You are given a 8*8 chess board. Along with the chess board there is a Bishop placed on board and its position is known. Position of Bishop is given in form of two digit integer where both digits are greater than 0 and less than 9 (like 67 denotes 6th row and 7 column). Now your task is to find the number of ways in which you can place a pawn safely on the board.
Input : Bishop's Position = 11 Output : Safe Positions = 56 Input : Bishop's Position = 44 Output : Safe Positions = 50
Brute Force Approach : One of the basic approach is to iterate through all the 64 possible positions on chess board and check whether that position is safe or not. This approach will require much more time.
Better Approach: As we know that movement of Bishop is in diagonal manner so from any position on the chess board a Bishop can move in both direction of both diagonals. So, all the positions which does not lie on the way of diagonal movement of the given Bishop are the safe positions.
Now our task is to find the maximum length in all possible four direction from the position of Bishop.
-> From any position a Bishop can move towards four corner that are (11, 18, 81, 88). So, we will try to find the find the maximum distance which the Bishop can move towards these corner.
Let position of bishop is ij then:
- Distance towards 11 = min (mod(1-i), mod(1-j) ).
- Distance towards 18 = min (mod(1-i), mod(8-j) ).
- Distance towards 81 = min (mod(8-i), mod(1-j) ).
- Distance towards 88 = min (mod(8-i), mod(8-j) ).
Beside all these four, one position at which Bishop is already placed is also not safe so total number of unsafe position is sum of above results + 1. and total number of safe position is 64 -(sum+1).
Safe Positions = 52
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