Given a binary matrix, find out the maximum size square sub-matrix with all 1s.
For example, consider the below binary matrix.
Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.
C#
// C# Code for Maximum size square // sub-matrix with all 1s using System; public class GFG { // method for Maximum size square sub-matrix with all 1s static void printMaxSubSquare(int[, ] M) { int i, j; // no of rows in M[, ] int R = M.GetLength(0); // no of columns in M[, ] int C = M.GetLength(1); int[, ] S = new int[R, C]; int max_of_s, max_i, max_j; /* Set first column of S[, ]*/ for (i = 0; i < R; i++) S[i, 0] = M[i, 0]; /* Set first row of S[][]*/ for (j = 0; j < C; j++) S[0, j] = M[0, j]; /* Construct other entries of S[, ]*/ for (i = 1; i < R; i++) { for (j = 1; j < C; j++) { if (M[i, j] == 1) S[i, j] = Math.Min(S[i, j - 1], Math.Min(S[i - 1, j], S[i - 1, j - 1])) + 1; else S[i, j] = 0; } } /* Find the maximum entry, and indexes of maximum entry in S[, ] */ max_of_s = S[0, 0]; max_i = 0; max_j = 0; for (i = 0; i < R; i++) { for (j = 0; j < C; j++) { if (max_of_s < S[i, j]) { max_of_s = S[i, j]; max_i = i; max_j = j; } } } Console.WriteLine("Maximum size sub-matrix is: "); for (i = max_i; i > max_i - max_of_s; i--) { for (j = max_j; j > max_j - max_of_s; j--) { Console.Write(M[i, j] + " "); } Console.WriteLine(); } } // Driver program public static void Main() { int[, ] M = new int[6, 5] { { 0, 1, 1, 0, 1 }, { 1, 1, 0, 1, 0 }, { 0, 1, 1, 1, 0 }, { 1, 1, 1, 1, 0 }, { 1, 1, 1, 1, 1 }, { 0, 0, 0, 0, 0 } }; printMaxSubSquare(M); } } |
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Output:
Maximum size sub-matrix is: 1 1 1 1 1 1 1 1 1
Please refer complete article on Maximum size square sub-matrix with all 1s for more details!
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