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.
CPP
// 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; } |
Java
// Java Program to find all occurrences of the word in // a matrix import java.util.*; class GFG { static final int ROW = 3 ; static final int COL = 5 ; // check whether given cell (row, col) is a valid // cell or not. static boolean 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 static int rowNum[] = {- 1 , - 1 , - 1 , 0 , 0 , 1 , 1 , 1 }; static 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 static void DFS( char mat[][], 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 += (word[index]) + "(" + String.valueOf(row) + ", " + String.valueOf(col) + ") " ; // current character matches with the last character // in the word if (index == n) { System.out.print(path + "\n" ); 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 static void findWords( char mat[][], 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 code public static void main(String[] args) { char mat[][]= { { 'B' , 'N' , 'E' , 'Y' , 'S' }, { 'H' , 'E' , 'D' , 'E' , 'S' }, { 'S' , 'G' , 'N' , 'D' , 'E' }}; char []word = "DES" .toCharArray(); findWords(mat, word, word.length - 1 ); } } // This code is contributed by PrinciRaj1992 |
Python3
# Python3 Program to find all occurrences of the word in # a matrix ROW = 3 COL = 5 # check whether given cell (row, col) is a valid # cell or not. def isvalid(row, col, prevRow, prevCol): # return true if row number and column number # is in range return (row > = 0 ) and (row < ROW) and (col > = 0 ) and \ (col < COL) and not (row = = prevRow and col = = prevCol) # These arrays are used to get row and column # numbers of 8 neighboursof a given cell rowNum = [ - 1 , - 1 , - 1 , 0 , 0 , 1 , 1 , 1 ] 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 def DFS(mat, row, col,prevRow, prevCol, word,path, index, n): # return if current character doesn't match with # the next character in the word if (index > n or mat[row][col] ! = word[index]): return # append current character position to path path + = word[index] + "(" + str (row) + ", " + str (col) + ") " # current character matches with the last character\ # in the word if (index = = n): print (path) return # Recur for all connected neighbours for k in range ( 8 ): 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 def findWords(mat,word, n): # traverse through the all cells of given matrix for i in range (ROW): for j in range (COL): # 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 code mat = [[ 'B' , 'N' , 'E' , 'Y' , 'S' ], [ 'H' , 'E' , 'D' , 'E' , 'S' ], [ 'S' , 'G' , 'N' , 'D' , 'E' ]] word = list ( "DES" ) findWords(mat, word, len (word) - 1 ) # This code is contributed by SHUBHAMSINGH10 |
C#
// C# Program to find all occurrences of the word in // a matrix using System; class GFG { static readonly int ROW = 3; static readonly int COL = 5; // check whether given cell (row, col) is a valid // cell or not. static 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 static int []rowNum = {-1, -1, -1, 0, 0, 1, 1, 1}; static int []colNum = {-1, 0, 1, -1, 1, -1, 0, 1}; // A utility function to do DFS for a 2D bool // matrix. It only considers the 8 neighbours as // adjacent vertices static void DFS( char [,]mat, 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 += (word[index]) + "(" + String.Join( "" ,row) + ", " + String.Join( "" ,col) + ") " ; // current character matches with the last character // in the word if (index == n) { Console.Write(path + "\n" ); 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 static void findWords( char [,]mat, 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 code public static void Main(String[] args) { char [,]mat= { { 'B' , 'N' , 'E' , 'Y' , 'S' }, { 'H' , 'E' , 'D' , 'E' , 'S' }, { 'S' , 'G' , 'N' , 'D' , 'E' }}; char []word = "DES" .ToCharArray(); findWords(mat, word, word.Length - 1); } } // This code is contributed by 29AjayKumar |
Javascript
<script> // Javascript Program to find all occurrences of the word in // a matrix let ROW = 3; let COL = 5; // check whether given cell (row, col) is a valid // cell or not. function isvalid(row, col, prevRow, 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 let rowNum=[-1, -1, -1, 0, 0, 1, 1, 1]; let 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 function DFS(mat, row, col, prevRow, prevCol, word, path, index, 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 += (word[index]) + "(" + (row).toString() + ", " + (col).toString() + ") " ; // current character matches with the last character // in the word if (index == n) { document.write(path + "<br>" ); return ; } // Recur for all connected neighbours for (let 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 function findWords(mat, word, n) { // traverse through the all cells of given matrix for (let i = 0; i < ROW; ++i) for (let 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 code let mat = [['B ', ' N ', ' E ', ' Y ', ' S '], [' H ', ' E ', ' D ', ' E ', ' S '], [' S ', ' G ', ' N ', ' D ', ' E']]; let word = "DES" .split( "" ); findWords(mat, word, word.length - 1); // This code is contributed by rag2127 </script> |
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)
Time Complexity: O(row x column)
Auxiliary Space: O(row x column)