# Find all occurrences of a given word in a matrix

Given a 2D grid of characters and a word, find all occurrences of given word in grid. A word can be matched in all 8 directions at any point. Word is said be found in a direction if all characters match in this direction (not in zig-zag form).

The solution should print all coordinates if a cycle is found. i.e.

The 8 directions are, Horizontally Left, Horizontally Right, Vertically Up, Vertically Down and 4 Diagonals.

```Input:
mat[ROW][COL]= { {'B', 'N', 'E', 'Y', 'S'},
{'H', 'E', 'D', 'E', 'S'},
{'S', 'G', 'N', 'D', 'E'}
};
Word = “DES”
Output:
D(1, 2) E(1, 1) S(2, 0)
D(1, 2) E(1, 3) S(0, 4)
D(1, 2) E(1, 3) S(1, 4)
D(2, 3) E(1, 3) S(0, 4)
D(2, 3) E(1, 3) S(1, 4)
D(2, 3) E(2, 4) S(1, 4)

Input:
char mat[ROW][COL] = { {'B', 'N', 'E', 'Y', 'S'},
{'H', 'E', 'D', 'E', 'S'},
{'S', 'G', 'N', 'D', 'E'}};
char word[] ="BNEGSHBN";
Output:
B(0, 0) N(0, 1) E(1, 1) G(2, 1) S(2, 0) H(1, 0)
B(0, 0) N(0, 1)
``` We strongly recommend you to minimize your browser and try this yourself first.
This is mainly an extension of this post. Here with locations path is also printed.

The problem can be easily solved by applying DFS() on each occurrence of first character of the word in the matrix. A cell in 2D matrix can be connected to 8 neighbours. So, unlike standard DFS(), where we recursively call for all adjacent vertices, here we can recursive call for 8 neighbours only.

 `// Program to find all occurrences of the word in ` `// a matrix ` `#include ` `using` `namespace` `std; ` ` `  `#define ROW 3 ` `#define COL 5 ` ` `  `// check whether given cell (row, col) is a valid ` `// cell or not. ` `bool` `isvalid(``int` `row, ``int` `col, ``int` `prevRow, ``int` `prevCol) ` `{ ` `    ``// return true if row number and column number ` `    ``// is in range ` `    ``return` `(row >= 0) && (row < ROW) && ` `           ``(col >= 0) && (col < COL) && ` `           ``!(row== prevRow && col == prevCol); ` `} ` ` `  `// These arrays are used to get row and column ` `// numbers of 8 neighboursof a given cell ` `int` `rowNum[] = {-1, -1, -1, 0, 0, 1, 1, 1}; ` `int` `colNum[] = {-1, 0, 1, -1, 1, -1, 0, 1}; ` ` `  `// A utility function to do DFS for a 2D boolean ` `// matrix. It only considers the 8 neighbours as ` `// adjacent vertices ` `void` `DFS(``char` `mat[][COL], ``int` `row, ``int` `col, ` `         ``int` `prevRow, ``int` `prevCol, ``char``* word, ` `         ``string path, ``int` `index, ``int` `n) ` `{ ` `    ``// return if current character doesn't match with ` `    ``// the next character in the word ` `    ``if` `(index > n || mat[row][col] != word[index]) ` `        ``return``; ` ` `  `    ``//append current character position to path ` `    ``path += string(1, word[index]) + ``"("` `+ to_string(row) ` `            ``+ ``", "` `+ to_string(col) + ``") "``; ` ` `  `    ``// current character matches with the last character ` `    ``// in the word ` `    ``if` `(index == n) ` `    ``{ ` `        ``cout << path << endl; ` `        ``return``; ` `    ``} ` ` `  `    ``// Recur for all connected neighbours ` `    ``for` `(``int` `k = 0; k < 8; ++k) ` `        ``if` `(isvalid(row + rowNum[k], col + colNum[k], ` `                    ``prevRow, prevCol)) ` ` `  `            ``DFS(mat, row + rowNum[k], col + colNum[k], ` `                ``row, col, word, path, index+1, n); ` `} ` ` `  `// The main function to find all occurrences of the ` `// word in a matrix ` `void` `findWords(``char` `mat[][COL], ``char``* word, ``int` `n) ` `{ ` `    ``// traverse through the all cells of given matrix ` `    ``for` `(``int` `i = 0; i < ROW; ++i) ` `        ``for` `(``int` `j = 0; j < COL; ++j) ` ` `  `            ``// occurrence of first character in matrix ` `            ``if` `(mat[i][j] == word) ` ` `  `                ``// check and print if path exists ` `                ``DFS(mat, i, j, -1, -1, word, ``""``, 0, n); ` `} ` ` `  `// Driver program to test above function ` `int` `main() ` `{ ` `    ``char` `mat[ROW][COL]= { {``'B'``, ``'N'``, ``'E'``, ``'Y'``, ``'S'``}, ` `                          ``{``'H'``, ``'E'``, ``'D'``, ``'E'``, ``'S'``}, ` `                          ``{``'S'``, ``'G'``, ``'N'``, ``'D'``, ``'E'``} ` `                        ``}; ` ` `  `    ``char` `word[] =``"DES"``; ` ` `  `    ``findWords(mat, word, ``strlen``(word) - 1); ` ` `  `    ``return` `0; ` `} `

Output :

```D(1, 2) E(1, 1) S(2, 0)
D(1, 2) E(1, 3) S(0, 4)
D(1, 2) E(1, 3) S(1, 4)
D(2, 3) E(1, 3) S(0, 4)
D(2, 3) E(1, 3) S(1, 4)
D(2, 3) E(2, 4) S(1, 4) ```

## tags:

Pattern Searching Pattern Searching