Given two integers ‘L’ and ‘R’, write a program to find the total numbers that are having prime number of set bits in their binary representation in the range [L, R].
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) Hence count is 4 Input : l = 10, r = 15 Output : 5 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) Hence count is 5
Explanation: In this program we find a total number, that’s having prime number of set bit. so we use a CPP predefined function __builtin_popcount() these functions provide a total set bit in number. as well as be check the total bit’s is prime or not if prime we increase the counter these process repeat till given range.
# Python3 program to count total prime
# number of set bits in given range
# Corner cases
if (n <= 1): return False; if (n <= 3): return True; # This is checked so that we can skip # middle five numbers in below loop if (n % 2 == 0 or n % 3 == 0): return False; i = 5; while (i * i <= n): if(n % i == 0 or n % (i + 2) == 0): return False; i = i + 6; return True; # count number, that contains # prime number of set bit def primeBitsInRange(l, r): # tot_bit store number of # bit in number count = 0; # iterate loop from l to r for i in range(l, r + 1): # use predefined function for finding # set bit it is return number of set bit tot_bit = bin(i).count('1'); # check tot_bit prime or, not if (isPrime(tot_bit)): count += 1; return count; # Driver Code l = 6; r = 10; print(primeBitsInRange(l, r)); # This code is contributed by mits [tabby title="C#"]
Time Complexity : Let’s n = (r-l)
so overall time complexity is N*sqrt(N)
We can optimize above solution using Sieve of Eratosthenes.
- Prime Number of Set Bits in Binary Representation | Set 2
- Number of mismatching bits in the binary representation of two integers
- Binary representation of a given number
- Binary representation of next number
- Count number of trailing zeros in Binary representation of a number using Bitset
- Check if the binary representation of a number has equal number of 0s and 1s in blocks
- Largest number with binary representation is m 1's and m-1 0's
- Binary representation of previous number
- Next greater number than N with exactly one bit different in binary representation of N
- Number of leading zeros in binary representation of a given number
- Find the n-th number whose binary representation is a palindrome
- Check if binary representation of a number is palindrome
- Occurrences of a pattern in binary representation of a number
- Find consecutive 1s of length >= n in binary representation of a number
- Check if actual binary representation of a number is palindrome
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Improved By : Mithun Kumar