Given a positive integer N, representing the count of players playing the game and an array of strings arr[], consisting of the numeric strings made up of digits from the range [ā1ā, āNā]. Considering ith player is assigned with the string arr[i], the task is to find the winner of the game when all N players play the game optimally as per the following rules:
- Player 1 starts the game, removes the first character of the string arr[1]( 1-based indexing ), say X, and in the next turn Xth player will play the game and remove the first character of arr[X] and so on.
- The player who is not able to remove any character from the assigned string will win the game.
Examples:
Input: N = 3, arr[] = { ā323ā, ā2ā, ā2ā }Ā
Output: Player 2Ā
Explanation:Ā
Turn 1: Removing arr[0][0] by Player 1 modifies arr[0] to ā23ā.Ā
Turn 2: Removing arr[2][0] by Player 3 modifies arr[2] to āā.Ā
Turn 3: Removing arr[1][0] by Player 2 modifies arr[1] to āā.Ā
Turn 4: Player 2 is not able to remove any characters from arr[1].Ā
Therefore, player 2 wins the game.Input: N = 3, arr[] = { ā121ā, ā21ā, ā23123ā }Ā
Output: Player 1
Approach: The problem can be solved using Queue to remove the first character of each string efficiently. Follow the steps below to solve the problem:
- Initialize an array of Queues, say Q[], such that Q[i] stores the characters of the string arr[i].
- Traverse the array Q[] using variable i as per the rules of the game and check if the count of characters in Q[i] is 0 or not. If found to be true, then print the āPlayer iā.
Below is the implementation of the above approach:
C++
// C++ program to implement// the above approachĀ
#include <bits/stdc++.h>using namespace std;Ā
// Function to find the winner of a game of// repeatedly removing the first character// to empty a stringvoid find_Winner(vector<string>& arr, int N){Ā
Ā Ā Ā Ā // Store characters of eachĀ Ā Ā Ā // string of the array arr[]Ā Ā Ā Ā vector<queue<char> > Q(N);Ā
Ā Ā Ā Ā // Stores count of strings in arr[]Ā Ā Ā Ā int M = arr.size();Ā
Ā Ā Ā Ā // Traverse the array arr[]Ā Ā Ā Ā for (int i = 0; i < M; i++) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores length of current stringĀ Ā Ā Ā Ā Ā Ā Ā int len = arr[i].length();Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Traverse the stringĀ Ā Ā Ā Ā Ā Ā Ā for (int j = 0; j < len; j++) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Insert arr[i][j]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i].push(arr[i][j] - 1);Ā Ā Ā Ā Ā Ā Ā Ā }Ā Ā Ā Ā }Ā
Ā Ā Ā Ā // 1st Player starts the gameĀ Ā Ā Ā int player = 0;Ā
Ā Ā Ā Ā while (Q[player].size() > 0) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores the player numberĀ Ā Ā Ā Ā Ā Ā Ā // for the next turnĀ Ā Ā Ā Ā Ā Ā Ā int nextPlayerĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā = Q[player].front() - '0';Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Remove 1st character ofĀ Ā Ā Ā Ā Ā Ā Ā // current stringĀ Ā Ā Ā Ā Ā Ā Ā Q[player].pop();Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Update player number forĀ Ā Ā Ā Ā Ā Ā Ā // the next turnĀ Ā Ā Ā Ā Ā Ā Ā player = nextPlayer;Ā Ā Ā Ā }Ā
Ā Ā Ā Ā cout << "Player " << (player + 1);}Ā
// Driver Codeint main(){Ā
Ā Ā Ā Ā int N = 3;Ā Ā Ā Ā vector<string> arrĀ Ā Ā Ā Ā Ā Ā Ā = { "323", "2", "2" };Ā
Ā Ā Ā Ā find_Winner(arr, N);Ā Ā Ā Ā return 0;} |
Java
// Java program to implement// the above approachimport java.util.*;Ā
class GFG{Ā
// Function to find the winner of a game of// repeatedly removing the first character// to empty a Stringstatic void find_Winner(String[] arr, int N){Ā
