The Attack of Queen Solution Codechef

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The Attack of Queen Solution Codechef

Chef has started developing interest in playing chess, and was learning how the Queen moves.

Chef has an empty N×N chessboard. He places a Queen at (X,Y) and wonders – What are the number of cells that are under attack by the Queen?

Notes:

The top-left cell is (1,1), the top-right cell is (1,N), the bottom-left cell is (N,1) and the bottom-right cell is (N,N).
The Queen can be moved any number of unoccupied cells in a straight line vertically, horizontally, or diagonally.
The cell on which the Queen is present, is not said to be under attack by the Queen.

Input Format
The first line contains a single integer T – the number of test cases. Then the test cases follow.
The first and only line of each test case contains three integers N, X and Y, as described in the problem statement.

Output Format
For each test case, output in a single line, the total number of cells that are under attack by the Queen.

Constraints
1≤T≤104
1≤N≤106
1≤X,Y≤N

Sample Input 1
5
1 1 1
3 2 2
3 2 1
2 2 2
150 62 41

Sample Output 1
0
8
6
3
527

Explanation

  • Test case 1: The only cell on the board is (1,1). Since Queen stands on this cell, it is not under attack.
  • Test case 2: The Queen can attack the following cells: {(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(3,3)}.
  • Test case 3: The Queen can attack the following cells: {(1,1),(1,2),(2,2),(2,3),(3,1),(3,2)}.
  • Test case 4: The Queen can attack the following cells: {(1,1),(1,2),(2,1)}.

SOLUTION

Program: The Attack of Queen Solution Codechef in Python

t=int(input())
for i in range(t):
    n,x,y=map(int,input().split())
    q=n-x+x-1+n-y+y-1
    a=min(x-1,y-1)
    b=min(x-1,n-y)
    c=min(n-x,y-1)
    d=min(n-x,n-y)
    print(q+a+b+c+d)

Program: The Attack of Queen Solution Codechef in C++

#include <bits/stdc++.h>
#include <math.h>
using namespace std;
int main(){
    int t;
    cin>>t;
    while(t--){
        long n,x,y;
        cin>>n>>x>>y;
        cout<<2*n-2 +
        min(abs(1-x),(abs(1-y)))+
        min(abs(n-x),(abs(n-y)))+
        min(abs(1-x),(abs(n-y)))+
        min(abs(n-x),(abs(1-y)));
        cout<<endl;
            
    }
    return 0;
}

Program: The Attack of Queen Solution Codechef in Java

import java.util.*;
import java.lang.*;
import java.io.*;
class Codechef
{ 	public static void main (String[] args) throws java.lang.Exception
	{
	Scanner sc=new Scanner(System.in);
	int t=sc.nextInt();
	for(int i=0;i<t;i++){
	    int n=sc.nextInt();
	    int x=sc.nextInt();
	    int y=sc.nextInt();
	    
	    int sum=2*(n-1);
	    sum=sum+Math.min(x,y)+Math.min(n-x,n-y);
	    sum=sum+Math.min(x-1,n-y)+Math.min(y-1,n-x);
	    
	    System.out.println(sum-1);
	    
	}
	}
        
    }

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