[Hacker Rank]: Project Euler #3: Largest prime factor. Solved ✓

Author: Gonzalo Diaz

docs/hackerrank/projecteuler/euler003-solution-notes.md

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+# About the **Largest prime factor** solution
+
+## Brute force method
+
+> [!WARNING]
+>
+> The penalty of this method is that it requires a large number of iterations as
+> the number grows.
+
+The first solution, using the algorithm taught in school, is:
+
+> Start by choosing a number $ i $ starting with $ 2 $ (the smallest prime number)
+> Test the divisibility of the number $ n $ by $ i $, next for each one:
+>
+>> - If $ n $ is divisible by $ i $, then the result is
+>> the new number $ n $ is reduced, while at the same time
+>> the largest number $i$ found is stored.
+>>
+>> - If $ n $ IS NOT divisible by $ i $, $i$ is incremented by 1
+> up to $ n $.
+>
+> Finally:
+>>
+>> - If you reach the end without finding any, it is because the number $n$
+>> is prime and would be the only factual prime it has.
+>>
+>> - Otherwise, then the largest number $i$ found would be the largest prime factor.
+
+## Second approach, limiting to half iterations
+
+> [!CAUTION]
+>
+> Using some test entries, quickly broke the solution at all. So, don't use it.
+> This note is just to record the failed idea.
+
+Since by going through and proving the divisibility of a number $ i $ up to $ n $
+there are also "remainder" numbers that are also divisible by their opposite,
+let's call it $ j $.
+
+At first it seemed attractive to test numbers $ i $ up to half of $ n $ then
+test whether $ i $ or $ j $ are prime. 2 problems arise:
+
+- Testing whether a number is prime could involve increasing the number of
+iterations since now the problem would become O(N^2) complex in the worst cases
+
+- Discarding all $ j $ could mean discarding the correct solution.
+
+Both problems were detected when using different sets of test inputs.
+
+## Final solution using some optimization
+
+> [!WARNING]
+>
+> No source was found with a mathematical proof proving that the highest prime
+> factor of a number n (non-prime) always lies under the limit of $ \sqrt{n} $
+
+A solution apparently accepted in the community as an optimization of the first
+brute force algorithm consists of limiting the search to $ \sqrt{n} $.
+
+Apparently it is a mathematical conjecture without proof
+(if it exists, please send it to me).
+
+Found the correct result in all test cases.

docs/hackerrank/projecteuler/euler003.md

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+# [Largest prime factor](https://www.hackerrank.com/contests/projecteuler/challenges/euler003)
+
+- Difficulty: #easy
+- Category: #ProjectEuler+
+
+The prime factors of $ 13195 $ are $ 5 $, $ 7 $, $ 13 $ and $ 29 $.
+
+What is the largest prime factor of a given number $ N $ ?
+
+## Input Format
+
+First line contains $ T $, the number of test cases. This is
+followed by $ T $ lines each containing an integer $ N $.
+
+## Constraints
+
+- $ 1 \leq T \leq 10 $
+- $ 10 \leq N \leq 10^{12} $
+
+## Output Format
+
+Print the required answer for each test case.
+
+## Sample Input 0
+
+```text
+2
+10
+17
+```
+
+## Sample Output 0
+
+```text
+5
+17
+```
+
+## Explanation 0
+
+- Prime factors of $ 10 $ are $ {2, 5} $, largest is $ 5 $.
+
+- Prime factor of $ 17 $ is $ 17 $ itselft, hence largest is $ 17 $.

src/lib/exercises/include/exercises/hackerrank/projecteuler/euler003.hpp

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+#pragma once
+
+namespace hackerrank::projecteuler {
+
+long euler003(long n);
+
+} // namespace hackerrank::projecteuler

src/lib/exercises/src/hackerrank/projecteuler/euler003.cpp

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+#include <exercises/hackerrank/projecteuler/euler003.hpp>
+
+/**
+ * @link Problem definition [[docs/hackerrank/projecteuler/euler003.md]]
+ */
+
+#include <cmath>
+#include <stdexcept>
+
+namespace hackerrank::projecteuler {
+
+long prime_factor(long n) {
+  if (n < 2) {
+    throw std::invalid_argument("n must be greater than 2");
+  }
+
+  long divisor = n;
+  long max_prime_factor;
+  bool mpf_initialized = false;
+
+  long i = 2;
+
+  while (static_cast<double>(i) <= sqrt(divisor)) {
+    if (0 == divisor % i) {
+      divisor = divisor / i;
+      max_prime_factor = divisor;
+      mpf_initialized = true;
+    } else {
+      i += 1;
+    }
+  }
+
+  if (!mpf_initialized) {
+    return n;
+  }
+
+  return max_prime_factor;
+}
+
+long euler003(long n) { return prime_factor(n); }
+
+} // namespace hackerrank::projecteuler

src/tests/unit/lib/hackerrank/projecteuler/euler003.test.cpp

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+#include <catch2/catch_test_macros.hpp>
+
+#include <exercises/hackerrank/projecteuler/euler003.hpp>
+#include <iostream>
+#include <vector>
+
+#include <filesystem>
+#include <fstream>
+#include <nlohmann/json.hpp>
+using json = nlohmann::json;
+
+TEST_CASE("euler003 JSON Test Cases",
+          "[hackerrank] [jsontestcase] [projecteuler]") {
+  std::filesystem::path cwd = std::filesystem::current_path();
+  std::string path =
+      cwd.string() +
+      "/unit/lib/hackerrank/projecteuler/euler003.testcases.json";
+
+  INFO("euler003 JSON test cases FILE: " << path);
+
+  std::ifstream f(path);
+  json data = json::parse(f);
+
+  for (auto testcase : data) {
+    long result = hackerrank::projecteuler::euler003(testcase["n"]);
+    CHECK(result == testcase["expected"]);
+  }
+}
+
+TEST_CASE("euler003 Edge Cases", "[hackerrank] [projecteuler]") {
+  CHECK_THROWS_AS(hackerrank::projecteuler::euler003(0), std::invalid_argument);
+  CHECK_THROWS_AS(hackerrank::projecteuler::euler003(1), std::invalid_argument);
+}

src/tests/unit/lib/hackerrank/projecteuler/euler003.testcases.json

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+[
+  { "n": 10, "expected": 5 },
+  { "n": 17, "expected": 17 }
+]