51 lines
1.1 KiB
Markdown
51 lines
1.1 KiB
Markdown
---
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id: 5900f4481000cf542c50ff5a
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title: 'Problem 219: Skew-cost coding'
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challengeType: 5
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forumTopicId: 301861
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dashedName: problem-219-skew-cost-coding
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---
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# --description--
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Let A and B be bit strings (sequences of 0's and 1's).
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If A is equal to the leftmost length(A) bits of B, then A is said to be a prefix of B.
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For example, 00110 is a prefix of 001101001, but not of 00111 or 100110.
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A prefix-free code of size n is a collection of n distinct bit strings such that no string is a prefix of any other. For example, this is a prefix-free code of size 6:
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0000, 0001, 001, 01, 10, 11
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Now suppose that it costs one penny to transmit a '0' bit, but four pence to transmit a '1'. Then the total cost of the prefix-free code shown above is 35 pence, which happens to be the cheapest possible for the skewed pricing scheme in question. In short, we write Cost(6) = 35.
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What is Cost(109) ?
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# --hints--
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`euler219()` should return 64564225042.
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```js
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assert.strictEqual(euler219(), 64564225042);
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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 euler219() {
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return true;
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}
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euler219();
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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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