Given an array of integers of size ‘n’ and an integer ‘k’,
We can perform the Bitwise AND operation between any array element and ‘k’ any number of times.
The task is to print the minimum number of such operations required to make any two elements of the array equal.
If it is not possible to make any two elements of the array equal after performing the above mentioned operation then print ‘-1’.
Input : k = 6 ; Array : 1, 2, 1, 2
Output : 0
Explanation : There are already two equal elements in the array so the answer is 0.
Input : k = 2 ; Array : 5, 6, 2, 4
Output : 1
Explanation : If we apply AND operation on element ‘6’, it will become 6&2 = 2
And the array will become 5 2 2 4,
Now, the array has two equal elements, so the answer is 1.
Input : k = 15 ; Array : 1, 2, 3
Output : -1
Explanation : No matter how many times we perform the above mentioned operation,
this array will never have equal element pair. So the answer is -1
The key observation is that if it is possible to make the desired array then the
answer will be either ‘0’, ‘1’ or ‘2’. It will never exceed ‘2’.
Because, if (x&k) = y
then, no matter how many times you perform (y&k)
it’ll always give ‘y’ as the result.
- The answer will be ‘0’, if there are already equal elements in the array.
- For the answer to be ‘1’, we will create a new array b which holds b[i] = (a[i]&K),
Now, for each a[i] we will check if there is any index ‘j’ such that i!=j and a[i]=b[j].
If yes, then the answer will be ‘1’.
- For the answer to be ‘2’, we will check for an index ‘i’ in the new array b,
if there is any index ‘j’ such that i != j and b[i] = b[j].
If yes, then the answer will be ‘2’.
- If any of the above conditions is not satisfied then the answer will be ‘-1’.
Below is the implementation of the above approach:
- Minimum Bitwise XOR operations to make any two array elements equal
- Minimum Bitwise OR operations to make any two array elements equal
- Minimum operations required to make all the array elements equal
- Minimum number of increment-other operations to make all array elements equal.
- Find the minimum number of operations required to make all array elements equal
- Minimum decrement operations to make Array elements equal by only decreasing K each time
- Minimum increment by k operations to make all elements equal
- Find if it is possible to make all elements of an array equal by the given operations
- Minimum gcd operations to make all array elements one
- Find the number of operations required to make all array elements Equal
- Minimum delete operations to make all elements of array same
- Minimum number of operations on an array to make all elements 0
- Minimum no. of operations required to make all Array Elements Zero
- Make all the array elements odd with minimum operations of given type
- Minimum operation to make all elements equal in array
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