algorithm - What is the right way to solve Codility's PermMissingElem test? (Java) -

i have following problem taken codility's code testing exercises:

a zero-indexed array consisting of n different integers given. array contains integers in range [1..(n + 1)], means 1 element missing.

your goal find missing element.

write function:

class solution { public int solution(int[] a); }

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

for example, given array such that:

a[0] = 2 a[1] = 3 a[2] = 1 a[3] = 5

the function should return 4, missing element.

assume that:

n integer within range [0..100,000]; elements of distinct; each element of array integer within range [1..(n + 1)].

complexity:

expected worst-case time complexity o(n); expected worst-case space complexity o(1), beyond input storage (not >counting storage required input arguments).

elements of input arrays can modified.

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my approach convert given array arraylist, use arraylist find lowest , highest values inside array, , iterate through possible values lowest highest, , return missing value.

this solves example problem, problem seems cannot right answers under following conditions of given array:

"empty list , single element"

"the first or last element missing"

"single element"

"two elements"

what doing wrong, , proper way go solving problem?

this problem has mathematical solution, based on fact sum of consecutive integers 1 n equal n(n+1)/2.

using formula can calculate sum 1 n+1. o(n) time complexity calculate actual sum of elements in array.

the difference between full , actual totals yield value of missing element.

space complexity o(1).