104 lines
2.8 KiB
Markdown
104 lines
2.8 KiB
Markdown
---
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id: 5900f39c1000cf542c50feae
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challengeType: 5
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title: 'Problem 47: Distinct primes factors'
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forumTopicId: 302145
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localeTitle: 'Проблема 47: Определенные коэффициенты простых чисел'
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---
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## Description
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<section id='description'>
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Первые два последовательных номера имеют два разных основных фактора: <div style="padding-left: 4em;"> 14 = 2 × 7 </div><div style="padding-left: 4em;"> 15 = 3 × 5 </div> Первые три последовательных номера имеют три различных основных фактора: <div style="padding-left: 4em;"> 644 = 2 × × 7 × 23 </div><div style="padding-left: 4em;"> 645 = 3 × 5 × 43 </div><div style="padding-left: 4em;"> 646 = 2 × 17 × 19 </div> Найдите первые четыре последовательных целых числа, каждый из которых имеет четыре различных основных фактора. Каков первый из этих чисел?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>distinctPrimeFactors(2, 2)</code> should return 14.
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testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14);
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- text: <code>distinctPrimeFactors(3, 3)</code> should return 644.
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testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644);
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- text: <code>distinctPrimeFactors(4, 4)</code> should return 134043.
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testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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// Good luck!
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return true;
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}
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distinctPrimeFactors(4, 4);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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function numberOfPrimeFactors(n) {
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let factors = 0;
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// Considering 2 as a special case
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let firstFactor = true;
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while (n % 2 == 0) {
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n = n / 2;
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if (firstFactor) {
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factors++;
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firstFactor = false;
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}
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}
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// Adding other factors
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for (let i = 3; i < Math.sqrt(n); i += 2) {
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firstFactor = true;
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while (n % i == 0) {
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n = n / i;
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if (firstFactor) {
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factors++;
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firstFactor = false;
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}
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}
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}
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if (n > 1) { factors++; }
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return factors;
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}
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let number = 0;
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let consecutive = 0;
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while (consecutive < targetConsecutive) {
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number++;
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if (numberOfPrimeFactors(number) >= targetNumPrimes) {
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consecutive++;
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} else {
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consecutive = 0;
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}
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}
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return number - targetConsecutive + 1;
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}
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```
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</section>
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