84 lines
1.9 KiB
Markdown
84 lines
1.9 KiB
Markdown
---
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id: 5900f39d1000cf542c50feb0
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title: 问题49:主要排列
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challengeType: 5
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videoUrl: ''
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dashedName: problem-49-prime-permutations
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---
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# --description--
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算术序列1487,4817,8147,其中每个项增加3330,在两个方面是不寻常的:(i)三个项中的每一个都是素数,并且,(ii)每个4位数字是彼此的排列。没有由三个1位,2位或3位数的素数组成的算术序列,表现出这种性质,但还有另外一个4位数的增加序列。你通过连接这个序列中的三个术语来形成12位数字?
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# --hints--
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`primePermutations()`应该返回296962999629。
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```js
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assert.strictEqual(primePermutations(), 296962999629);
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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 primePermutations() {
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return true;
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}
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primePermutations();
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```
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# --solutions--
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```js
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function primePermutations() {
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function arePermutations(num1, num2) {
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const numStr1 = num1.toString();
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let numStr2 = num2.toString();
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if (numStr1.length !== numStr2.length) {
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return false;
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}
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for (let i = 0; i < numStr1.length; i++) {
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const index = numStr2.indexOf(numStr1[i]);
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if (index === -1) {
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return false;
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}
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numStr2 = numStr2.slice(0, index) + numStr2.slice(index + 1);
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}
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return true;
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}
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function isPrime(num) {
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if (num < 2) {
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return false;
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} else if (num === 2) {
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return true;
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}
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const sqrtOfNum = Math.floor(num ** 0.5);
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for (let i = 2; i <= sqrtOfNum + 1; i++) {
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if (num % i === 0) {
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return false;
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}
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}
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return true;
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}
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for (let num1 = 1000; num1 <= 9999; num1++) {
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const num2 = num1 + 3330;
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const num3 = num2 + 3330;
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if (isPrime(num1) && isPrime(num2) && isPrime(num3)) {
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if (arePermutations(num1, num2) && arePermutations(num1, num3)
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&& num1 !== 1487) {
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// concatenate and return numbers
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return (num1 * 100000000) + (num2 * 10000) + num3;
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}
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}
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}
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return 0;
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}
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```
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