Consider a matrix with rows and columns, where each cell contains either a ‘0’ or a ‘1’ and any cell containing a 1 is called a filled cell. Two cells are said to be connected if they are adjacent to each other horizontally, vertically, or diagonally .If one or more filled cells are also connected, they form a region. find the length of the largest region.

Examples:

Input : M[][5] = { 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 } Output : 6 Ex: in the following example, there are 2 regions one with length 1 and the other as 6. so largest region : 6

Asked in : Amazon interview

Idea is based on the problem or finding number of islands in Boolean 2D-matrix

A cell in 2D matrix can be connected to at most 8 neighbors. So in DFS, we make recursive calls for 8 neighbors. We keep track of the visited 1’s in every DFS and update maximum length region.

Below is C++ implementation of above idea.

`// Program to find the length of the largest ` `// region in boolean 2D-matrix ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` `#define ROW 4 ` `#define COL 5 ` ` ` `// A function to check if a given cell (row, col) ` `// can be included in DFS ` `int` `isSafe(` `int` `M[][COL], ` `int` `row, ` `int` `col, ` ` ` `bool` `visited[][COL]) ` `{ ` ` ` `// row number is in range, column number is in ` ` ` `// range and value is 1 and not yet visited ` ` ` `return` `(row >= 0) && (row < ROW) && ` ` ` `(col >= 0) && (col < COL) && ` ` ` `(M[row][col] && !visited[row][col]); ` `} ` ` ` `// A utility function to do DFS for a 2D boolean ` `// matrix. It only considers the 8 neighbours as ` `// adjacent vertices ` `void` `DFS(` `int` `M[][COL], ` `int` `row, ` `int` `col, ` ` ` `bool` `visited[][COL], ` `int` `&count) ` `{ ` ` ` `// These arrays are used to get row and column ` ` ` `// numbers of 8 neighbours of a given cell ` ` ` `static` `int` `rowNbr[] = {-1, -1, -1, 0, 0, 1, 1, 1}; ` ` ` `static` `int` `colNbr[] = {-1, 0, 1, -1, 1, -1, 0, 1}; ` ` ` ` ` `// Mark this cell as visited ` ` ` `visited[row][col] = ` `true` `; ` ` ` ` ` `// Recur for all connected neighbours ` ` ` `for` `(` `int` `k = 0; k < 8; ++k) ` ` ` `{ ` ` ` `if` `(isSafe(M, row + rowNbr[k], col + colNbr[k], ` ` ` `visited)) ` ` ` `{ ` ` ` `// increment region length by one ` ` ` `count++; ` ` ` `DFS(M, row + rowNbr[k], col + colNbr[k], ` ` ` `visited, count); ` ` ` `} ` ` ` `} ` `} ` ` ` `// The main function that returns largest length region ` `// of a given boolean 2D matrix ` `int` `largestRegion(` `int` `M[][COL]) ` `{ ` ` ` `// Make a bool array to mark visited cells. ` ` ` `// Initially all cells are unvisited ` ` ` `bool` `visited[ROW][COL]; ` ` ` `memset` `(visited, 0, ` `sizeof` `(visited)); ` ` ` ` ` `// Initialize result as 0 and travesle through the ` ` ` `// all cells of given matrix ` ` ` `int` `result = INT_MIN; ` ` ` `for` `(` `int` `i = 0; i < ROW; ++i) ` ` ` `{ ` ` ` `for` `(` `int` `j = 0; j < COL; ++j) ` ` ` `{ ` ` ` `// If a cell with value 1 is not ` ` ` `if` `(M[i][j] && !visited[i][j]) ` ` ` `{ ` ` ` `// visited yet, then new region found ` ` ` `int` `count = 1 ; ` ` ` `DFS(M, i, j, visited , count); ` ` ` ` ` `// maximum region ` ` ` `result = max(result , count); ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `return` `result ; ` `} ` ` ` `// Driver program to test above function ` `int` `main() ` `{ ` ` ` `int` `M[][COL] = { {0, 0, 1, 1, 0}, ` ` ` `{1, 0, 1, 1, 0}, ` ` ` `{0, 1, 0, 0, 0}, ` ` ` `{0, 0, 0, 0, 1}}; ` ` ` ` ` `cout << largestRegion(M); ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:

6

Time complexity: O(ROW x COL)

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

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

## Recommended Posts:

- Find the length of largest subarray with 0 sum
- Find maximum path length in a binary matrix
- A Boolean Matrix Question
- Print unique rows in a given boolean matrix
- Lexicographically largest prime path from top-left to bottom-right in a matrix
- Find if there is a path of more than k length from a source
- Find the largest BST subtree in a given Binary Tree | Set 1
- Boolean Parenthesization Problem | DP-37
- Find whether there is path between two cells in matrix
- Find the number of distinct islands in a 2D matrix
- Find the longest path in a matrix with given constraints
- Evaluate a boolean expression represented as string
- Find the minimum number of moves needed to move from one cell of matrix to another
- Run Length Encoding
- Check if a graphs has a cycle of odd length