How do you solve Maximum Possible Number by Binary Concatenation on LeetCode?

Maximum Possible Number by Binary Concatenation (LeetCode #3309) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Sorting based on binary length and value maximizes the concatenated number.

What is the brute force solution for Maximum Possible Number by Binary Concatenation?

The brute force approach for Maximum Possible Number by Binary Concatenation is Brute Force, with O(n!) time complexity and O(n) space complexity. The brute force approach involves generating all possible permutations of the array and calculating the binary concatenation for each permutation. This is straightforward but inefficient as it checks every possible order. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Possible Number by Binary Concatenation?

Maximum Possible Number by Binary Concatenation uses the following concepts: Array, Bit Manipulation, Enumeration. The recommended patterns to study are: Sorting, Array.

What are the interview tips for Maximum Possible Number by Binary Concatenation?

Think about the properties of binary numbers when concatenating. Practice generating permutations but also look for patterns that can simplify the problem. Always check edge cases, such as the smallest and largest numbers in the input.

What are common mistakes when solving Maximum Possible Number by Binary Concatenation?

Not considering the order of binary concatenation. Forgetting to convert binary strings back to decimal correctly.

#3309

Maximum Possible Number by Binary Concatenation

Medium

ArrayBit ManipulationEnumerationSortingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n!)	O(n log n)
Space	O(n)	O(n)

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Intuition

Time O(n log n)Space O(n)

Instead of generating all permutations, we can leverage the fact that the maximum binary number is formed by prioritizing larger binary representations. We can sort the numbers based on their binary length and value.

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Algorithm

3 steps

1Step 1: Sort the array based on the binary representation length and value.
2Step 2: Concatenate the binary representations of the sorted numbers.
3Step 3: Convert the concatenated binary string to a decimal number.

solution.py4 lines

1def maxBinaryConcatenation(nums):
2    nums.sort(key=lambda x: (len(bin(x)[2:]), x), reverse=True)
3    binary_string = ''.join(bin(num)[2:] for num in nums)
4    return int(binary_string, 2)

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the array based on binary representation characteristics. The space complexity is O(n) for storing the binary string.

1Sorting based on binary length and value maximizes the concatenated number.
2Binary representations can be compared directly based on their lengths.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.