Is Maximum Sized Array easy or hard?

Maximum Sized Array is generally considered a Medium difficulty problem. The main challenge is recognizing that the cost function is monotonic and that bit contributions can be counted mathematically instead of iterating through every number.

Maximum Sized Array Python/Java solution

The implementation is identical across languages: binary search the answer and compute the cost with bit operations. Python, Java, C++, Go, and TypeScript versions all follow the same logic with loops over bit positions and integer arithmetic.

What is the best approach for Maximum Sized Array?

The optimal solution uses binary search on the answer combined with bit-counting formulas. Because the total cost for numbers 1..n increases monotonically, you can binary search the largest valid n and compute the cost using bit manipulation patterns. This reduces the complexity to O(log n * log n).

Is Maximum Sized Array asked at Google/Amazon/Meta?

Problems combining binary search on the answer with bit manipulation frequently appear in interviews at large tech companies. Variants of bit-counting and range bit contribution problems are common in Google and Meta interview question sets.

What data structure is used in Maximum Sized Array?

The solution does not rely on complex data structures. It mainly uses arithmetic, bit manipulation, and binary search over the answer space. The key technique is counting set bits at specific positions using repeating binary cycles.

What is the time complexity of Maximum Sized Array?

The optimized approach runs in O(log n * log n) time. Binary search contributes one log n factor, and each feasibility check iterates over possible bit positions (also about log n). Space complexity is O(1).

How to solve Maximum Sized Array in O(log n * log n)?

Binary search the largest possible array size n. For each candidate value, compute the total cost contributed by relevant bit positions across numbers 1..n using repeating binary patterns. Counting set bits per position avoids iterating through every number.

3344. Maximum Sized Array - Practice Online

Given a positive integer s, let A be a 3D array of dimensions n × n × n, where each element A[i][j][k] is defined as:

A[i][j][k] = i * (j OR k), where 0 <= i, j, k < n.

Return the maximum possible value of n such that the sum of all elements in array A does not exceed s.

Example 1:

Input: s = 10

Output: 2

Explanation:

Elements of the array A for n = 2:
- A[0][0][0] = 0 * (0 OR 0) = 0
- A[0][0][1] = 0 * (0 OR 1) = 0
- A[0][1][0] = 0 * (1 OR 0) = 0
- A[0][1][1] = 0 * (1 OR 1) = 0
- A[1][0][0] = 1 * (0 OR 0) = 0
- A[1][0][1] = 1 * (0 OR 1) = 1
- A[1][1][0] = 1 * (1 OR 0) = 1
- A[1][1][1] = 1 * (1 OR 1) = 1
The total sum of the elements in array A is 3, which does not exceed 10, so the maximum possible value of n is 2.

Example 2:

Input: s = 0

Output: 1

Explanation:

Elements of the array A for n = 1:
- A[0][0][0] = 0 * (0 OR 0) = 0
The total sum of the elements in array A is 0, which does not exceed 0, so the maximum possible value of n is 1.

Constraints:

0 <= s <= 10¹⁵