Byzantine Generals Problem: A Simplified Consensus Algorithm

Consensus algorithms are fundamental to distributed systems, ensuring that all nodes agree on a single value despite potential failures or malicious actors. This challenge asks you to implement a simplified version of a consensus algorithm inspired by the Byzantine Generals Problem, focusing on achieving agreement among a group of nodes in the presence of faulty nodes. This is a simplified model, but it illustrates core concepts of distributed consensus.

Problem Description

You are tasked with creating a JavaScript function achieveConsensus that simulates a simplified consensus algorithm among a set of nodes. The algorithm should determine a single agreed-upon value from a set of proposed values, even if some nodes are faulty and propose incorrect values. The algorithm will use a majority voting approach.

What needs to be achieved:

Given an array of proposed values from different nodes, the function should return the value that appears most frequently (the majority). If there's a tie, the function should return null.

Key Requirements:

• The function must handle an arbitrary number of nodes (represented by the length of the input array).
• The function must correctly identify the majority value if one exists.
• The function must return null if no majority value exists (i.e., there's a tie).
• The function should be efficient enough to handle a reasonable number of nodes (e.g., up to 100).

Expected Behavior:

The function should iterate through the proposed values, count the occurrences of each value, and determine the value with the highest count. If the highest count is greater than half the total number of nodes, that value is the consensus.

Edge Cases to Consider:

• Empty input array: Should return null.
• All nodes propose the same value: Should return that value.
• Tie: Should return null.
• Input array containing mixed data types (e.g., numbers and strings): The algorithm should treat them as distinct values.

Examples

Example 1:

Input: [1, 2, 2, 2, 3]
Output: 2
Explanation: The value 2 appears 3 times, which is more than half (5/2 = 2.5). Therefore, 2 is the consensus.

Example 2:

Input: [1, 2, 2, 3, 3]
Output: null
Explanation: The value 2 appears 2 times, and the value 3 appears 2 times. Neither value appears more than half the time. Therefore, the function returns null.

Example 3:

Input: []
Output: null
Explanation: The input array is empty, so there's no consensus.

Example 4:

Input: [1, 1, 1, 1, 1]
Output: 1
Explanation: The value 1 appears 5 times, which is more than half (5/2 = 2.5).

Constraints

• The input array proposals will contain only primitive data types (numbers, strings, booleans).
• The length of the proposals array will be between 0 and 100, inclusive.
• The function achieveConsensus must have a time complexity of O(n), where n is the length of the proposals array. (This is to ensure reasonable performance).

Notes

• You can use a JavaScript object (or Map) to store the counts of each proposed value.
• Remember to handle the edge case of an empty input array.
• Consider how to efficiently determine if a value is a majority (appears more than half the time).
• This is a simplified model. Real-world consensus algorithms are significantly more complex and robust. This exercise focuses on the core concept of majority agreement.