Given two non-negative numbers a and b and two values l and r. The problem is to check whether all bits at corresponding positions in the range l to r in both the given numbers are complement of each other or not.
The bits are numbered from right to left, i.e., the least significant bit is considered to be at first position.
Input: a = 10, b = 5 l = 1, r = 3 Output: Yes (10)10 = (1010)2 (5)10 = (101)2 = (0101)2 All the bits in the range 1 to 3 are complement of each other. Input: a = 21, b = 13 l = 2, r = 4 Output: No (21)10 = (10101)2 (13)10 = (1101)2 = (1101)2 All the bits in the range 2 to 4 are not complement of each other.
Approach: Below are the steps to solve the problem
- Calculate xor_value = a ^ b.
- Check whether all the bits are set or not in the range l to r in xor_value. Refer this post.
Below is the implementation of the above approach.
# Python 3 implementation to check whether
# all the bits in the given range of two
# numbers are complement of each other
# function to check whether all the bits
# are set in the given range or not
def allBitsSetInTheGivenRange(n, l, r):
# calculating a number ‘num’ having ‘r’
# number of bits and bits in the range l
# to r are the only set bits
num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1) # new number which will only have one # or more set bits in the range l to r # and nowhere else new_num = n & num # if both are equal, then all bits # are set in the given range if (num == new_num): return True # else all bits are not set return False # function to check whether all the bits # in the given range of two numbers are # complement of each other def bitsAreComplement(a, b, l, r): xor_value = a ^ b return allBitsSetInTheGivenRange(xor_value, l, r) # Driver Code if __name__ == "__main__": a = 10 b = 5 l = 1 r = 3 if (bitsAreComplement(a, b, l, r)): print("Yes") else: print("No") # This code is contributed by ita_c [tabby title="C#"]
- Check if one of the numbers is one's complement of the other
- Check whether all the bits are set in the given range
- Check whether all the bits are unset in the given range
- Check whether all the bits are unset in the given range or not
- Check whether bits are in alternate pattern in the given range
- Check whether bits are in alternate pattern in the given range | Set-2
- Print numbers in the range 1 to n having bits in alternate pattern
- Check whether XOR of all numbers in a given range is even or odd
- Subtraction of two numbers using 2's Complement
- Check if bits of a number has count of consecutive set bits in increasing order
- Why are negative numbers stored as 2's complement?
- Check if binary representation of a given number and its complement are anagram
- Print numbers having first and last bits as the only set bits
- Set bits in N equals to M in the given range.
- Count set bits in a range
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