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Question 1: Quality Assurance Bug Sorting

Problem Statement: You are helping Amazon's Quality Assurance engineers process bug reports generated from automated testing logs across various devices and services. Each log contains an integer bug code, and a single test session may include duplicate bug codes if the same issue is triggered multiple times.

To effectively prioritise debugging and resolution, the following rules are applied:

• Less frequent bugs are considered more important, as they may indicate rare or edge-case issues.
• If two bugs occur the same number of times, the bug with the lower code number has higher priority.

The task is to sort the bug codes in order of decreasing importance, using the above rules.

Example: bugs = [8, 4, 6, 5, 4, 8]

Item Code Frequency:

• 8: 2 occurrences
• 4: 2 occurrences
• 6: 1 occurrence
• 5: 1 occurrence

Question 2: Package Sorting Optimization (Prefix Division)

Problem Statement:

A team at Amazon is working to ensure all packages are correctly sorted for delivery. Each package has a label represented by an uppercase English letter. The full list of labels is given as string packages, where the ith character is the label of the i^{th} package.

To optimize the sorting process, the team wants to analyze each prefix of the string packages (from length 1 to n) and determine the maximum number of equal parts it can be divided into.

Each part must satisfy the following condition:

• Each part must have the same frequency of every character as every other part in that division.

Given a string packages, calculate for each prefix t (from length 1 to n), the maximum number of equal parts into which the prefix can be divided, such that each part has the same number of occurrences of each character.

Example:

n = 4

packages = "ABAB"

In the given example, t represents the prefix string and length represents the length of the prefix string.

Explanation Table:

• length = 1, t = A: A single-character string (length=1) cannot be divided. (Maximum parts = 1)
• length = 2, t = AB: For the count of each character to be the same, the string cannot be divided. (Maximum parts = 1)
• length = 3, t = ABA: For the count of each character to be the same, the string cannot be divided. (Maximum parts = 1)
• length = 4, t = ABAB: The string can be divided into 2 equal parts: "AB" and "AB". (Maximum parts = 2)