Solve Several Algorithm Problems

The interview included several coding tasks: 1. **Longest symmetric substring**: Given a string `s`, return the longest contiguous substring that reads the same forward and backward. 2. **Point connectivity on a 2D plane**: You are given many points `(x, y)` and a threshold `d`. Two points are directly connected if they are in the same row (`y` is equal) or the same column (`x` is equal), and their distance along that row or column is strictly less than `d`. Connectivity is transitive. Return the number of connected components. 3. **Dynamic land additions**: Start with an `m x n` grid of water. Land cells are added one at a time. After each addition, report the current number of connected land masses using 4-directional adjacency. Follow-up: discuss how you would support deleting existing land cells as well. 4. **Square root by binary search**: Implement a function that computes the square root of a non-negative number using binary search. Clarify whether the expected result is the integer floor or a floating-point approximation within a chosen precision. 5. **Evaluate nested arithmetic expressions**: Given an expression string such as `sub(1,add(2,3))`, evaluate its integer result. Supported operations are `add(a,b)` and `sub(a,b)`, and expressions may be nested arbitrarily. Example: `sub(1,add(2,3)) = -4`.