Given three positive integers X, Y and P. Here P denotes the number of turns. Whenever the turn is odd X is multiplied by 2 and in every even turn Y is multiplied by 2. The task is to find the value of max(X, Y) ÷ min(X, Y) after the complete P turns.
Input : X = 1, Y = 2, P = 1 Output : 1 As turn is odd, X is multiplied by 2 and becomes 2. Now, X is 2 and Y is also 2. Therefore, 2 ÷ 2 is 1. Input : X = 3, Y = 7, p = 2 Output : 2 Here we have 2 turns. In the 1st turn which is odd X is multiplied by 2. And the values are 6 and 7. In the next turn which is even Y is multiplied by 2. Now the final values are 6 and 14. Therefore, 14 ÷ 6 is 2.
Lets play the above game for 8 turns :
| i | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |------|---|----|----|----|----|----|----|-----|-----| | X(i) | X | 2X | 2X | 4X | 4X | 8X | 8X | 16X | 16X | | Y(i) | Y | Y | 2Y | 2Y | 4Y | 4Y | 8Y | 8Y | 16Y |
Here we can easily spot a pattern :
if i is even, then X(i) = z * X and Y(i) = z * Y. if i is odd, then X(i) = 2*z * X and Y(i) = z * Y.
Here z is actually the power of 2. So, we can simply say –
If P is even output will be max(X, Y) ÷ min(X, Y) else output will be max(2*X, Y) ÷ min(2*X, Y).
Below is the implementation :
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