Given four numbers M, N, A and B, the task is to check whether M and N can be made equal to each other by doing any of the below operations:
- M can be increased by A and N can be decreased by B
- Leave both of them as it is.
Input: M = 2, N = 8, A = 3, B = 3
After first Operation:
M can be increased by A. Therefore, M = 2 + 3 = 5
N can be decreased by B. Therefore, N = 8 – 3 = 5
Finally, M = N = 5.
Input: M = 6, N = 4, A = 2, B = 1
Approach: On careful observation, it can be observed that since we are increasing M and decreasing N, they can be made equal only when M is less than N. Therefore when M is less than N, there are two cases at each step:
- M can be increased by A and N can be decreased by B.
- Leave both of them as it is.
Another observation which can be made is that when M is increased and N is decreased, the absolute distance between M and N is reduced by the factor of A + B. For example:
Let M = 2, N = 14, A = 3 and B = 3.
- In step 1, M = 5 and N = 11. The absolute distance between M and N got reduced by 6. That is, initially, the absolute distance was 12(14 – 2). After performing the given step, the absolute distance became 6(11 – 5).
- In step 2, M = 8 and N = 8. The absolute distance between M and N again got reduced by 6 thereby making M and N equal.
From the above example, we can come to the conclusion that this problem can be solved in a constant time only by checking if the absolute distance between M and N is a multiple of (A + B) or not.
- If it is a multiple, then M and N can be made equal.
- Else, they cannot be made equal.
Below is the implementation of the above approach:
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Improved By : Yash_R