1318. Minimum Flips to Make a OR b Equal to c
Description
Given 3 positives numbers a
, b
and c
. Return the minimum flips required in some bits of a
and b
to make ( a
OR b
== c
). (bitwise OR operation).
Flip operation consists of change any single bit 1 to 0 or change the bit 0 to 1 in their binary representation.
Example 1:
Input: a = 2, b = 6, c = 5 Output: 3 Explanation: After flips a = 1 , b = 4 , c = 5 such that (a OR b == c)
Example 2:
Input: a = 4, b = 2, c = 7 Output: 1
Example 3:
Input: a = 1, b = 2, c = 3 Output: 0
Constraints:
1 <= a <= 10^9
1 <= b <= 10^9
1 <= c <= 10^9
Solutions
Solution 1: Bit Manipulation
We can enumerate each bit of the binary representation of $a$, $b$, and $c$, denoted as $x$, $y$, and $z$ respectively. If the bitwise OR operation result of $x$ and $y$ is different from $z$, we then check if both $x$ and $y$ are $1$. If so, we need to flip twice, otherwise, we only need to flip once. We accumulate all the required flip times.
The time complexity is $O(\log M)$, where $M$ is the maximum value of the numbers in the problem. The space complexity is $O(1)$.
1 2 3 4 5 6 7 |
|
1 2 3 4 5 6 7 8 9 10 |
|
1 2 3 4 5 6 7 8 9 10 11 |
|
1 2 3 4 5 6 7 8 9 10 11 |
|
1 2 3 4 5 6 7 8 |
|