762. Prime Number of Set Bits in Binary Representation


Given two integers L and R, find the count of numbers in the range [L, R] (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: L = 6, R = 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: L = 10, R = 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. L, R will be integers L <= R in the range [1, 10^6].
  2. R - L will be at most 10000.


Approach #1: Direct [Accepted]

Intuition and Approach

For each number from L to R, let's find out how many set bits it has. If that number is 2, 3, 5, 7, 11, 13, 17, or 19, then we add one to our count. We only need primes up to 19 because .

Complexity Analysis

  • Time Complexity: , where is the number of integers considered. In a bit complexity model, this would be as we have to count the bits in time.

  • Space Complexity: .

Analysis written by: @awice.

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