# Even-odd turn game with two integers

• Difficulty Level : Easy
• Last Updated : 17 May, 2021

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.```

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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 contributed 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

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## Javascript

 ``

Output:

```1
2```

Time Complexity:O(1)

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