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: YesInput: 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
- 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
- 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> |
Yes
Complexity Analysis:
- Time Complexity: O(1)
- Auxiliary Space: O(1)
Contact Us