21 Matchsticks Problem
Given 21 Matchsticks and 2 users, A and B (computer and user respectively). Users can pick matchsticks not more than four at a time. The one who is forced to pick the last matchstick loses.
Given an array arr[] which contains the moves of the computer. The task is to print the moves of the user so that the user wins the game.
Examples:
Input : N = 4, arr=[ 3, 4, 2, 2]
Output : 2, 1, 3, 3
When the computer chooses 3 sticks, the user chooses 2 sticks
When the computer chooses 4 sticks, the user chooses 1 stick
When the computer chooses 2 sticks, the user chooses 3 sticks
When the computer chooses 2 sticks, the user chooses 3 sticks
Now only 1 stick is left and the computer is forced to pick that stick
Hence the user wins the game.Input : N = 4 arr=[ 1, 1, 4, 3]
Output : 4, 4, 1, 2
Approach:
- Idea is to think for 20 matchsticks as the user who would pick the last one will lose the game.
- Divide 20 into four parts that is, each part is of size 5. So if the computer picks x matchsticks then the user should pick (5-x) matchsticks and should proceed in the same way.
- In this way, 20 matchsticks will be used and the last matchstick would be picked by the computer.
Below is the implementation of the above approach
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the optimal strategy void TwentyoneMatchstick( int arr[], int N) { // Removing matchsticks in blocks of five for ( int i = 0; i < N; i += 1) { cout << 5 - arr[i] << " " ; } cout << endl; } // Driver code int main() { int arr[] = { 3, 4, 2, 2 }; int N = sizeof (arr) / sizeof (arr[0]); TwentyoneMatchstick(arr, N); return 0; } |
Java
// Java implementation of the approach class GFG { // Function to return the optimal strategy static void TwentyoneMatchstick( int arr[], int N) { // Removing matchsticks in blocks of five for ( int i = 0 ; i < N; i += 1 ) { System.out.print( 5 - arr[i] + " " ); } System.out.println(); } // Driver code public static void main(String[] args) { int arr[] = { 3 , 4 , 2 , 2 }; int N = arr.length; TwentyoneMatchstick(arr, N); } } // This code is contributed by Princi Singh |
Python3
# Python3 implementation of the approach # Function to return the optimal strategy def TwentyoneMatchstick(arr, N): # Removing matchsticks in blocks of five for i in range (N): print ( 5 - arr[i], end = " " ) # Driver code arr = [ 3 , 4 , 2 , 2 ] N = len (arr) TwentyoneMatchstick(arr, N) # This code is contributed # by Mohit Kumar |
C#
// C# implementation of the approach using System; class GFG { // Function to return the optimal strategy static void TwentyoneMatchstick( int []arr, int N) { // Removing matchsticks in blocks of five for ( int i = 0; i < N; i += 1) { Console.Write(5 - arr[i] + " " ); } Console.Write( "\n" ); } // Driver code public static void Main(String[] args) { int []arr = {3, 4, 2, 2}; int N = arr.Length; TwentyoneMatchstick(arr, N); } } // This code is contributed by Princi Singh |
Javascript
// javascript implementation of the approach // Function to return the optimal strategy function TwentyoneMatchstick(arr, N) { // Removing matchsticks in blocks of five for ( var i = 0; i < N; i += 1) { document.write(5 - arr[i] + " " ); } document.write( "<br>" ); } // Driver code var arr = [3, 4, 2, 2]; var N = arr.length; TwentyoneMatchstick(arr, N); // This code is contributed by bunnyram19. |
2 1 3 3
Time Complexity: O(N)
Auxiliary Space: O(1)
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