Solve three algorithmic OA tasks

Task 1 (Odd-frequency string): Given an integer N in [1..200000], write an algorithm that returns any length-N string of lowercase letters (a–z) such that every letter that appears occurs an odd number of times.

Task 2 (Min-difference with minimal swaps): Given two equal-length digit strings S and T (length N up to 100000, digits only, no leading zeros), you may choose a subset of indices and swap S[i] with T[i] at each chosen index. Among all swap choices that minimize |int(S) − int(T)|, return the minimum number of swaps required. For example, S = "29162" and T = "10524" should return 2.

Task 3 (Two-choice slot assignment): Given arrays A and B of length N (1 ≤ A[k], B[k] ≤ S, A[k] ≠ B[k]) and an integer S (2. 100000), determine whether it is possible to assign every patient k to either A[k] or B[k] so that at most one patient is assigned to each slot. Return true if such an assignment exists, otherwise false.

What a Strong Answer Covers

• A clear algorithm with the right data structures and enough pseudocode or code-level detail to implement it.
• A correctness argument that explains why the algorithm covers all required cases.
• Time and space complexity, plus at least one alternative approach when relevant.
• Focused tests for normal cases, edge cases, and failure modes.

Follow-up Questions

• How would the approach change if the input were streaming or too large for memory?
• What invariants would you assert in production code?
• Which tests would catch off-by-one, duplicate, or tie-breaking bugs?

Solution

Solution Alignment

The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests.

Problem Restatement

Task 1 (Odd-frequency string): Given an integer N in [1..200000], write an algorithm that returns any length-N string of lowercase letters (a–z) such that every letter that appears occurs an odd number of times. Task 2 (Min-difference with minimal swaps): Given two equal-length digit strings S and T (length N up to 100000, digits only, no leading zeros), you may choose a subset of indices and swap S[i] with T[i] at each chosen index. Among all swap choices that minimize |int(S) − int(T)|, return the minimum number of swaps required. For example, S = "29162" and T = "10524" should return 2. Task 3 (Two-choice slot assignment): Given arrays A and B of length N (1 ≤ A[k], B[k] ≤ S, A[k] ≠ B[k])...

Recommended Approach

Use the string constraints to choose between two pointers, a stack, frequency counts, prefix/suffix state, or dynamic programming. Maintain the invariant that processed characters have already been normalized, counted, or matched according to the operation.

Correctness

The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call.

Complexity

Most direct string scans are O(n) time. Space ranges from O(1) for two pointers to O(n) for stacks, maps, or DP tables.

Edge Cases and Tests

Empty string, length 1, repeated characters, invalid characters, case sensitivity, Unicode vs ASCII, and very long input.