# Possible moves of knight

Given a chess board of dimension m * n. Find number of possible moves where knight can be moved on a chessboard from given position. If mat[i][j] = 1 then the block is filled by something else, otherwise empty. Assume that board consist of all pieces of same color, i.e., there are no blocks being attacked.

Examples:

```Input : mat[][] = {{1, 0, 1, 0},
{0, 1, 1, 1},
{1, 1, 0, 1},
{0, 1, 1, 1}}
pos = (2, 2)
Output : 4
Knight can moved from (2, 2) to (0, 1), (0, 3),
(1, 0) and (3, 0).```

We can observe that knight on a chessboard moves either:

1. Two moves horizontal and one move vertical
2. Two moves vertical and one move horizontal

The idea is to store all possible moves of knight and then count the number of valid moves. A move will be invalid if:

1. A block is already occupied by another piece.
2. Move is out of the chessboard.

Implementation:

## C++

 `// CPP program to find number of possible moves of knight` `#include ` `#define n 4` `#define m 4` `using` `namespace` `std;`   `// To calculate possible moves` `int` `findPossibleMoves(``int` `mat[n][m], ``int` `p, ``int` `q)` `{` `    ``// All possible moves of a knight` `    ``int` `X[8] = { 2, 1, -1, -2, -2, -1, 1, 2 };` `    ``int` `Y[8] = { 1, 2, 2, 1, -1, -2, -2, -1 };`   `    ``int` `count = 0;`   `    ``// Check if each possible move is valid or not` `    ``for` `(``int` `i = 0; i < 8; i++) {`   `        ``// Position of knight after move` `        ``int` `x = p + X[i];` `        ``int` `y = q + Y[i];`   `        ``// count valid moves` `        ``if` `(x >= 0 && y >= 0 && x < n && y < m` `            ``&& mat[x][y] == 0)` `            ``count++;` `    ``}`   `    ``// Return number of possible moves` `    ``return` `count;` `}`   `// Driver program to check findPossibleMoves()` `int` `main()` `{` `    ``int` `mat[n][m] = { { 1, 0, 1, 0 },` `                      ``{ 0, 1, 1, 1 },` `                      ``{ 1, 1, 0, 1 },` `                      ``{ 0, 1, 1, 1 } };`   `    ``int` `p = 2, q = 2;`   `    ``cout << findPossibleMoves(mat, p, q);`   `    ``return` `0;` `}`

## Java

 `// Java program to find number of possible moves of knight` `public` `class` `Main {` `public` `static` `final` `int` `n = ``4``;` `public` `static` `final` `int` `m = ``4``;`   `    ``// To calculate possible moves` `    ``static` `int` `findPossibleMoves(``int` `mat[][], ``int` `p, ``int` `q)` `    ``{` `        ``// All possible moves of a knight` `        ``int` `X[] = { ``2``, ``1``, -``1``, -``2``, -``2``, -``1``, ``1``, ``2` `};` `        ``int` `Y[] = { ``1``, ``2``, ``2``, ``1``, -``1``, -``2``, -``2``, -``1` `};`   `        ``int` `count = ``0``;`   `        ``// Check if each possible move is valid or not` `        ``for` `(``int` `i = ``0``; i < ``8``; i++) {`   `            ``// Position of knight after move` `            ``int` `x = p + X[i];` `            ``int` `y = q + Y[i];`   `            ``// count valid moves` `            ``if` `(x >= ``0` `&& y >= ``0` `&& x < n && y < m` `                ``&& mat[x][y] == ``0``)` `                ``count++;` `        ``}`   `        ``// Return number of possible moves` `        ``return` `count;` `    ``}`   `    ``// Driver program to check findPossibleMoves()` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `mat[][] = { { ``1``, ``0``, ``1``, ``0` `},` `                        ``{ ``0``, ``1``, ``1``, ``1` `},` `                        ``{ ``1``, ``1``, ``0``, ``1` `},` `                        ``{ ``0``, ``1``, ``1``, ``1` `} };`   `        ``int` `p = ``2``, q = ``2``;`   `        ``System.out.println(findPossibleMoves(mat, p, q));` `    ``}` `}`

