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Determine the winner of a game of deleting Characters from a String
• Last Updated : 27 Aug, 2020

Given numeric string str, the task is to determine the winner of the game when two players play a game optimally with the string as per the given conditions:

• Player 1 always starts first.
• In one turn one player can remove the contiguous elements from the string and the number of elements removed will add up to his score. Player 1 will remove odd contiguous elements and Player 1 will remove even contiguous elements.
• Any player who is not able to make a move loses the game.
• After all the strings are removed, the player with maximum scores wins the game and if scores are equal then print “-1”.

Examples:

Input: str = “7788”
Output: -1
Explanation:
First move for player 1 is to remove 77 and for player 2 is 88. Score for both is 2. Hence -1.

Input: str = “8822”
Output: Player 2
Explanation:
There are no odd elements so player 1 cant make amove so player 2 wins.

Approach: Follow the steps below in order to solve the problem:

1. Create an array A[] of size 10 to store the frequency of all the digits in the given string.
2. Iterate the given string and update the frequency of each digit in the above array.
3. Traverse the array A[] and take two variables as sum1 = 0 and sum2 = 0 to store the sum of scores.
4. Increment sum1 if the index is odd i.e., Player 1 turn else increment sum2 if the index is even i.e., Player 2 turn.
5. After the above steps check if sum1 is equal to sum2 then print -1 otherwise print the player number who wins the game on the basis of the score.

Below is the implementation of the above approach:

C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;`` ` `// Function to find the winner of the``// game when both players play optimally``void` `determineWinner(string str)``{``    ``// Stores the frequency of all digit``    ``vector<``int``> A(10);`` ` `    ``// Stores the scores of player1``    ``// and player2 respectively``    ``int` `sum1 = 0, sum2 = 0;`` ` `    ``// Iterate to store frequencies``    ``for` `(``int` `i = 0; i < str.length(); i++) {``        ``A[``int``(str[i]) - 48]++;``    ``}`` ` `    ``for` `(``int` `i = 0; i <= 9; i++) {`` ` `        ``// Turn for the player1``        ``if` `(i % 2 != 0) {`` ` `            ``// Add score of player1``            ``sum1 = sum1 + A[i];``        ``}``        ``else` `{`` ` `            ``// Add score of player2``            ``sum2 = sum2 + A[i];``        ``}``    ``}`` ` `    ``// Check if its a draw``    ``if` `(sum1 == sum2) {``        ``cout << ``"-1"``;``    ``}`` ` `    ``// If score of player 1 is greater``    ``else` `if` `(sum1 > sum2) {``        ``cout << ``"Player 1"``;``    ``}`` ` `    ``// Otherwise``    ``else` `{``        ``cout << ``"Player 2"``;``    ``}``}`` ` `// Driver Code``int` `main()``{``    ``string str = ``"78787"``;``    ``determineWinner(str);``    ``return` `0;``}`

Java

 `// Java program for the above approach ``import` `java.util.*;`` ` `class` `GFG{`` ` `// Function to find the winner of the``// game when both players play optimally``static` `void` `determineWinner(String str)``{``     ` `    ``// Stores the frequency of all digit``    ``int``[] A = ``new` `int``[``10``];`` ` `    ``// Stores the scores of player1``    ``// and player2 respectively``    ``int` `sum1 = ``0``, sum2 = ``0``;`` ` `    ``// Iterate to store frequencies``    ``for``(``int` `i = ``0``; i < str.length(); i++)``    ``{``        ``A[(``int``)str.charAt(i) - ``48``]++;``    ``}`` ` `    ``for``(``int` `i = ``0``; i <= ``9``; i++)``    ``{``         ` `        ``// Turn for the player1``        ``if` `(i % ``2` `!= ``0``) ``        ``{`` ` `            ``// Add score of player1``            ``sum1 = sum1 + A[i];``        ``}``        ``else``        ``{`` ` `            ``// Add score of player2``            ``sum2 = sum2 + A[i];``        ``}``    ``}`` ` `    ``// Check if its a draw``    ``if` `(sum1 == sum2) ``    ``{``        ``System.out.print(``"-1"``);``    ``}`` ` `    ``// If score of player 1 is greater``    ``else` `if` `(sum1 > sum2)``    ``{``        ``System.out.print(``"Player 1"``);``    ``}`` ` `    ``// Otherwise``    ``else` `    ``{``        ``System.out.print(``"Player 2"``);``    ``}``}`` ` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``String str = ``"78787"``;``     ` `    ``determineWinner(str);``}``}`` ` `// This code is contributed by offbeat`

