perm_missing_element.py

"""
A zero-indexed array A consisting of N different integers is given.
The array contains integers in the range [1..(N + 1)],
 which means that exactly one element is missing.

Your goal is to find that missing element.

Write a function:

    def solution(A)

that, given a zero-indexed array A, returns the value of the missing element.

For example, given array A such that:

  A[0] = 2
  A[1] = 3
  A[2] = 1
  A[3] = 5
the function should return 4, as it is the missing element.

Assume that:

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)].
Complexity:

expected worst-case time complexity is O(N);
expected worst-case space complexity is O(1), beyond input storage
(not counting the storage required for input arguments).
Elements of input arrays can be modified.
"""

def solution(nums):
    n = len(nums) + 1
    if n == 1:
        return 1
    expected_sum = (n * (n + 1)) // 2
    return expected_sum - sum(nums)