Solve anagram grouping and in-place allocator

You are asked to solve **two coding tasks**. ## 1) Group anagrams Given an array of strings `strs`, group the strings that are anagrams of each other. - Two strings are anagrams if they contain the same characters with the same counts (order can differ). - Return the groups in any order. **Input:** `strs: string[]` **Output:** `string[][]` where each inner array is one anagram group. **Constraints (typical):** - `1 <= len(strs) <= 10^5` - Each string length `<= 100` - Characters are lowercase English letters (unless otherwise stated). --- ## 2) Implement `allocate()` / `free()` with no extra space You have a fixed memory pool represented by an array `mem` of **32 slots**: - `mem` has length `N = 32`. - Each `mem[i]` is a **64-bit unsigned value**. - Each allocated slot stores exactly one 64-bit value. Implement the following API: - `init(mem)`: initialize the pool so all slots are free. - `allocate(x) -> handle`: stores value `x` into one free slot and returns a `handle` (an integer index `0..31`). If no space is available, return `-1`. - `free(handle)`: marks the slot at `handle` as free. **Key constraint:** - You may not use additional data structures proportional to `N` (no separate boolean/bitmap arrays, hash sets, etc.). Only **O(1)** extra variables are allowed beyond the given `mem` array. **Clarifications to state/assume in your solution (as an interviewer would):** - Whether `free()` may be called on an invalid or already-freed handle, and what to do in that case. - Whether all 64 bits are available for user data, or whether you are allowed to reserve some bits for metadata. Design for good time complexity (ideally O(1) per operation).