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<li>$ r_0 $ is a seed.</li>
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<li>$r_1$, $r_2$, $r_3$, ..., are the random numbers.</li>
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<li>$a$, $c$, $m$ are constants.</li>
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</ul>
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If one chooses the values of $a$, $c$ and $m$ with care, then the generator produces a uniform distribution of integers from $0$ to $m - 1$.
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LCG numbers have poor quality. $r_n$ and $r\_{n + 1}$ are not independent, as true random numbers would be. Anyone who knows $r_n$ can predict $r\_{n + 1}$, therefore LCG is not cryptographically secure. The LCG is still good enough for simple tasks like [Miller-Rabin primality test](http://rosettacode.org/wiki/Miller-Rabin primality test), or [FreeCell deals](http://rosettacode.org/wiki/deal cards for FreeCell). Among the benefits of the LCG, one can easily reproduce a sequence of numbers, from the same $r_0$. One can also reproduce such sequence with a different programming language, because the formula is so simple.
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# --instructions--
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Write a function that takes $r_0,a,c,m,n$ as parameters and returns $r_n$.
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# --hints--
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`linearCongGenerator` should be a function.
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```js
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assert(typeof linearCongGenerator == 'function');
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```
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`linearCongGenerator(324, 1145, 177, 2148, 3)` should return a number.
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```js
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assert(typeof linearCongGenerator(324, 1145, 177, 2148, 3) == 'number');
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```
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`linearCongGenerator(324, 1145, 177, 2148, 3)` should return `855`.
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```js
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assert.equal(linearCongGenerator(324, 1145, 177, 2148, 3), 855);
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```
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`linearCongGenerator(234, 11245, 145, 83648, 4)` should return `1110`.
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```js
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assert.equal(linearCongGenerator(234, 11245, 145, 83648, 4), 1110);
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```
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`linearCongGenerator(85, 11, 1234, 214748, 5)` should return `62217`.
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```js
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assert.equal(linearCongGenerator(85, 11, 1234, 214748, 5), 62217);
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```
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`linearCongGenerator(0, 1103515245, 12345, 2147483648, 1)` should return `12345`.
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```js
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assert.equal(linearCongGenerator(0, 1103515245, 12345, 2147483648, 1), 12345);
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```
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`linearCongGenerator(0, 1103515245, 12345, 2147483648, 2)` should return `1406932606`.
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```js
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assert.equal(
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linearCongGenerator(0, 1103515245, 12345, 2147483648, 2),
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1406932606
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);
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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 linearCongGenerator(r0, a, c, m, n) {
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}
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```
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# --solutions--
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```js
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function linearCongGenerator(r0, a, c, m, n) {
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for (let i = 0; i < n; i++) {
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r0 = (a * r0 + c) % m;
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}
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return r0;
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}
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```
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