Find all occurrences of a given word in a matrix

4.1

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) 

find-all-occurences-of-given-word
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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 <bits/stdc++.h>
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[0])

                // 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) 

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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