feat(algorithms, findmissingelem): add implementation and tests for finding missing element in an array

Author: BrianLusina

puzzles/find_missing_elem/README.md …ithms/arrays/find_missing_elem/README.mdpuzzles/find_missing_elem/README.md renamed to algorithms/arrays/find_missing_elem/README.md puzzles/find_missing_elem/README.md renamed to algorithms/arrays/find_missing_elem/README.md

@@ -18,4 +18,25 @@ A[0] = 2 A[1] = 3 A[2] = 1 A[3] = 5 the function should return 4, as it is the m
 Write an efficient algorithm for the following assumptions:
 
 N is an integer within the range [0..100,000]; the elements of A are all distinct; each element of array A is an integer
-within the range [1..(N + 1)].
+within the range [1..(N + 1)].
+
+## Constraints
+
+- n = `nums.length`
+- 1 ≤ n 10^3
+- 0 ≤ `nums[i]` ≤ n
+- There are no duplicates in the array
+
+## Examples
+
+![Example 1](images/examples/find_missing_element_example_1.png)
+![Example 2](images/examples/find_missing_element_example_2.png)
+
+## Topics
+
+- Array
+- Hash Table
+- Math
+- Binary Search
+- Bit Manipulation
+- Sorting

algorithms/arrays/find_missing_elem/__init__.py

@@ -0,0 +1,57 @@
+from typing import List
+
+
+def find_missing_element(numbers: List[int]) -> int:
+    """
+    Finds the missing element in a list of numbers
+    Args:
+        numbers (List[int]): list of numbers
+    Returns:
+        int: missing element
+    """
+    missing_element = len(numbers)
+
+    for index, number in enumerate(numbers):
+        missing_element = missing_element ^ number ^ index
+
+    return missing_element
+
+
+def find_missing_number(nums):
+    len_nums = len(nums)
+    index = 0
+
+    while index < len_nums:
+        value = nums[index]
+
+        if value < len_nums and value != nums[value]:
+            nums[index], nums[value] = nums[value], nums[index]
+
+        else:
+            index += 1
+
+    for x in range(len_nums):
+        if x != nums[x]:
+            return x
+    return len_nums
+
+
+def find_missing_number_sum_of_n_terms(nums):
+    """
+    Finds the missing element in a list of numbers
+
+    The sum of the first n natural numbers is given by the formula (n * (n + 1)) / 2. The idea is to compute this sum
+    and subtract the sum of all elements in the array from it to get the missing number.
+
+    Args:
+        nums (List[int]): list of numbers
+    Returns:
+        int: missing element
+    """
+    len_nums = len(nums)
+
+    total_sum = sum(nums)
+
+    expected_sum = len_nums * (len_nums + 1) // 2
+
+    return expected_sum - total_sum

algorithms/arrays/find_missing_elem/images/examples/find_missing_element_example_1.png

@@ -0,0 +1,45 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from . import (
+    find_missing_element,
+    find_missing_number,
+    find_missing_number_sum_of_n_terms,
+)
+
+FIND_MISSING_ELEMENT_TEST_CASES = [
+    ([0, 2, 3, 4, 5], 1),
+    ([0, 1, 2, 3, 5, 6, 7], 4),
+    ([0, 1, 2, 3, 4, 5, 6, 7], 8),
+    ([1], 0),
+    ([1, 0, 2, 3, 4, 5, 6, 8, 9, 7, 11], 10),
+    ([1, 4, 5, 6, 8, 2, 0, 7], 3),
+    ([3, 0, 1, 4], 2),
+    ([0, 1, 2, 4], 3),
+    ([9, 6, 4, 2, 3, 5, 7, 0, 1], 8),
+    ([0, 1], 2),
+    ([3, 0, 1], 2),
+    ([8, 2, 4, 5, 3, 7, 1, 0], 6),
+    ([0, 1, 2, 3, 5], 4),
+]
+
+
+class FindMissingElementTestCases(unittest.TestCase):
+    @parameterized.expand(FIND_MISSING_ELEMENT_TEST_CASES)
+    def test_find_missing_element(self, nums: List[int], expected: int):
+        actual = find_missing_element(nums)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(FIND_MISSING_ELEMENT_TEST_CASES)
+    def test_find_missing_number(self, nums: List[int], expected: int):
+        actual = find_missing_number(nums)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(FIND_MISSING_ELEMENT_TEST_CASES)
+    def test_find_missing_number_sum_of_n_terms(self, nums: List[int], expected: int):
+        actual = find_missing_number_sum_of_n_terms(nums)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()