Given integers X, Y, and K, the task is to make X and Y equal in not more than K operations by applying the following operations:
- Choose an integer A and make X = X/A, (where A is an integer that is greater than 1 and not equal to X).
- Choose an integer A and make Y = Y/A, (where A is an integer that is greater than 1 and not equal to Y).
Examples:
Input: X = 10, Y = 20, K = 4
Output: YES
Explanation: One optimal solution to make them equal is:
First choose A = 2 and do X = X/2 so now X is equal to 5.
Now choose A = 4 and do Y = Y/4 so now Y is equal to 5.
Since we have applied only two operations here which is less than K
to make X and Y equal and also greater than one.
Therefore the answer is YES.Input: X = 2, Y = 27, K = 1
Output: NO
Explanation: There is no possible way to make X and Y equal
in less than or equal to 1 Operation.
Approach: To solve the problem follow the below idea:
Here are only two cases possible:
- When K is equal to one and
- When K is greater than 1
If K is equal to one then it is possible to make X and Y equal only when either X is divisible by Y or Y is divisible by X
If K is greater than 1 then X and Y can be equal and greater than 1 only when their GCD is greater than 1.
Follow the steps mentioned below to implement the idea:
- Check if K = 1:
- In that case, find out if any of them is a divisor of the other.
- Otherwise, find the GCD of the numbers.
- If the GCD is 1 then it is not possible.
- Otherwise, an answer always exists.
Below is the implementation for the above approach:
C++
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Time Complexity: O(1)
Auxiliary Space: O(1)