[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/hackerrank/interview_preparation_kit/miscellaneous/ctci_big_o.py

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+# pylint: disable=line-too-long
+# @link Problem definition [[docs/hackerrank/interview_preparation_kit/miscellaneous/ctci-big-o.md]] # noqa
+# pylint: enable=line-too-long
+
+import math
+
+
+# pylint: disable=duplicate-code
+def primeFactor(n: int) -> 'int | None':
+
+    if n < 2:
+        return None
+
+    divisor = n
+    max_prime_factor = None
+
+    i = 2
+    while i <= math.sqrt(divisor):
+        if 0 == divisor % i:
+            divisor = int(divisor / i)
+            max_prime_factor = divisor
+        else:
+            i += 1
+
+    if max_prime_factor is None:
+        return n
+
+    return max_prime_factor
+# pylint: enable=duplicate-code
+
+
+def primality(n):
+    return "Prime" if primeFactor(n) == n else "Not prime"

src/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"
+      }
+    ]
+  }
+]

src/hackerrank/interview_preparation_kit/miscellaneous/ctci_big_o_test.py

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+import unittest
+from pathlib import Path
+
+from ....lib.loader import loadTestCases
+from .ctci_big_o import primality
+
+
+FILE_PATH = str(Path(__file__).resolve().parent)
+
+TEST_CASES = loadTestCases(
+    FILE_PATH + '/ctci_big_o.testcases.json')
+
+
+class TestCtciBigO(unittest.TestCase):
+
+    def test_ctci_big_o(self):
+
+        for _, testset in enumerate(TEST_CASES):
+
+            for _, _tt in enumerate(testset['tests']):
+
+                self.assertEqual(
+                    primality(_tt['input']), _tt['answer'],
+                    f"{_} | primality({_tt['input']}) must be "
+                    f"=> {_tt['answer']}")
+
+    def test_ctci_big_o_edge_cases(self):
+        self.assertEqual(primality(1), "Not prime")