110 lines
2.1 KiB
Markdown
110 lines
2.1 KiB
Markdown
---
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id: 5900f3951000cf542c50fea8
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title: 问题41：Pandigital prime
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challengeType: 5
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videoUrl: ''
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dashedName: problem-41-pandigital-prime
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---
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# --description--
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我们将说*n*数字是pandigital，如果它使用所有数字1到*n*恰好一次。例如，2143是一个4位数的pandigital，也是素数。什么是最大的*n长*数字pandigital素数？
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# --hints--
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`pandigitalPrime(4)`应该返回4231。
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```js
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assert(pandigitalPrime(4) == 4231);
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```
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`pandigitalPrime(7)`应该返回7652413。
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```js
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assert(pandigitalPrime(7) == 7652413);
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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 pandigitalPrime(n) {
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return n;
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}
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pandigitalPrime(7);
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```
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# --solutions--
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```js
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function pandigitalPrime(n) {
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function isPrime(num) {
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for (let i = 2, s = Math.sqrt(num); i <= s; 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 num !== 1;
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}
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function getPermutations(n) {
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if (n === 1) {
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permutations.push(digitsArr.join(''));
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} else {
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for (let i = 0; i < n - 1; i++) {
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getPermutations(n - 1);
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// swap(n % 2 === 0 ? i : 0, n - 1);
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if (n % 2 === 0) {
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swap(i, n - 1);
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} else {
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swap(0, n - 1);
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}
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}
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getPermutations(n - 1);
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}
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}
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function swap(x, y) {
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let temp = digitsArr[x];
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digitsArr[x] = digitsArr[y];
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digitsArr[y] = temp;
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}
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let max = 0;
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let permutations = [];
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let digitsArr;
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let pandigitalNum = '';
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for (let max = n; max > 0; max--) {
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pandigitalNum += max;
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}
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for (let i = 0; i < pandigitalNum.length; i++) {
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if (max > 0) {
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break;
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} else {
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permutations = [];
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const currMax = pandigitalNum.slice(i);
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digitsArr = currMax.split('');
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getPermutations(digitsArr.length);
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// sort permutations in descending order
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permutations.sort(function(a, b) {
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return b - a;
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});
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for (let perm of permutations) {
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const thisPerm = parseInt(perm);
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if (isPrime(thisPerm)) {
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max = thisPerm;
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break;
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}
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}
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}
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}
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return max;
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}
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```
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