How do you solve Construct the Minimum Bitwise Array I on LeetCode?

Construct the Minimum Bitwise Array I (LeetCode #3314) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The bitwise OR operation has specific patterns that can be exploited, especially with prime numbers.

What is the brute force solution for Construct the Minimum Bitwise Array I?

The brute force approach for Construct the Minimum Bitwise Array I is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try every possible value for ans[i] starting from 0 and check if it satisfies the condition. This is straightforward but inefficient as it may require checking many values. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Construct the Minimum Bitwise Array I?

Construct the Minimum Bitwise Array I uses the following concepts: Array, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Array.

What are the interview tips for Construct the Minimum Bitwise Array I?

Always clarify the problem statement and constraints before diving into coding. Think about edge cases and how they might affect your solution. Practice explaining your thought process clearly as you code, as communication is key in interviews.

What are common mistakes when solving Construct the Minimum Bitwise Array I?

Not considering edge cases like the smallest prime (2) which directly leads to -1. Overlooking the properties of bitwise operations and how they relate to binary representations.

#3314

Construct the Minimum Bitwise Array I

Easy

ArrayBit ManipulationBit ManipulationArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

We can derive ans[i] directly by using the property of bitwise operations. Since nums[i] is prime, we can find the largest power of 2 less than nums[i] and derive ans[i] from it.

⚙️

Algorithm

5 steps

1Step 1: Initialize an empty list ans to store the results.
2Step 2: For each prime number in nums, check if it is 2. If so, append -1 to ans.
3Step 3: For other primes, find the largest power of 2 less than the prime number.
4Step 4: Set ans[i] to this power of 2 minus 1.
5Step 5: Return the list ans.

solution.py16 lines

1# Full working Python code
2
3def construct_min_bitwise_array(nums):
4    ans = []
5    for num in nums:
6        if num == 2:
7            ans.append(-1)
8        else:
9            power = 1
10            while power * 2 < num:
11                power *= 2
12            ans.append(power - 1)
13    return ans
14
15# Example usage
16print(construct_min_bitwise_array([2, 3, 5, 7]))

ℹ

Complexity note: The outer loop runs n times, and finding the largest power of 2 is logarithmic relative to the size of the numbers, making this approach linear overall.

1The bitwise OR operation has specific patterns that can be exploited, especially with prime numbers.
2Understanding powers of 2 helps in deriving the minimum values efficiently.

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