LeetCode 762. Prime Number of Set Bits in Binary Representation

Description

https://leetcode.com/problems/prime-number-of-set-bits-in-binary-representation/

Given two integers left and right, find the count of numbers in the range [left, right] (inclusive) 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 1s present when written in binary. For example, 21 written in binary is 10101 which has 3 set bits. Also, 1 is not a prime.)

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)
9 -> 1001 (2 set bits , 2 is prime)
10->1010 (2 set bits , 2 is prime)

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)

Note:

  1. left, right will be integers left <= right in the range [1, 10^6].
  2. right - left will be at most 10000.

Explanation

Convert integer to bits and count how many bits are there. And then check if the count of bits is a prime number

Python Solution

class Solution:
    def countPrimeSetBits(self, L: int, R: int) -> int:
        count = 0
        
        for i in range(L, R + 1):
            bin_i = bin(i)[2:]
            count_bits = bin_i.count('1')
                            
            if count_bits > 1 and self.is_prime(count_bits):
                count += 1
            
        return count
        
    def is_prime(self, n):
        for i in range(2, floor(sqrt(n)) + 1):
            if n % i == 0:
                return False
            
        return True
  • Time Complexity: O(N^2).
  • Space Complexity: O(N).

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