Check whether Bishop can take down Pawn or not

Given the position of a Bishop and a Pawn on a 8 * 8 chessboard, the task is to check whether the Bishop can take down the Pawn in one move or not. The position of Bishop and Pawn is denoted using row and column number of the chessboard.

Examples:

Input: bishopX = 5, bishopY = 5, pawnX = 1, pawnY = 1 
Output: Yes

Input: bishopX = 5, bishopY = 5, pawnX = 1, pawnY = 3 
Output: No 

Approach:

In a game of chess, the Bishop can only move diagonally and there is no restriction in the distance for each move. If we consider Bishop’s position as origin, it can be concluded that Bishop can attack at 45 degree, 135 degree, 225 degree and 315 degree angles only. So, the Bishop can attack the Pawn only if they are in such position that the slope obtained from their position is equal to tangent of 45 degree or 135 degree or 225 degree or 315 degree angle.

As we know the equation of slope for two points- 

Also, 

For all the attacking angles of Bishop (i.e 45°, 135°, 225°, and 315°) value of slope will be either 1 or -1. 

tan(45°) = 1 
tan(135°) = -1 
tan(225°) = 1 
tan(315°) = -1 

So, for angle 45° and 225°, equation of slope will be 

x2 – x1 = y2 – y1

and for angle 135° and 315°, equation of slope will be 

-x2 + x1 = y2 – y1

1. Considering the position of Bishop and Pawn as points on 2-D co-ordinate, Check if any of two equation is true 
   • x2 – x1 = y2 – y1
   • -x2 + x1 = y2 – y1
2. Otherwise, print No.

Below is the implementation of the above approach

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function that return true if
// the Bishop can take down the pawn
bool canTakeDown(int bishopX, int bishopY, int pawnX, int pawnY)
{

    // If pawn is at angle
    // 45 or 225 degree from
    // bishop's Position
    if (pawnX - bishopX == pawnY - bishopY)
        return true;

    // If pawn is at angle
    // 135 or 315 degree from
    // bishop's Position
    else if (-pawnX + bishopX == pawnY - bishopY)
        return true;

    else
        return false;
}

// Driver code
int main()
{
    // Bishop's Position
    int bishopX = 5, bishopY = 5;

    // Pawn's Position
    int pawnX = 1, pawnY = 1;

    if (canTakeDown(bishopX, bishopY, pawnX, pawnY))
        cout << "Yes";
    else
        cout << "No";
}

Java

// Java implementation of above approach
class GFG {

    // Function that return true if
    // the Bishop can take down the pawn
    static boolean canTakeDown(int bishopX, int bishopY, int pawnX, int pawnY)
    {

        // If pawn is at angle
        // 45 or 225 degree from
        // bishop's Position
        if (pawnX - bishopX == pawnY - bishopY)
            return true;

        // If pawn is at angle
        // 135 or 315 degree from
        // bishop's Position
        else if (-pawnX + bishopX == pawnY - bishopY)
            return true;

        else
            return false;
    }

    // Driver code
    public static void main(String[] args)
    {
        // Bishop's Position
        int bishopX = 5, bishopY = 5;

        // Pawn's Position
        int pawnX = 1, pawnY = 1;

        if (canTakeDown(bishopX, bishopY, pawnX, pawnY))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3

# Python3 implementation of above approach

# Function that return true if
# the Bishop can take down the pawn
def canTakeDown(bishopX, bishopY, pawnX, pawnY) :


    # If pawn is at angle
    # 45 or 225 degree from
    # bishop's Position
    if (pawnX - bishopX == pawnY - bishopY) :
        return True

    # If pawn is at angle
    # 135 or 315 degree from
    # bishop's Position
    elif (-pawnX + bishopX == pawnY - bishopY):
        return True

    else:
        return False


# Driver code

# Bishop's Position
bishopX = 5
bishopY = 5

# Pawn's Position
pawnX = 1
pawnY = 1

if (canTakeDown(bishopX, bishopY, pawnX, pawnY)) :
    print("Yes")
else :
    print("No")

C#

// C# implementation of above approach
using System;
class GFG {

    // Function that return true if
    // the Bishop can take down the pawn
    static bool canTakeDown(int bishopX, int bishopY, int pawnX, int pawnY)
    {

        // If pawn is at angle
        // 45 or 225 degree from
        // bishop's Position
        if (pawnX - bishopX == pawnY - bishopY)
            return true;

        // If pawn is at angle
        // 135 or 315 degree from
        // bishop's Position
        else if (-pawnX + bishopX == pawnY - bishopY)
            return true;

        else
            return false;
    }

    // Driver code
    public static void Main()
    {
        // Bishop's Position
        int bishopX = 5, bishopY = 5;

        // Pawn's Position
        int pawnX = 1, pawnY = 1;

        if (canTakeDown(bishopX, bishopY, pawnX, pawnY))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

PHP

<?php
// PHP implementation of above approach

// Function that return true if
// the Bishop can take down the pawn
function canTakeDown($bishopX, $bishopY,
                       $pawnX, $pawnY)
{

    // If pawn is at angle
    // 45 or 225 degree from
    // bishop's Position
    if ($pawnX -
        $bishopX == $pawnY - $bishopY)
        return true;

    // If pawn is at angle
    // 135 or 315 degree from
    // bishop's Position
    else if (-$pawnX +
              $bishopX == $pawnY -
                          $bishopY)
        return true;

    else
        return false;
}

// Driver code

// Bishop's Position
$bishopX = 5;
$bishopY = 5;

// Pawn's Position
$pawnX = 1;
$pawnY = 1;

if (canTakeDown($bishopX, $bishopY,
                $pawnX, $pawnY))
    echo "Yes";
else
    echo "No";

// This code is contributed by jit_t
?>

Javascript

<script>

// Javascript implementation of above approach

// Function that return true if
// the Bishop can take down the pawn
function canTakeDown(bishopX, bishopY, pawnX, pawnY)
{

    // If pawn is at angle
    // 45 or 225 degree from
    // bishop's Position
    if (pawnX - bishopX == pawnY - bishopY)
        return true;

    // If pawn is at angle
    // 135 or 315 degree from
    // bishop's Position
    else if (-pawnX + bishopX == pawnY - bishopY)
        return true;

    else
        return false;
}

// Driver code
// Bishop's Position
var bishopX = 5, bishopY = 5;
// Pawn's Position
var pawnX = 1, pawnY = 1;
if (canTakeDown(bishopX, bishopY, pawnX, pawnY))
    document.write( "Yes");
else
    document.write( "No");


</script>

Output

Yes

Complexity Analysis:

• Time Complexity: O(1)
• Auxiliary Space: O(1)