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 largest(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; }

Output:

6

Time complexity: O(ROW x COL)

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