# 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) ans (3, 0).
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 number of valid moves. A move will be invalid if:
1. A block is already occupied by another piece.
2. Move is out of chessboard.

## 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)); ` `    ``} ` `} `

## 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 ` `?> `

Output:

```4
```

References:
https://en.wikipedia.org/wiki/Knight_(chess)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

## tags:

Matrix chessboard-problems Matrix

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