Ā Ā Ā Ā // Store characters of eachĀ Ā Ā Ā // String of the array arr[]Ā Ā Ā Ā @SuppressWarnings("unchecked")Ā Ā Ā Ā Vector<Character> [] Q = new Vector[N];Ā Ā Ā Ā for (int i = 0; i < Q.length; i++)Ā Ā Ā Ā Ā Ā Ā Ā Q[i] = new Vector<Character>();Ā Ā Ā Ā Ā Ā Ā // Stores count of Strings in arr[]Ā Ā Ā Ā int M = arr.length;Ā
Ā Ā Ā Ā // Traverse the array arr[]Ā Ā Ā Ā for (int i = 0; i < M; i++) Ā Ā Ā Ā {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores length of current StringĀ Ā Ā Ā Ā Ā Ā Ā int len = arr[i].length();Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Traverse the StringĀ Ā Ā Ā Ā Ā Ā Ā for (int j = 0; j < len; j++)Ā Ā Ā Ā Ā Ā Ā Ā {Ā
Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Insert arr[i][j]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i].add(arr[i].charAt(j));Ā Ā Ā Ā Ā Ā Ā Ā }Ā Ā Ā Ā Ā Ā Ā Ā Ā }Ā
Ā Ā Ā Ā // 1st Player starts the gameĀ Ā Ā Ā int player = 0;Ā
Ā Ā Ā Ā while (Q[player].size() > 0 ) Ā Ā Ā Ā {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores the player numberĀ Ā Ā Ā Ā Ā Ā Ā // for the next turnĀ Ā Ā Ā Ā Ā Ā Ā int nextPlayerĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā = Q[player].get(0) - '0'-1;Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Remove 1st character ofĀ Ā Ā Ā Ā Ā Ā Ā // current StringĀ Ā Ā Ā Ā Ā Ā Ā Q[player].remove(0);Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Update player number forĀ Ā Ā Ā Ā Ā Ā Ā // the next turnĀ Ā Ā Ā Ā Ā Ā Ā player = nextPlayer;Ā Ā Ā Ā }Ā Ā Ā Ā System.out.print("Player " +Ā (player + 1));}Ā
// Driver Codepublic static void main(String[] args){Ā Ā Ā Ā int N = 3;Ā Ā Ā Ā String[] arrĀ Ā Ā Ā Ā Ā Ā Ā = { "323", "2", "2" };Ā Ā Ā Ā find_Winner(arr, N);}}Ā
// This code is contributed by gauravrajput1 |
Python3
# Python3 program to implement# the above approachĀ
# Function to find the winner of a game of# repeatedly removing the first character# to empty a stringdef find_Winner(arr, N) :Ā Ā Ā Ā Ā Ā # Store characters of eachĀ Ā Ā Ā # string of the array arr[]Ā Ā Ā Ā Q = [0]*NĀ Ā Ā Ā Ā Ā for i in range(N) :Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i] = []Ā Ā Ā Ā Ā Ā # Stores count of strings in arr[]Ā Ā Ā Ā M = len(arr)Ā Ā Ā Ā Ā Ā # Traverse the array arr[]Ā Ā Ā Ā for i in range(M) :Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Stores length of current stringĀ Ā Ā Ā Ā Ā Ā Ā Len = len(arr[i])Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Traverse the stringĀ Ā Ā Ā Ā Ā Ā Ā for j in range(Len) :Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Insert arr[i][j]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i].append(ord(arr[i][j]) - 1)Ā Ā Ā Ā Ā Ā # 1st Player starts the gameĀ Ā Ā Ā player = 0Ā Ā Ā Ā Ā Ā while (len(Q[player]) > 0) :Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Stores the player numberĀ Ā Ā Ā Ā Ā Ā Ā # for the next turnĀ Ā Ā Ā Ā Ā Ā Ā nextPlayer = Q[player][0] - ord('0')Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Remove 1st character ofĀ Ā Ā Ā Ā Ā Ā Ā # current stringĀ Ā Ā Ā Ā Ā Ā Ā del Q[player][0]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā # Update player number forĀ Ā Ā Ā Ā Ā Ā Ā # the next turnĀ Ā Ā Ā Ā Ā Ā Ā player = nextPlayerĀ Ā Ā Ā Ā Ā print("Player", (player + 1))Ā Ā Ā Ā Ā N = 3arr = [ "323", "2", "2" ]Ā
find_Winner(arr, N)Ā
# This code is contributed by divyeshrabadiya07. |
C#
// C# program to implement// the above approachusing System;using System.Collections.Generic;Ā
class GFG{Ā
