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 column and 7th row). Now your task is to find the number of ways in which you can place a pawn safely on the board.
Examples:
Input : Bishop’s Position = 11
Output : Safe Positions = 56Input : 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 i,j 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).
C++
// CPP program to find total safe position// to place your Bishop#include<bits/stdc++.h>using namespace std;// function to calc total safe positionint calcSafe(int pos){ // i,j denotes row and column of position of bishop int j = pos % 10; int i = pos /10; // calc distance in four direction int dis_11 = min ( abs(1-i), abs (1-j)); int dis_18 = min ( abs(1-i), abs (8-j)); int dis_81 = min ( abs(8-i), abs (1-j)); int dis_88 = min ( abs(8-i), abs (8-j)); // calc total sum of distance + 1 for unsafe positions int sum = dis_11 + dis_18 + dis_81 + dis_88 + 1; // return total safe positions return (64- sum);}// driver functionint main(){ int pos = 34; cout << "Safe Positions = " << calcSafe(pos); return 0;} |
Java
// Java program to find total safe position// to place your Bishopclass GFG{ // function to calc total safe position static int calcSafe(int pos) { // i,j denotes row and column of position of bishop int j = pos % 10; int i = pos /10; // calc distance in four direction int dis_11 = Math.min ( Math.abs(1-i), Math.abs (1-j)); int dis_18 = Math.min ( Math.abs(1-i), Math.abs (8-j)); int dis_81 = Math.min ( Math.abs(8-i), Math.abs (1-j)); int dis_88 = Math.min ( Math.abs(8-i), Math.abs (8-j)); // calc total sum of distance + 1 for unsafe positions int sum = dis_11 + dis_18 + dis_81 + dis_88 + 1; // return total safe positions return (64- sum); } // Driver function public static void main (String[] args) { int pos = 34; System.out.print("Safe Positions = "+calcSafe(pos)); }}// This code is contributed by Anant Agarwal. |
Python3
# python program to find total safe# position to place your Bishopimport math # function to calc total safe positiondef calcSafe(pos): # i,j denotes row and column of # position of bishop j = pos % 10 i = pos /10 # calc distance in four direction dis_11 = min ( abs(1-i), abs (1-j)) dis_18 = min ( abs(1-i), abs (8-j)) dis_81 = min ( abs(8-i), abs (1-j)) dis_88 = min ( abs(8-i), abs (8-j)) # calc total sum of distance + 1 # for unsafe positions sum = (dis_11 + dis_18 + dis_81 + dis_88 + 1) # return total safe positions return (64- sum)# driver functionpos = 34print("Safe Positions = " , math.ceil(calcSafe(pos)))# This code is contributed by Sam007 |
C#
// Program to find the total safe// positions to place your Bishopusing System;class GFG { // function to calc total safe position static int calcSafe(int pos) { // i, j denotes row and column of // position of bishop int j = pos % 10; int i = pos / 10; // calc distance in four direction int dis_11 = Math.Min(Math.Abs(1 - i), Math.Abs(1 - j)); int dis_18 = Math.Min(Math.Abs(1 - i), Math.Abs(8 - j)); int dis_81 = Math.Min(Math.Abs(8 - i), Math.Abs(1 - j)); int dis_88 = Math.Min(Math.Abs(8 - i), Math.Abs(8 - j)); // calc total sum of distance + 1 // for unsafe positions int sum = dis_11 + dis_18 + dis_81 + dis_88 + 1; // return total safe positions return (64 - sum); } // Driver function public static void Main() { int pos = 34; Console.WriteLine("Safe Positions = " + calcSafe(pos)); }}// This code is contributed by vt_m. |
Javascript
<script>// Javascript program to find total safe position// to place your Bishop// function to calc total safe positionfunction calcSafe( pos){ // i,j denotes row and column of position of bishop let j = pos % 10; let i = Math.floor(pos /10); // calc distance in four direction let dis_11 = Math.min( Math.abs(1-i), Math.abs(1-j)); let dis_18 = Math.min( Math.abs(1-i), Math.abs(8-j)); let dis_81 = Math.min( Math.abs(8-i), Math.abs(1-j)); let dis_88 = Math.min( Math.abs(8-i), Math.abs(8-j)); // calc total sum of distance + 1 for unsafe positions let sum = dis_11 + dis_18 + dis_81 + dis_88 + 1; // return total safe positions return (64- sum);}// driver code let pos = 34; document.write("Safe Positions = " + calcSafe(pos));</script> |
PHP
<?php// PHP program to find // total safe position// to place your Bishop// function to calculate// total safe positionfunction calcSafe( $pos){ // i,j denotes row and // column of position // of bishop $j = $pos % 10; $i = $pos /10; // calc distance in four direction $dis_11 = min(abs(1 - $i), abs (1 - $j)); $dis_18 = min(abs(1 - $i), abs (8 - $j)); $dis_81 = min(abs(8 - $i), abs (1 - $j)); $dis_88 = min(abs(8 - $i), abs (8 - $j)); // calc total sum of // distance + 1 for // unsafe positions $sum = $dis_11 + $dis_18 + $dis_81 + $dis_88 + 1; // return total safe positions return ceil(64- $sum);} // Driver Code $pos = 34; echo "Safe Positions = " ,calcSafe($pos);// This code is contributed by vt_m.?> |
Safe Positions = 52
Time Complexity: O(1)
Auxiliary Space: O(1)
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