Solve three coding interview problems

You are given three independent coding questions. ## 1) Decode an encoded string Given an encoded string `s`, decode it using the following rule: - Patterns of the form `k[encoded_string]` mean that `encoded_string` is repeated exactly `k` times. - `k` is a positive integer and may have multiple digits. - Encoded strings may be nested. **Example**: `s = "3[a2[c]]"` should decode to `"accaccacc"`. **Task**: Return the decoded string. **Assumptions/constraints** (you may state any reasonable ones in your solution): - `s` contains only digits, letters, and brackets `[` `]`. - The input is valid (balanced brackets, well-formed encoding). --- ## 2) Max profit with jump decisions Given a 1D array `arr` of integers and starting at index `0`, you can make a decision at each index `i`: - **Take**: gain profit `arr[i]`, then jump to index `i + 1 + arr[i]`. - **Skip**: gain profit `0`, then move to index `i + 1`. You may stop when your index is out of bounds (i.e., `i >= n`). **Task**: Compute the maximum total profit achievable. ### Follow-up How does your approach change if `arr` can contain **negative numbers**? - If you **take** at index `i`, you still gain `arr[i]`, and you still move to index `i + 1 + arr[i]` (which could move backward if `arr[i] < 0`). - Clarify any assumptions needed to ensure termination and handle potential cycles. --- ## 3) Count connected land components in a grid Given an `m x n` grid of characters `'1'` and `'0'`: - `'1'` represents land - `'0'` represents water Two land cells are connected if they are adjacent **horizontally or vertically** (4-directional adjacency). **Task**: Return the number of connected components of land (i.e., the number of “islands”). **Example**: ``` 1 1 0 0 1 0 1 0 1 ``` Answer: `3`.