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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

2 1 3 3

Time Complexity: O(N)



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COMPETITIVE PROGRAMMER | KAGGLE BEGINNER | MACHINE LEARNING EXPLORER

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