Find missing value in sorted consecutive array

Given a sorted array nums of distinct integers. The numbers are supposed to form a consecutive sequence starting from some unknown integer start:

• If nothing is missing, the sequence would be: start, start+1, start+2, ..., start+n-1 where n = len(nums).
• But at most one number from this sequence may be missing in nums.

Return the missing number if one exists; otherwise return null (or -1, but be consistent).

Requirements

• Time complexity must be O(log n).
• Space complexity must be O(1).

Examples

• nums = [4,5,6,8,9] → missing is 7
• nums = [-3,-2,-1,0,1] → no missing → return null
• nums = [10,11,12,13,15] → missing is 14

Notes

• start can be any integer (including negative).
• nums is already sorted ascending and contains no duplicates.

Missing Value In Sorted Consecutive Array

Given a sorted distinct array that should be consecutive except for at most one interior missing value, return the missing number or None if no value is missing.

Constraints

• nums is sorted ascending with distinct integers.
• At most one interior value is missing.
• Return None when no missing value is detectable.

Hints

1. For a perfect consecutive array, nums[i] - nums[0] equals i.
2. Binary search for the first index where that invariant fails.