Given a non-negative number n and two values l and r. The problem is to check whether all the bits are unset or not in the range l to r in the binary representation of n.
Constraint: 1 <= l <= r <= number of bits in the binary representation of n.
Input : n = 17, l = 2, r = 4 Output : Yes (17)10 = (10001)2 The bits in the range 2 to 4 are all unset. Input : n = 36, l = 3, r = 5 Output : No (36)10 = (100100)2 The bits in the range 3 to 5 are all not unset.
Approach: Following are the steps:
- Calculate num = ((1 << r) – 1) ^ ((1 << (l-1)) – 1). This will produce a number num having r number of bits and bits in the range l to r are the only set bits.
- Calculate new_num = n & num.
- If new_num == 0, return “Yes” (all bits are unset in the given range).
- Else return “No” (all bits are not unset in the given range).
# Python 3 implementation to check whether
# all the bits are unset in the given range
# or not
# function to check whether all the bits
# are unset 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 new num is 0, then all bits # are unset in the given range if (new_num == 0): return "Yes" # else all bits are not unset return "No" # Driver Code if __name__ == "__main__": n = 17 l = 2 r = 4 print(allBitsSetInTheGivenRange(n, l, r)) # This code is contributed by ita_c [tabby title="C#"]
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