Maximum prime moves to convert X to Y
Given two integers X and Y, the task is to convert X to Y using the following operations:
- Add any prime number to X.
- Subtract any prime number from Y.
Print the maximum number of such operations required or -1 if it is not possible to convert X to Y.
Input: X = 2, Y = 4
2 -> 4
Input: X = 5, Y = 6
It is impossible to convert 5 to 6
with the given operations.
Approach: As the task is to maximize the operations, so the minimum possible value must be added to X in every operation. Since the value has to be prime, so the minimum two primes i.e. 2 and 3 can be used as they both are prime and can cover both even and odd parity. Now, there are three cases:
- If X > Y then the answer will be -1 as X cannot be made equal to Y with the given operation.
- If X = Y then the answer will be 0.
- If X < Y then calculate P = Y – X and,
- If P = 1 then the answer will be -1 as 1 is not prime and it cannot be added or subtracted.
- If P is even then 2 can be repeatedly added to X and the answer will be P / 2
- If P is even then add 3 to X and then 2 can again be repeatedly added to the new X to make it equal to Y, the result, in this case, will be 1 + ((P – 3) / 2).
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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