From 82a834af37cfb8e51f98ba2605787a46e90f8808 Mon Sep 17 00:00:00 2001
From: gikf <60067306+gikf@users.noreply.github.com>
Date: Tue, 15 Jun 2021 07:32:34 +0200
Subject: [PATCH] fix(curriculum): rework Project Euler 51 (#42459)

* fix: rework challenge to use argument in function

* fix: add solution
---
 .../problem-51-prime-digit-replacements.md    | 93 +++++++++++++++++--
 1 file changed, 85 insertions(+), 8 deletions(-)

diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-51-prime-digit-replacements.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-51-prime-digit-replacements.md
index 7190e580ae..d890d42133 100644
--- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-51-prime-digit-replacements.md
+++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-51-prime-digit-replacements.md
@@ -12,20 +12,32 @@ By replacing the 1st digit of the 2-digit number \*3, it turns out that six of t
 
 By replacing the 3rd and 4th digits of 56\*\*3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.
 
-Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.
+Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an `n` prime value family.
 
 # --hints--
 
-`primeDigitReplacements()` should return a number.
+`primeDigitReplacements(6)` should return a number.
 
 ```js
-assert(typeof primeDigitReplacements() === 'number');
+assert(typeof primeDigitReplacements(6) === 'number');
 ```
 
-`primeDigitReplacements()` should return 121313.
+`primeDigitReplacements(6)` should return `13`.
 
 ```js
-assert.strictEqual(primeDigitReplacements(), 121313);
+assert.strictEqual(primeDigitReplacements(6), 13);
+```
+
+`primeDigitReplacements(7)` should return `56003`.
+
+```js
+assert.strictEqual(primeDigitReplacements(7), 56003);
+```
+
+`primeDigitReplacements(8)` should return `121313`.
+
+```js
+assert.strictEqual(primeDigitReplacements(8), 121313);
 ```
 
 # --seed--
@@ -33,16 +45,81 @@ assert.strictEqual(primeDigitReplacements(), 121313);
 ## --seed-contents--
 
 ```js
-function primeDigitReplacements() {
+function primeDigitReplacements(n) {
 
   return true;
 }
 
-primeDigitReplacements();
+primeDigitReplacements(6);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function primeDigitReplacements(n) {
+  function isNFamily(number, primesMap, n) {
+    const prime = number.toString();
+    const lastDigit = prime[prime.length - 1];
+    return (
+      doesReplacingMakeFamily(prime, '0', primesMap, n) ||
+      (lastDigit !== '1' &&
+        doesReplacingMakeFamily(prime, '1', primesMap, n)) ||
+      doesReplacingMakeFamily(prime, '2', primesMap, n)
+    );
+  }
+
+  function doesReplacingMakeFamily(prime, digitToReplace, primesMap, family) {
+    let count = 0;
+    const replaceWith = '0123456789';
+
+    for (let i = 0; i < replaceWith.length; i++) {
+      const nextNumber = parseInt(
+        prime.replace(new RegExp(digitToReplace, 'g'), replaceWith[i]),
+        10
+      );
+
+      if (isPartOfFamily(nextNumber, prime, primesMap)) {
+        count++;
+      }
+    }
+    return count === family;
+  }
+
+  function isPartOfFamily(number, prime, primesMap) {
+    return (
+      isPrime(number, primesMap) && number.toString().length === prime.length
+    );
+  }
+
+  function getSievePrimes(max) {
+    const primesMap = new Array(max).fill(true);
+    primesMap[0] = false;
+    primesMap[1] = false;
+
+    for (let i = 2; i < max; i++) {
+      if (primesMap[i]) {
+        let j = i * i;
+        for (j; j < max; j += i) {
+          primesMap[j] = false;
+        }
+      }
+    }
+    return primesMap;
+  }
+
+  function isPrime(num, primesMap) {
+    return primesMap[num];
+  }
+
+  const primesMap = getSievePrimes(1000000);
+
+  for (let number = 1; number < 300000; number++) {
+    if (primesMap[number]) {
+      if (isNFamily(number, primesMap, n)) {
+        return number;
+      }
+    }
+  }
+  return -1;
+}
 ```