Python3

 `# Python3 program for the above approach `` ` `# Function to find the winner of the``# game when both players play optimally``def` `determineWinner(``str``):`` ` `    ``# Stores the frequency of all digit``    ``A ``=` `[``0` `for` `i ``in` `range``(``9``)];`` ` `    ``# Stores the scores of player1``    ``# and player2 respectively``    ``sum1 ``=` `0``; sum2 ``=` `0``;`` ` `    ``# Iterate to store frequencies``    ``for` `i ``in` `range``(``0``, ``len``(``str``)):``        ``A[``int``(``str``[i])] ``+``=` `1``;``     ` `    ``for` `i ``in` `range``(``0``, ``9``):`` ` `        ``# Turn for the player1``        ``if` `(i ``%` `2` `!``=` `0``):`` ` `            ``# Add score of player1``            ``sum1 ``=` `sum1 ``+` `A[i];``        ``else``:`` ` `            ``# Add score of player2``            ``sum2 ``=` `sum2 ``+` `A[i];``         ` `    ``# Check if its a draw``    ``if` `(sum1 ``=``=` `sum2):``        ``print``(``"-1"``);``     ` `    ``# If score of player 1 is greater``    ``elif``(sum1 > sum2):``        ``print``(``"Player 1"``);``     ` `    ``# Otherwise``    ``else``:``        ``print``(``"Player 2"``);``     ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``     ` `    ``str` `=` `"78787"``;`` ` `    ``determineWinner(``str``);``     ` `# This code is contributed by Amit Katiyar `

C#

 `// C# program for the above approach ``using` `System;``class` `GFG{`` ` `// Function to find the winner of the``// game when both players play optimally``static` `void` `determineWinner(String str)``{``     ` `    ``// Stores the frequency of all digit``    ``int``[] A = ``new` `int``[10];`` ` `    ``// Stores the scores of player1``    ``// and player2 respectively``    ``int` `sum1 = 0, sum2 = 0;`` ` `    ``// Iterate to store frequencies``    ``for``(``int` `i = 0; i < str.Length; i++)``    ``{``        ``A[(``int``)str[i] - 48]++;``    ``}`` ` `    ``for``(``int` `i = 0; i <= 9; i++)``    ``{``         ` `        ``// Turn for the player1``        ``if` `(i % 2 != 0) ``        ``{`` ` `            ``// Add score of player1``            ``sum1 = sum1 + A[i];``        ``}``        ``else``        ``{`` ` `            ``// Add score of player2``            ``sum2 = sum2 + A[i];``        ``}``    ``}`` ` `    ``// Check if its a draw``    ``if` `(sum1 == sum2) ``    ``{``        ``Console.Write(``"-1"``);``    ``}`` ` `    ``// If score of player 1 is greater``    ``else` `if` `(sum1 > sum2)``    ``{``        ``Console.Write(``"Player 1"``);``    ``}`` ` `    ``// Otherwise``    ``else` `    ``{``        ``Console.Write(``"Player 2"``);``    ``}``}`` ` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``String str = ``"78787"``;``     ` `    ``determineWinner(str);``}``}`` ` `// This code is contributed by Rohit_ranjan`
Output:
```Player 1
```

Time Complexity: O(N)
Auxiliary Space: O(N)

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