[Hacker Rank] Interview Preparation Kit: Miscellaneous: Time Complexi…

docs/hackerrank/interview_preparation_kit/miscellaneous/ctci-big-o.md

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+# [Time Complexity: Primality](https://www.hackerrank.com/challenges/ctci-big-o)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingBasic`
+
+## Using bitwise operations
+
+A prime is a natural number greater than `1` that has no positive divisors other
+than `1` and itself.
+Given `p` integers, determine the primality of each integer and return `Prime`
+or `Not prime` on a new line.
+
+**Note**: If possible, try to come up with an $ \mathcal{O}(\sqrt{n}) $
+primality algorithm, or see what sort of optimizations you can come up with for
+san $ \mathcal{O}(\sqrt{n}) $ algorithm. Be sure to check out the Editorial
+after submitting your code.
+
+## Function Description
+
+Complete the primality function in the editor below.
+primality has the following parameter(s):
+
+- `int` n: an integer to test for primality
+
+## Returns
+
+- string: Prime if  is prime, or Not prime
+
+## Input Format
+
+The first line contains an integer, , the number of integers to check for primality.
+Each of the  subsequent lines contains an integer, , the number to test.
+
+## Constraints
+
+- $ 1 \leq p \leq 30 $
+- $ 1 \leq n \leq 2 × 10^9 $
+
+## Sample Input
+
+```text
+STDIN   Function
+-----   --------
+3       p = 3 (number of values to follow)
+12      n = 12 (first number to check)
+5       n = 5
+7       n = 7
+```
+
+## Sample Output
+
+```text
+Not prime
+Prime
+Prime
+```
+
+## Explanation
+
+We check the following $ p = 3 $ integers for primality:
+
+1. $ n = 12 $ is divisible by numbers other than $ 1 $ and itself
+  (i.e.: $ 2 $, $ 3 $, $ 4 $, $ 6 $).
+1. $ n = 5 $ is only divisible  and itself.
+1. $ n = 7 $ is only divisible  and itself.

src/algorithm_exercises_csharp/hackerrank/interview_preparation_kit/miscellaneous/TimeComplexityPrimality.cs

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+// @link Problem definition [[docs/hackerrank/interview_preparation_kit/miscellaneous/ctci-big-o.md]]
+
+namespace algorithm_exercises_csharp.hackerrank.interview_preparation_kit.miscellaneous;
+
+using System.Diagnostics.CodeAnalysis;
+using System.Text;
+
+
+public static class TimeComplexityPrimality
+{
+  private const string PRIME = "Prime";
+  private const string NOT_PRIME = "Not prime";
+
+
+  private static Int32? primeFactor(int n)
+  {
+    if (n < 2)
+    {
+      return null;
+    }
+
+    int divisor = n;
+    Int32? maxPrimeFactor = null;
+    int i = 2;
+    while (i <= Math.Sqrt(divisor))
+    {
+      if (divisor % i == 0)
+      {
+        divisor = divisor / i;
+        maxPrimeFactor = i;
+      }
+      else
+      {
+        i += 1;
+      }
+    }
+
+    if (maxPrimeFactor == null)
+    {
+      return n;
+    }
+
+    return maxPrimeFactor;
+  }
+
+
+  /**
+   * primality.
+   */
+  public static string primality(int n)
+  {
+    Int32? pf = primeFactor(n);
+
+    return (pf == null || pf != n) ? NOT_PRIME : PRIME;
+  }
+}

src/algorithm_exercises_csharp_test/Resources/hackerrank/interview_preparation_kit/miscellaneous/ctci_big_o.testcases.json

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+[
+  {
+    "title": "Sample Test case 0",
+    "tests": [
+      {
+        "input": 12,
+        "answer": "Not prime"
+      },
+      {
+        "input": 5,
+        "answer": "Prime"
+      },
+      {
+        "input": 7,
+        "answer": "Prime"
+      }
+    ]
+  },
+  {
+    "title": "Sample Test case 1",
+    "tests": [
+      {
+        "input": 31,
+        "answer": "Prime"
+      },
+      {
+        "input": 33,
+        "answer": "Not prime"
+      }
+    ]
+  },
+  {
+    "title": "Sample Test case 2",
+    "tests": [
+      {
+        "input": 2,
+        "answer": "Prime"
+      },
+      {
+        "input": 7,
+        "answer": "Prime"
+      },
+      {
+        "input": 1982,
+        "answer": "Not prime"
+      },
+      {
+        "input": 14582734,
+        "answer": "Not prime"
+      },
+      {
+        "input": 9891,
+        "answer": "Not prime"
+      }
+    ]
+  },
+  {
+    "title": "Sample Test case 0",
+    "tests": [
+      {
+        "input": 1,
+        "answer": "Not prime"
+      }
+    ]
+  }
+]

src/algorithm_exercises_csharp_test/hackerrank/interview_preparation_kit/miscellaneous/TimeComplexityPrimalityTest.cs

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+namespace algorithm_exercises_csharp_test.hackerrank.interview_preparation_kit.miscellaneous;
+
+using algorithm_exercises_csharp_test.common;
+using algorithm_exercises_csharp.hackerrank.interview_preparation_kit.miscellaneous;
+
+[TestClass]
+public class TimeComplexityPrimalityTest
+{
+  public class TimeComplexityPrimalityTestCaseTest(int input, String answer)
+  {
+    public int Input { get; } = input;
+    public String Answer { get; } = answer;
+  }
+
+  public class TimeComplexityPrimalityTestCase(string title, List<TimeComplexityPrimalityTestCaseTest> tests)
+  {
+    public string Title { get; } = title;
+    public List<TimeComplexityPrimalityTestCaseTest> Tests { get; } = tests;
+  }
+
+  private List<TimeComplexityPrimalityTestCase> testCases { get; set; } = default!;
+
+  [TestInitialize]
+  public void testInitialize()
+  {
+    testCases = JsonLoader.resourceLoad<List<TimeComplexityPrimalityTestCase>>(
+      "hackerrank/interview_preparation_kit/miscellaneous/ctci_big_o.testcases.json"
+    ) ?? [];
+  }
+
+  [TestMethod]
+  public void testTimeComplexityPrimality()
+  {
+    foreach (TimeComplexityPrimalityTestCase tests in testCases)
+    {
+      foreach (TimeComplexityPrimalityTestCaseTest test in tests.Tests)
+      {
+        String result = TimeComplexityPrimality.primality(test.Input);
+
+        Assert.AreEqual(
+          test.Answer,
+          result,
+          string.Format(
+            System.Globalization.CultureInfo.InvariantCulture,
+            "TimeComplexityPrimality.primality({0}) => must be: {1}",
+            test.Input,
+            test.Answer
+          )
+        );
+      }
+    }
+  }
+}