Given a rectangular matrix which has only two possible values ‘X’ and ‘O’. The values ‘X’ always appear in form of rectangular islands and these islands are always row-wise and column-wise separated by at least one line of ‘O’s. Note that islands can only be diagonally adjacent. Count the number of islands in the given matrix.

Examples:

mat[M][N] = {{'O', 'O', 'O'}, {'X', 'X', 'O'}, {'X', 'X', 'O'}, {'O', 'O','X'}, {'O', 'O','X'}, {'X', 'X', 'O'} }; Output: Number of islands is 3 mat[M][N] = {{'X', 'O', 'O', 'O', 'O', 'O'}, {'X', 'O','X', 'X', 'X', 'X'}, {'O', 'O', 'O', 'O', 'O', 'O'}, {'X', 'X', 'X', 'O','X', 'X'}, {'X', 'X', 'X', 'O','X', 'X'}, {'O', 'O', 'O', 'O','X', 'X'}, }; Output: Number of islands is 4

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The idea is to count all top-leftmost corners of given matrix. We can check if a ‘X’ is top left or not by checking following conditions.

1) A ‘X’ is top of rectangle if the cell just above it is a ‘O’

2) A ‘X’ is leftmost of rectangle if the cell just left of it is a ‘O’

Note that we must check for both conditions as there may be more than one top cells and more than one leftmost cells in a rectangular island. Below is C++ implementation of above idea.

// A C++ program to count the number of rectangular // islands where every island is separated by a line #include<iostream> using namespace std; // Size of given matrix is M X N #define M 6 #define N 3 // This function takes a matrix of 'X' and 'O' // and returns the number of rectangular islands // of 'X' where no two islands are row-wise or // column-wise adjacent, the islands may be diagonaly // adjacent int countIslands(int mat[][N]) { int count = 0; // Initialize result // Traverse the input matrix for (int i=0; i<M; i++) { for (int j=0; j<N; j++) { // If current cell is 'X', then check // whether this is top-leftmost of a // rectangle. If yes, then increment count if (mat[i][j] == 'X') { if ((i == 0 || mat[i-1][j] == 'O') && (j == 0 || mat[i][j-1] == 'O')) count++; } } } return count; } // Driver program to test above function int main() { int mat[M][N] = {{'O', 'O', 'O'}, {'X', 'X', 'O'}, {'X', 'X', 'O'}, {'O', 'O', 'X'}, {'O', 'O', 'X'}, {'X', 'X', 'O'} }; cout << "Number of rectangular islands is " << countIslands(mat); return 0; }

Output:

Number of rectangular islands is 3

Time complexity of this solution is O(MN).

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