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).