Comparing leading zeros in binary representations of two numbers
Given two integer numbers x and y. Compare and print which one of them has more leading zeros using Bitwise operation. If both the no. have the same no. of leading zeros, print “Equal”.
Note:- A leading zero is any 0 digit that comes before the first nonzero digit in the binary notation of the number.
Input : 10, 16 Output :10 Explanation: If we represent the no.s using 8 bit only then Binary(10) = 00001010 Binary(16) = 00010000 Clearly, 10 has 4 leading zeros and 16 has 3 leading zeros Input : 10, 12 Output : Equal Binary(10) = 00001010 Binary(12) = 00001100 Both have equal no. of leading zeros.
Solution 1: The Naive approach is to first find the binary representation of the numbers and then count the no. of leading zeros.
Solution 2: Find largest power of twos smaller than given numbers, and compare these powers of twos to decide answer.
Solution 3: An efficient approach is to bitwise XOR and AND operators.
Case 1: If both have same no. of leading zeros then (x^y) <= (x & y) because same number of leading 0s would cause a 1 at higher position in x & y.
Case 2 : If we do negation of y and do bitwise AND with x, we get a one at higher position than in y when y has more number of leading 0s.
Case 3: Else x has more leading zeros
Time Complexity: O(1)
Space Complexity: O(1)