Problem Description
You are given an array of integers nums of size 3. Return the maximum possible number whose binary representation can be formed by concatenating the binary representation of all elements in nums in some order. Note that the binary representation of any number does not contain leading zeros.
Key Insights
- The problem requires finding the optimal order to concatenate the binary representations of the integers.
- The binary representation of numbers can be compared based on their lengths and values to determine the best concatenation order.
- A brute-force approach is feasible due to the small size of the input array (only 3 elements).
Space and Time Complexity
Time Complexity: O(1) - since the input size is constant (3 elements). Space Complexity: O(1) - no additional space is used that scales with input.
Solution
To solve the problem, we can utilize a brute-force approach that generates all permutations of the array of integers. For each permutation, we concatenate their binary representations and convert the result back to a decimal integer. We then keep track of the maximum integer found during this process. Given that there are only 3 integers, there will be a maximum of 6 permutations to evaluate.