Implement short algorithms on logs, grids, and strings

You are given several independent short coding tasks. For each task, implement the requested function(s). Assume standard library data structures are allowed. ## 1) Detect CPU temperature spikes You receive CPU temperature readings as a list of pairs `(timestamp, tempC)` sorted by `timestamp` ascending. Define a **spike** at reading `i` (time `t_i`, temperature `x_i`) if there exists some earlier reading `j < i` such that: - `t_i - t_j <= windowSeconds`, and - `x_i - x_j >= deltaC`. **Input:** - `readings: List[Tuple[int timestamp, int tempC]]` (timestamps are seconds) - `windowSeconds: int` - `deltaC: int` **Output:** - Return the list of timestamps `t_i` where reading `i` is a spike. **Constraints (example):** up to `2e5` readings. --- ## 2) Minimum possible sum after K operations Given an array of non-negative integers `a` and an integer `k`, you may perform the following operation exactly `k` times: - Choose an index `i` and replace `a[i]` with `ceil(a[i] / 2)`. **Goal:** minimize the final sum of the array. **Input:** `a: List[int]`, `k: int` **Output:** the minimum achievable sum after `k` operations. **Constraints (example):** `n` up to `2e5`, values up to `1e9`, `k` up to `2e5`. --- ## 3) Verify matching brackets in a mathematical expression Given a string `s` representing a mathematical expression containing characters including `()[]{}` and other non-bracket characters, determine whether the brackets are correctly matched and nested. **Input:** `s: str` **Output:** `True` if valid, else `False`. **Notes:** Non-bracket characters should be ignored. --- ## 4) Aggregate HTTP logs by status code You are given log lines. Each line contains a status code and a response time in milliseconds: Format: `"<statusCode> <responseTimeMs>"` Example: `"200 153"`, `"500 12"`. **Task:** aggregate by `statusCode`: - count of requests - average response time (as a floating-point value) **Input:** `logs: List[str]` **Output:** a mapping/dictionary `statusCode -> (count, avgResponseTime)`. **Edge cases:** empty input; malformed lines may be ignored (state and implement a consistent rule). --- ## 5) Tree planting on a grid (no adjacent trees) You are given an `m x n` grid `land` with: - `1` meaning an existing tree - `0` meaning empty land You may plant additional trees on empty cells, but **no two trees** (existing or newly planted) may be adjacent in the 4-neighborhood (up/down/left/right). **Task:** determine a set of cells to plant new trees that is **maximum in size**. **Input:** `land: List[List[int]]` **Output:** - `maxNewTrees: int`, the maximum number of new trees that can be planted - optionally (if asked), one valid resulting grid configuration **Constraints (example):** `m, n` up to ~`50` (state assumptions and optimize accordingly).