## Python3

 `# Python3 program to find number` `# of possible moves of knight` `n ``=` `4``;` `m ``=` `4``;`   `# To calculate possible moves` `def` `findPossibleMoves(mat, p, q):` `    ``global` `n, m;` `    `  `    ``# All possible moves of a knight` `    ``X ``=` `[``2``, ``1``, ``-``1``, ``-``2``, ``-``2``, ``-``1``, ``1``, ``2``];` `    ``Y ``=` `[``1``, ``2``, ``2``, ``1``, ``-``1``, ``-``2``, ``-``2``, ``-``1``];`   `    ``count ``=` `0``;`   `    ``# Check if each possible move` `    ``# is valid or not` `    ``for` `i ``in` `range``(``8``):` `        `  `        ``# Position of knight after move` `        ``x ``=` `p ``+` `X[i];` `        ``y ``=` `q ``+` `Y[i];`   `        ``# count valid moves` `        ``if``(x >``=` `0` `and` `y >``=` `0` `and` `x < n ``and` `           ``y < m ``and` `mat[x][y] ``=``=` `0``):` `            ``count ``+``=` `1``;`   `    ``# Return number of possible moves` `    ``return` `count;`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``mat ``=` `[[``1``, ``0``, ``1``, ``0``], [``0``, ``1``, ``1``, ``1``], ` `           ``[``1``, ``1``, ``0``, ``1``], [``0``, ``1``, ``1``, ``1``]];`   `    ``p, q ``=` `2``, ``2``;`   `    ``print``(findPossibleMoves(mat, p, q));`   `# This code is contributed by 29AjayKumar`

## C#

 `// C# program to find number of` `// possible moves of knight` `using` `System;`   `class` `GFG` `{` `    ``static` `int` `n = 4;` `    ``static` `int` `m = 4;`   `    ``// To calculate ` `    ``// possible moves` `    ``static` `int` `findPossibleMoves(``int` `[,]mat, ` `                                 ``int` `p, ``int` `q)` `    ``{` `        ``// All possible moves` `        ``// of a knight` `        ``int` `[]X = { 2, 1, -1, -2,` `                   ``-2, -1, 1, 2 };` `        ``int` `[]Y = { 1, 2, 2, 1, ` `                   ``-1, -2, -2, -1 };`   `        ``int` `count = 0;`   `        ``// Check if each possible` `        ``// move is valid or not` `        ``for` `(``int` `i = 0; i < 8; i++)` `        ``{`   `            ``// Position of knight` `            ``// after move` `            ``int` `x = p + X[i];` `            ``int` `y = q + Y[i];`   `            ``// count valid moves` `            ``if` `(x >= 0 && y >= 0 && ` `                ``x < n && y < m && ` `                ``mat[x, y] == 0)` `                ``count++;` `        ``}`   `        ``// Return number ` `        ``// of possible moves` `        ``return` `count;` `    ``}`   `    ``// Driver Code` `    ``static` `public` `void` `Main ()` `    ``{` `        ``int` `[,]mat = { { 1, 0, 1, 0 },` `                       ``{ 0, 1, 1, 1 },` `                       ``{ 1, 1, 0, 1 },` `                       ``{ 0, 1, 1, 1 }};`   `        ``int` `p = 2, q = 2;`   `        ``Console.WriteLine(findPossibleMoves(mat, ` `                                            ``p, q));` `    ``}` `}`   `// This code is contributed by m_kit`

## PHP

 `= 0 && ``\$y` `>= 0 && ` `            ``\$x` `< ``\$n` `&& ``\$y` `< ``\$m` `&& ` `            ``\$mat``[``\$x``][``\$y``] == 0)` `            ``\$count``++;` `    ``}`   `    ``// Return number ` `    ``// of possible moves` `    ``return` `\$count``;` `}`   `// Driver Code` `\$mat` `= ``array``(``array``(1, 0, 1, 0),` `             ``array``(0, 1, 1, 1),` `             ``array``(1, 1, 0, 1),` `             ``array``(0, 1, 1, 1));`   `\$p` `= 2; ``\$q` `= 2;`   `echo` `findPossibleMoves(``\$mat``, ` `                       ``\$p``, ``\$q``);`   `// This code is contributed by ajit` `?>`

## Javascript

 ``

Output

`4`

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

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