How do you solve Prime Number of Set Bits in Binary Representation on LeetCode?

Prime Number of Set Bits in Binary Representation (LeetCode #762) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding binary representation and set bits is crucial for this problem.

What is the time complexity of Prime Number of Set Bits in Binary Representation?

The optimal solution for Prime Number of Set Bits in Binary Representation runs in O(n) time and uses O(1) space. The time complexity is O(n) since we iterate through the range once, and the space complexity is O(1) as we only store a fixed number of primes.

What is the brute force solution for Prime Number of Set Bits in Binary Representation?

The brute force approach for Prime Number of Set Bits in Binary Representation is Brute Force, with O(n log m) time complexity and O(1) space complexity. The brute force approach checks each number in the range from left to right, counts the set bits in its binary representation, and checks if that count is a prime number. This method is straightforward but can be slow for larger ranges. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Prime Number of Set Bits in Binary Representation?

Prime Number of Set Bits in Binary Representation uses the following concepts: Math, Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Set and Hash Map.

What are the interview tips for Prime Number of Set Bits in Binary Representation?

Always clarify the constraints and edge cases before diving into coding. Discuss your thought process and approach before writing code. Consider optimizing your solution if you notice a pattern or redundancy.

What are common mistakes when solving Prime Number of Set Bits in Binary Representation?

Not handling edge cases where left and right are the same. Forgetting to check if the count of set bits is prime.

#762

Prime Number of Set Bits in Binary Representation

Easy

MathBit ManipulationBit ManipulationSet and Hash Map

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

The optimal solution precomputes the prime numbers and uses a bit manipulation technique to count set bits efficiently. This reduces the number of checks needed during the main loop, making it faster.

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Algorithm

7 steps

1Step 1: Precompute all prime numbers up to 20 (maximum possible set bits for numbers <= 10^6).
2Step 2: Create a set of these prime numbers for O(1) lookup.
3Step 3: Iterate through each number from left to right.
4Step 4: Count the number of set bits using bit manipulation.
5Step 5: Check if the count of set bits is in the set of prime numbers.
6Step 6: If it is, increment the count.
7Step 7: Return the final count.

solution.py13 lines

1# Full working Python code
2
3def count_prime_set_bits(left, right):
4    primes = {2, 3, 5, 7, 11, 13, 17, 19}
5    count = 0
6    for num in range(left, right + 1):
7        set_bits = bin(num).count('1')
8        if set_bits in primes:
9            count += 1
10    return count
11
12# Example usage
13print(count_prime_set_bits(6, 10))

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Complexity note: The time complexity is O(n) since we iterate through the range once, and the space complexity is O(1) as we only store a fixed number of primes.

1Understanding binary representation and set bits is crucial for this problem.
2Precomputing primes allows for faster checks during the main loop.

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