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Total position where king can reach on a chessboard in exactly M moves
  • Last Updated : 16 Apr, 2021

Given an integer M, an 8 * 8 chessboard and the king is placed on one of the square of the chessboard. Let the coordinate of the king be (R, C)
Note that the king can move to a square whose coordinate is (R1, C1) if and only if below condition is satisfied. 
 

The task is to count the number of position where the king can reach (excluding the initial position) from the given square in exactly M moves.
Examples: 
 

Input: row = 1, column = 3, moves = 1 
Output: Total number of position where king can reached = 5 
 



Input: row = 2, column = 5, moves = 2 
Output: Total number of position where king can reached = 19 
 

 

Approach: Calculate the coordinates of the top left square that can be visited by the king (a, b) and the coordinates of the bottom right square (c, d) of the chessboard that the king can visit. Then the total number of cells that the king can visit will be (c – a + 1) * (d – b + 1) – 1.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of above approach
#include <iostream>
using namespace std;
 
// Function to return the number of squares that
// the king can reach in the given number of moves
int Square(int row, int column, int moves)
{
    int a = 0, b = 0, c = 0, d = 0, total = 0;
 
    // Calculate initial and final coordinates
    a = row - moves;
    b = row + moves;
    c = column - moves;
    d = column + moves;
 
    // Since chessboard is of size 8X8 so if
    // any coordinate is less than 1 or greater than 8
    // make it 1 or 8.
    if (a < 1)
        a = 1;
    if (c < 1)
        c = 1;
    if (b > 8)
        b = 8;
    if (d > 8)
        d = 8;
 
    // Calculate total positions
    total = (b - a + 1) * (d - c + 1) - 1;
    return total;
}
 
// Driver code
int main()
{
    int R = 4, C = 5, M = 2;
    cout << Square(R, C, M);
 
    return 0;
}

Java




// Java implementation of above approach
class GFG
{
 
// Function to return the number
// of squares that the king can
// reach in the given number of moves
static int Square(int row, int column,
                            int moves)
{
    int a = 0, b = 0, c = 0,
        d = 0, total = 0;
 
    // Calculate initial and final coordinates
    a = row - moves;
    b = row + moves;
    c = column - moves;
    d = column + moves;
 
    // Since chessboard is of size 8X8
    // so if any coordinate is less
    // than 1 or greater than 8 make
    // it 1 or 8.
    if (a < 1)
        a = 1;
    if (c < 1)
        c = 1;
    if (b > 8)
        b = 8;
    if (d > 8)
        d = 8;
 
    // Calculate total positions
    total = (b - a + 1) * (d - c + 1) - 1;
    return total;
}
 
// Driver code
public static void main(String []args)
{
    int R = 4, C = 5, M = 2;
    System.out.println(Square(R, C, M));
}
}
 
// This code is contributed by Ita_c.

Python3




# Python3 implementation of above approach
 
# Function to return the number of
# squares that the king can reach
# in the given number of moves
def Square(row, column, moves) :
     
    a = 0; b = 0; c = 0;
    d = 0; total = 0;
 
    # Calculate initial and final
    # coordinates
    a = row - moves;
    b = row + moves;
    c = column - moves;
    d = column + moves;
 
    # Since chessboard is of size 8X8
    # so if any coordinate is less than
    # 1 or greater than 8 make it 1 or 8.
    if (a < 1) :
        a = 1;
    if (c < 1) :
        c = 1;
    if (b > 8) :
        b = 8;
    if (d > 8) :
        d = 8;
 
    # Calculate total positions
    total = (b - a + 1) * (d - c + 1) - 1;
    return total;
 
# Driver code
if __name__ == "__main__" :
 
    R = 4; C = 5; M = 2;
    print(Square(R, C, M));
     
# This code is contributed by Ryuga

C#




// C# implementation of above approach
using System;
 
class GFG
{
 
// Function to return the number
// of squares that the king can
// reach in the given number of moves
static int Square(int row, int column,
                            int moves)
{
    int a = 0, b = 0, c = 0,
        d = 0, total = 0;
 
    // Calculate initial and final coordinates
    a = row - moves;
    b = row + moves;
    c = column - moves;
    d = column + moves;
 
    // Since chessboard is of size 8X8
    // so if any coordinate is less
    // than 1 or greater than 8 make
    // it 1 or 8.
    if (a < 1)
        a = 1;
    if (c < 1)
        c = 1;
    if (b > 8)
        b = 8;
    if (d > 8)
        d = 8;
 
    // Calculate total positions
    total = (b - a + 1) * (d - c + 1) - 1;
    return total;
}
 
// Driver code
public static void Main()
{
    int R = 4, C = 5, M = 2;
    Console.Write(Square(R, C, M));
}
}
 
// this code is contributed by Ita_c.

PHP




<?php
// PHP implementation of above approach
 
// Function to return the number of
// squares that the king can reach
// in the given number of moves
function Square($row, $column, $moves)
{
    $a = 0; $b = 0; $c = 0;
    $d = 0; $total = 0;
 
    // Calculate initial and final coordinates
    $a = $row - $moves;
    $b = $row + $moves;
    $c = $column - $moves;
    $d = $column + $moves;
 
    // Since chessboard is of size 8X8 so
    // if any coordinate is less than 1
    // or greater than 8 make it 1 or 8.
    if ($a < 1)
        $a = 1;
    if ($c < 1)
        $c = 1;
    if ($b > 8)
        $b = 8;
    if ($d > 8)
        $d = 8;
 
    // Calculate total positions
    $total = ($b - $a + 1) *
             ($d - $c + 1) - 1;
    return $total;
}
 
// Driver code
$R = 4; $C = 5; $M = 2;
echo Square($R, $C, $M);
 
// This code is contributed
// by Akanksha Rai
?>

Javascript




<script>
 
// Javascript implementation of above approach
 
// Function to return the number of squares that
// the king can reach in the given number of moves
function Square(row, column, moves)
{
    var a = 0, b = 0, c = 0, d = 0, total = 0;
 
    // Calculate initial and final coordinates
    a = row - moves;
    b = row + moves;
    c = column - moves;
    d = column + moves;
 
    // Since chessboard is of size 8X8 so if
    // any coordinate is less than 1 or greater than 8
    // make it 1 or 8.
    if (a < 1)
        a = 1;
    if (c < 1)
        c = 1;
    if (b > 8)
        b = 8;
    if (d > 8)
        d = 8;
 
    // Calculate total positions
    total = (b - a + 1) * (d - c + 1) - 1;
    return total;
}
 
// Driver code
var R = 4, C = 5, M = 2;
document.write( Square(R, C, M));
 
// This code is contributed by rrrtnx.
</script>
Output: 
24

 

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