Prime Number of Set Bits in Binary Representation

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.

  • For example, 21 written in binary is 10101, which has 3 set bits.

 

Example 1:

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.

Example 2:

Input: left = 10, right = 15
Output: 5
Explanation:
10 -> 1010 (2 set bits, 2 is prime)
11 -> 1011 (3 set bits, 3 is prime)
12 -> 1100 (2 set bits, 2 is prime)
13 -> 1101 (3 set bits, 3 is prime)
14 -> 1110 (3 set bits, 3 is prime)
15 -> 1111 (4 set bits, 4 is not prime)
5 numbers have a prime number of set bits.

 

Constraints:

  • 1 <= left <= right <= 106
  • 0 <= right - left <= 104
SOLUTION:
class Solution:
    def countPrimeSetBits(self, left: int, right: int) -> int:
        isPrime = [True] * 33
        isPrime[0], isPrime[1] = False, False
        for i in range(33):
            if isPrime[i]:
                for j in range(2, 1 + 32 // i):
                    isPrime[i * j] = False
        ctr = 0
        for i in range(left, right + 1):
            curr = "{:b}".format(i).count("1")
            if isPrime[curr]:
                ctr += 1
        return ctr

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