"""
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).

"""

"""
the intution we have here is that exactly 1 element is missing in between, thus if there are 5 elements in the array then max of all
the numbers will be 6 and minimum obviously is 1.

so finding the sum of first n natural numbers is (n*(n+1))/2(enforces integer division)
and the from that if we subtract the  sum of the present array then we get the missing number 
"""


def solution(A):
    length = len(A)
    expectedSum = ((length+1)*(length+2))//2
    actualsum = sum(A)

    return expectedSum-actualsum

print(solution([2,3,1,5]))