# Even-odd turn game with two integers

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.

Examples :

```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.
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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 :

## C++

 `// CPP program to find max(X, Y) / min(X, Y) ` `// after P turns ` `#include ` `using` `namespace` `std; ` ` `  `int` `findValue(``int` `X, ``int` `Y, ``int` `P) ` `{ ` `    ``if` `(P % 2 == 0) ` `        ``return` `(max(X, Y) / min(X, Y)); ` ` `  `    ``else` `        ``return` `(max(2 * X, Y) / min(2 * X, Y)); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// 1st test case ` `    ``int` `X = 1, Y = 2, P = 1; ` `    ``cout << findValue(X, Y, P) << endl; ` ` `  `    ``// 2nd test case ` `    ``X = 3, Y = 7, P = 2; ` `    ``cout << findValue(X, Y, P) << endl; ` `} `

## Java

 `// Java program to find max(X, Y) / min(X, Y) ` `// after P turns ` `import` `java.util.*; ` ` `  `class` `Even_odd{ ` `    ``public` `static` `int` `findValue(``int` `X, ``int` `Y,  ` `                                        ``int` `P) ` `    ``{ ` `        ``if` `(P % ``2` `== ``0``) ` `            ``return` `(Math.max(X, Y) /  ` `                            ``Math.min(X, Y)); ` ` `  `        ``else` `            ``return` `(Math.max(``2` `* X, Y) / ` `                            ``Math.min(``2` `* X, Y)); ` `    ``} ` `     `  `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``// 1st test case ` `        ``int` `X = ``1``, Y = ``2``, P = ``1``; ` `        ``System.out.println(findValue(X, Y, P)); ` `         `  `        ``// 2nd test case ` `        ``X = ``3``; ` `        ``Y = ``7``; ` `        ``P = ``2``; ` `        ``System.out.print(findValue(X, Y, P)); ` `    ``} ` `} ` ` `  `//This code is contributed by rishabh_jain `

## Python3

 `# Python3 code to find max(X, Y) / min(X, Y) ` `# after P turns ` ` `  `def` `findValue( X , Y , P ): ` `    ``if` `P ``%` `2` `=``=` `0``: ` `        ``return` `int``(``max``(X, Y) ``/` `min``(X, Y)) ` ` `  `    ``else``: ` `        ``return` `int``(``max``(``2` `*` `X, Y) ``/` `min``(``2` `*` `X, Y)) ` ` `  `# Driver code ` `# 1st test case ` `X ``=` `1` `Y ``=` `2` `P ``=` `1` `print``(findValue(X, Y, P)) ` ` `  `# 2nd test case ` `X ``=` `3` `Y ``=` `7` `P ``=` `2` `print``((findValue(X, Y, P))) ` ` `  `# This code is contribted by "Sharad_Bhardwaj". `

## C#

 `// C# program to find max(X, Y) / min(X, Y) ` `// after P turns ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `int` `findValue(``int` `X, ``int` `Y,  ` `                                        ``int` `P) ` `    ``{ ` `        ``if` `(P % 2 == 0) ` `            ``return` `(Math.Max(X, Y) /  ` `                    ``Math.Min(X, Y)); ` ` `  `        ``else` `            ``return` `(Math.Max(2 * X, Y) / ` `                    ``Math.Min(2 * X, Y)); ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``// 1st test case ` `        ``int` `X = 1, Y = 2, P = 1; ` `        ``Console.WriteLine(findValue(X, Y, P)); ` `         `  `        ``// 2nd test case ` `        ``X = 3; ` `        ``Y = 7; ` `        ``P = 2; ` `        ``Console.WriteLine(findValue(X, Y, P)); ` `    ``} ` `} ` ` `  `//This code is contributed by vt_m `

## PHP

 ` `

Output:

```1
2
```

Time Complexity:O(1)

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