# Game of replacing array elements

There are two players A and B who are interested in playing a game of numbers. In each move a player pick two distinct number, let’s say *a1* and *a2* and then replace all *a2* by *a1* or *a1* by *a2*. They stop playing game if any one of them is unable to pick two number and the player who is unable to pick two distinct number in an array, looses the game. First player always move first and then second. Task is to find which player wins.

Examples:

Input : arr[] = { 1, 3, 3, 2,, 2, 1 } Output : Player 2 wins Explanation: First plays always looses irrespective of the numbers chosen by him. For example, say first player picks ( 1 & 3) replace all 3 by 1 Now array Become { 1, 1, 1, 2, 2, 1 } Then second player picks ( 1 2 ) either he replace 1 by 2 or 2 by 1 Array Become { 1, 1, 1, 1, 1, 1 } Now first player is not able to choose. Input : arr[] = { 1, 2, 1, 2 } Output : Player 1 wins

From above examples, we can observe that if number of count of distinct element is even, first player always wins. Else second player wins.

Lets take an another example :

int arr[] = 1, 2, 3, 4, 5, 6

Here number of distinct element is even(n). If player 1 pick any two number lets say (4, 1), then we left with n-1 distinct element. So player second left with n-1 distinct element. This precess go on until distinct element become 1. Here **n = 6**

Player : P1 p2 P1 p2 P1 P2 distinct : [n, n-1, n-2, n-3, n-4, n-5 ] "At this point no distinct element left, so p2 is unable to pick two Dis element."

Below implementation of above idea :

## C++

`// CPP program for Game of Replacement ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function return which player win the game ` `int` `playGame(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `// Create hash that will stores ` ` ` `// all distinct element ` ` ` `unordered_set<` `int` `> hash; ` ` ` ` ` `// Traverse an array element ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `hash.insert(arr[i]); ` ` ` ` ` `return` `(hash.size() % 2 == 0 ? 1 : 2); ` `} ` ` ` `// Driver Function ` `int` `main() ` `{ ` ` ` `int` `arr[] = { 1, 1, 2, 2, 2, 2 }; ` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` ` ` ` ` `cout << ` `"Player "` `<< playGame(arr, n) << ` `" Wins"` `<< endl; ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for Game of Replacement ` `import` `java.util.HashSet; ` `public` `class` `GameOfReplacingArrayElements ` `{ ` ` ` `// Function return which player win the game ` ` ` `public` `static` `int` `playGame(` `int` `arr[]) ` ` ` `{ ` ` ` `// Create hash that will stores ` ` ` `// all distinct element ` ` ` `HashSet<Integer> set=` `new` `HashSet<>(); ` ` ` ` ` `// Traverse an array element ` ` ` `for` `(` `int` `i:arr) ` ` ` `set.add(i); ` ` ` `return` `(set.size()%` `2` `==` `0` `)?` `1` `:` `2` `; ` ` ` `} ` ` ` ` ` `public` `static` `void` `main(String args[]) { ` ` ` `int` `arr[] = { ` `1` `, ` `1` `, ` `2` `, ` `2` `, ` `2` `, ` `2` `}; ` ` ` `System.out.print(` `"Player "` `+playGame(arr)+` `" wins"` `); ` ` ` `} ` `} ` `//This code is contributed by Gaurav Tiwari ` |

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## Python3

`# Python program for Game of Replacement ` ` ` `# Function return which player win the game ` `def` `playGame(arr, n): ` ` ` ` ` `# Create hash that will stores ` ` ` `# all distinct element ` ` ` `s ` `=` `set` `() ` ` ` ` ` `# Traverse an array element ` ` ` `for` `i ` `in` `range` `(n): ` ` ` `s.add(arr[i]) ` ` ` `return` `1` `if` `len` `(s) ` `%` `2` `=` `=` `0` `else` `2` ` ` `# Driver code ` `arr ` `=` `[` `1` `, ` `1` `, ` `2` `, ` `2` `, ` `2` `, ` `2` `] ` `n ` `=` `len` `(arr) ` `print` `(` `"Player"` `,playGame(arr, n),` `"Wins"` `) ` ` ` `# This code is contributed by Shrikant13 ` |

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## C#

`// C# program for Game of Replacement ` `using` `System; ` `using` `System.Collections.Generic; ` ` ` `public` `class` `GameOfReplacingArrayElements ` `{ ` ` ` `// Function return which player win the game ` ` ` `public` `static` `int` `playGame(` `int` `[]arr) ` ` ` `{ ` ` ` `// Create hash that will stores ` ` ` `// all distinct element ` ` ` `HashSet<` `int` `> ` `set` `= ` `new` `HashSet<` `int` `>(); ` ` ` ` ` `// Traverse an array element ` ` ` `foreach` `(` `int` `i ` `in` `arr) ` ` ` `set` `.Add(i); ` ` ` `return` `(` `set` `.Count % 2 == 0) ? 1 : 2; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main(String []args) ` ` ` `{ ` ` ` `int` `[]arr = { 1, 1, 2, 2, 2, 2 }; ` ` ` `Console.Write(` `"Player "` `+ playGame(arr) + ` `" wins"` `); ` ` ` `} ` `} ` ` ` `// This code has been contributed by 29AjayKumar ` |

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**Output:**

Player 1 Wins

**Time Complexity :** O(n)

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