You are asked to solve two coding problems and analyze the time and space complexity of each. 1. **Palindrome check** Given a string `s`, determine whether it reads the same forward and backward. Treat the empty string as a valid palindrome. If `s` is `null`, return `false`. 2. **Missing number with arbitrary start** Given a sorted array `nums` of distinct integers, the values should form a consecutive sequence with step size 1, but exactly one number is missing. The sequence does **not** necessarily start at 0. Examples: - `[4, 5, 6, 8, 9]` -> `7` - `[10, 11, 13]` -> `12` First describe an `O(n)` solution, then improve it to an `O(log n)` solution using binary search. For both problems, be prepared to explain your time and space complexity and discuss edge cases.