A Chessboard Game


Problem Statement :


Two players are playing a game on a  chessboard. The rules of the game are as follows:

The game starts with a single coin located at some  coordinates. The coordinates of the upper left cell are , and of the lower right cell are .

In each move, a player must move the coin from cell  to one of the following locations:

Note: The coin must remain inside the confines of the board.

Beginning with player 1, the players alternate turns. The first player who is unable to make a move loses the game.

The figure below shows all four possible moves using an  board for illustration:


Function Description

Complete the chessboardGame function in the editor below. It should return a string, either First or Second.

chessboardGame has the following parameter(s):

x: an integer that represents the starting column position
y: an integer that represents the starting row position


Input Format

The first line contains an integer , the number of test cases.
Each of the next  lines contains  space-separated integers  and .


Solution :



title-img 


                            Solution in C :

In  C :






#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int main() {

    /* Enter your code here. Read input from STDIN. Print output to STDOUT */    
    int t;
    scanf("%d",&t);
    while(t--)
        {
        int x,y;
        scanf("%d %d",&x,&y);
        int dp[15][15];
        x--;
        y--;
        dp[1][0]=dp[0][0]=dp[0][1]=dp[1][1]=1;
        int i=2;
        while(i<15)
            {
            int temp=0;
            while(temp<=i)
                {
                if((i-2>=0&&temp+1<15?dp[i-2][temp+1]:0)||(i-2>=0&&temp-1>=0?dp[i-2][temp-1]:0)||(i+1<15&&temp-2>=0?dp[i+1][temp-2]:0)||(i-1>=0&&temp-2>=0?dp[i-1][temp-2]:0))
                    dp[i][temp]=0;
                else
                    dp[i][temp]=1;
                if((i-2>=0&&temp+1<15?dp[temp+1][i-2]:0)||(i-2>=0&&temp-1>=0?dp[temp-1][i-2]:0)||(i+1<15&&temp-2>=0?dp[temp-2][i+1]:0)||(i-1>=0&&temp-2>=0?dp[temp-2][i-1]:0))
                    dp[temp][i]=0;
                else
                    dp[temp][i]=1;
                temp++;
            }
            i++;
        }
        if(dp[x][y])
            printf("Second\n");
        else
            printf("First\n");
    }
    return 0;
}
                        


                        Solution in C++ :

In  C++  :






#include <bits/stdc++.h>
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
long DP[16][16];
long dx[4]={-2,-2,1,-1};
long dy[4]={1,-1,-2,-2};
bool inside(long u,long v)
{
	return (u>0 && v>0 && u<=15 && v<=15);
}

bool dp(long x,long y)
{
	if (DP[x][y]!=-1) return DP[x][y];
	bool res=false;
	for (long i=0; i<4; ++i)
	{
		long xx=x+dx[i],yy=y+dy[i];
		if (inside(xx,yy)) res=res|(!dp(xx,yy));
	}
	DP[x][y]=res;
	return res;
}
int main()
{
	long nTest,x,y;
	memset(DP,-1,sizeof(DP));
	DP[1][1]=DP[1][2]=DP[2][1]=DP[2][2]=false;
	scanf("%ld",&nTest);
	while (nTest--)
	{
		scanf("%ld%ld",&x,&y);
		puts(dp(x,y)?"First":"Second");
	}
}
                    


                        Solution in Java :

In   Java :






import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {
    
    private static void pasteTessalation(boolean[][] board, int r, int c) {
        board[r][c] = true;
        board[r][c+1] = true;
        board[r+1][c] = true;
        board[r+1][c+1] = true;
    }

    public static void main(String[] args) {
        boolean[][] loss = new boolean[16][16];
        for (int i=0; i<16; i+=4) {
            for (int j=0; j<16; j+=4) {
                pasteTessalation(loss,i,j);
            }
        }
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        for (int t=0; t<T; t++) {
            int r = sc.nextInt()-1;
            int c = sc.nextInt()-1;
            if (loss[r][c]) {
                System.out.println("Second");
            } else {
                System.out.println("First");
            }
        }
        
    }
    
}
                    


                        Solution in Python : 
                            
in    Python3 :







import copy

move = [(-2,1),(-2,-1),(1,-2),(-1,-2)]
grid_copy = set()
for i in range(1,16):
    for j in range(1,16):
        grid_copy.add((i,j))

First = set()
Second = set()

t=0
while len(First) + len(Second) != 225:
    if t%2 ==0:
        for i,j in grid_copy:
            n=0
            for x,y in move:
                if (i+x,j+y) not in grid_copy or (i+x,j+y) in First:
                    n+=1
            if n==4:
                Second.add((i,j))
    else:
        for i,j in grid_copy:
            for x,y in move:
                if (i+x,j+y) in Second:
                    First.add((i,j))
    t+=1        
#print('--------')
#print(sorted(list(First)))
#print(len(First))
#print(sorted(list(Second)))
#print(len(Second))
test = int(input())
for _ in range(test):
    x,y = map(int,input().strip().split())
    if (x,y) in First:
        print('First')
    else:
        print('Second')


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