Solution Explanation for Guess the Majority in a Hidden Array

This problem involves interacting with a hidden array through an API, ArrayReader. The API provides two functions:

• query(a, b, c, d): Returns the distribution of values among four elements (a, b, c, d) of the array. It returns:
  • 4: if all four elements are the same (all 0s or all 1s).
  • 2: if three elements are the same and one is different.
  • 0: if two elements are 0 and two are 1.
• length(): Returns the length of the hidden array.

The goal is to find the index of the most frequent element (0 or 1) using at most 2*n calls to query(), where n is the array length.

Approach

The solution uses a clever approach based on comparing groups of elements and tracking the consistency of results. Here's a breakdown:

1. Initial Query: The solution starts by querying the first four elements (reader.query(0, 1, 2, 3)) to get an initial distribution (x).

2. Iterative Comparison: It then iterates through the remaining elements, comparing each with the first three elements (reader.query(0, 1, 2, i)). If the result matches the initial distribution (x), it increments a counter (a); otherwise, it increments another counter (b) and records the index (k) of the differing element. This helps determine whether the majority is among the first three elements or in the rest.

3. Refining the Majority: After this loop, we have a preliminary count (a and b).However, this is insufficient to determine the majority if it's not contained within the first 3 or last element. Thus, we query a few more combinations of the first 4 elements to get a more conclusive estimate.

4. Final Check: Finally, it compares a and b. If they are equal, it means there's a tie, and -1 is returned. Otherwise, the index of the most frequent element is returned.

Time and Space Complexity

• Time Complexity: O(n), where n is the length of the array. The solution iterates through the array once in the main loop, and performs a few additional constant time operations.

• Space Complexity: O(1). The solution uses a constant amount of extra space to store variables and counters. The space used doesn't scale with the input size.

Code in Different Languages

The code implementations provided earlier show this solution in Python, Java, C++, Go, and TypeScript. All versions follow the same algorithmic approach described above. They differ only in syntax and specific language features. The core logic remains consistent across all implementations.