Leetcode #762: Prime Number of Set Bits in Binary Representation
In this guide, we solve Leetcode #762 Prime Number of Set Bits in Binary Representation in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given two integers left and right, return the count of numbers in the inclusive range [left, right] having a prime number of set bits in their binary representation. Recall that the number of set bits an integer has is the number of 1's present when written in binary.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Bit Manipulation, Math
Intuition
The problem structure lets us track state with bitwise operations.
Bit operations are constant time and avoid extra memory.
Approach
Apply XOR/AND/OR and shifts to maintain the required invariant.
Aggregate the result in a single pass.
Steps:
- Identify a bitwise invariant.
- Combine values with bit operations.
- Return the aggregated result.
Example
Input: left = 6, right = 10
Output: 4
Explanation:
6 -> 110 (2 set bits, 2 is prime)
7 -> 111 (3 set bits, 3 is prime)
8 -> 1000 (1 set bit, 1 is not prime)
9 -> 1001 (2 set bits, 2 is prime)
10 -> 1010 (2 set bits, 2 is prime)
4 numbers have a prime number of set bits.
Python Solution
class Solution:
def countPrimeSetBits(self, left: int, right: int) -> int:
primes = {2, 3, 5, 7, 11, 13, 17, 19}
return sum(i.bit_count() in primes for i in range(left, right + 1))
Complexity
The time complexity is O(n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.