// Function to find the winner of a game of// repeatedly removing the first character// to empty a Stringstatic void find_Winner(String[] arr, int N){Ā Ā Ā Ā Ā Ā Ā Ā Ā // Store characters of eachĀ Ā Ā Ā // String of the array []arrĀ Ā Ā Ā List<char> [] Q = new List<char>[N];Ā Ā Ā Ā for(int i = 0; i < Q.Length; i++)Ā Ā Ā Ā Ā Ā Ā Ā Q[i] = new List<char>();Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Stores count of Strings in []arrĀ Ā Ā Ā int M = arr.Length;Ā
Ā Ā Ā Ā // Traverse the array []arrĀ Ā Ā Ā for(int i = 0; i < M; i++) Ā Ā Ā Ā {Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Stores length of current StringĀ Ā Ā Ā Ā Ā Ā Ā int len = arr[i].Length;Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Traverse the StringĀ Ā Ā Ā Ā Ā Ā Ā for(int j = 0; j < len; j++)Ā Ā Ā Ā Ā Ā Ā Ā {Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Insert arr[i,j]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i].Add(arr[i][j]);Ā Ā Ā Ā Ā Ā Ā Ā }Ā Ā Ā Ā }Ā
Ā Ā Ā Ā // 1st Player starts the gameĀ Ā Ā Ā int player = 0;Ā
Ā Ā Ā Ā while (Q[player].Count > 0 ) Ā Ā Ā Ā {Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Stores the player numberĀ Ā Ā Ā Ā Ā Ā Ā // for the next turnĀ Ā Ā Ā Ā Ā Ā Ā int nextPlayer = Q[player][0] - '0'- 1;Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Remove 1st character ofĀ Ā Ā Ā Ā Ā Ā Ā // current StringĀ Ā Ā Ā Ā Ā Ā Ā Q[player].RemoveAt(0);Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Update player number forĀ Ā Ā Ā Ā Ā Ā Ā // the next turnĀ Ā Ā Ā Ā Ā Ā Ā player = nextPlayer;Ā Ā Ā Ā }Ā Ā Ā Ā Console.Write("Player " + (player + 1));}Ā
// Driver Codepublic static void Main(String[] args){Ā Ā Ā Ā int N = 3;Ā Ā Ā Ā String[] arr = { "323", "2", "2" };Ā Ā Ā Ā Ā Ā Ā Ā Ā find_Winner(arr, N);}}Ā
// This code is contributed by Rajput-Ji |
Javascript
<script>Ā
// Javascript program to implement// the above approachĀ
// Function to find the winner of a game of// repeatedly removing the first character// to empty a stringfunction find_Winner( arr, N){Ā
Ā Ā Ā Ā // Store characters of eachĀ Ā Ā Ā // string of the array arr[]Ā Ā Ā Ā var Q = Array.from(Array(N), ()=>Array())Ā
Ā Ā Ā Ā // Stores count of strings in arr[]Ā Ā Ā Ā var M = arr.length;Ā
Ā Ā Ā Ā // Traverse the array arr[]Ā Ā Ā Ā for (var i = 0; i < M; i++) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores length of current stringĀ Ā Ā Ā Ā Ā Ā Ā var len = arr[i].length;Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Traverse the stringĀ Ā Ā Ā Ā Ā Ā Ā for (var j = 0; j < len; j++) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā // Insert arr[i][j]Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Q[i].push(arr[i][j] - 1);Ā Ā Ā Ā Ā Ā Ā Ā }Ā Ā Ā Ā }Ā
Ā Ā Ā Ā // 1st Player starts the gameĀ Ā Ā Ā var player = 0;Ā
Ā Ā Ā Ā while (Q[player].length > 0) {Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Stores the player numberĀ Ā Ā Ā Ā Ā Ā Ā // for the next turnĀ Ā Ā Ā Ā Ā Ā Ā var nextPlayerĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā = Q[player][0] - '0';Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Remove 1st character ofĀ Ā Ā Ā Ā Ā Ā Ā // current stringĀ Ā Ā Ā Ā Ā Ā Ā Q[player].shift();Ā
Ā Ā Ā Ā Ā Ā Ā Ā // Update player number forĀ Ā Ā Ā Ā Ā Ā Ā // the next turnĀ Ā Ā Ā Ā Ā Ā Ā player = nextPlayer;Ā Ā Ā Ā }Ā
Ā Ā Ā Ā document.write( "Player " + (player + 1));}Ā
// Driver Codevar N = 3;var arrĀ Ā Ā Ā = ["323", "2", "2"];find_Winner(arr, N);Ā
// This code is contributed by rutvik_56.</script> |
Output:Ā
Player 2
Ā
Time Complexity: O(N * M), where M is the length of the longest string present in the array.
Auxiliary Space: O(N * M)
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