Given a 2D binary matrix filled with 0's and 1's, find the largest square containing all 1's and return its area.
For example, given the following matrix:
1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0Return 4.
This question can be solved by using DP.
-- Define dp[i][j] as the length of the maximal square of which the right bottom point ended with matrix[i][j].
-- Initial value dp[0][j] = matrix[0][j]; dp[i][0] = matrix[i][0];
-- Transit function: If matrix[i][j] == 1, dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]) + 1;
-- Final state, max(dp[i][j] * dp[i][j])
Code (Java):
public class Solution { public int maximalSquare(char[][] matrix) { if (matrix == null || matrix.length == 0) { return 0; } int rows = matrix.length; int cols = matrix[0].length; int[][] dp = new int[rows][cols]; // Initialization for (int i = 0; i < cols; i++) { dp[0][i] = matrix[0][i] - '0'; } for (int i = 0; i < rows; i++) { dp[i][0] = matrix[i][0] - '0'; } for (int i = 1; i < rows; i++) { for (int j = 1; j < cols; j++) { if (matrix[i][j] == '1') { dp[i][j] = Math.min(Math.min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]) + 1; } } } int maxArea = 0; for (int i = 0; i < rows; i++) { for (int j = 0; j < cols; j++) { maxArea = Math.max(maxArea, dp[i][j] * dp[i][j]); } } return maxArea; } }
Update on 4/2/19: Rolling array
public class Solution { /** * @param matrix: a matrix of 0 and 1 * @return: an integer */ public int maxSquare(int[][] matrix) { if (matrix == null || matrix.length == 0) { return 0; } int m = matrix.length; int n = matrix[0].length; int maxLen = 0; int[][] dp = new int[2][n]; for (int i = 0; i < n; i++) { if (matrix[0][i] == 1) { dp[0][i] = 1; maxLen = Math.max(maxLen, dp[0][i]); } } int cur = 0; int old = 0; for (int i = 1; i < m; i++) { old = cur; cur = 1 - cur; dp[cur][0] = matrix[i][0] == 1 ? 1 : 0; maxLen = Math.max(maxLen, dp[cur][0]); for (int j = 1; j < n; j++) { if (matrix[i][j] == 1) { dp[cur][j] = Math.min(dp[old][j - 1], Math.min(dp[old][j], dp[cur][j - 1])) + 1; } else { dp[cur][j] = 0; } maxLen = Math.max(maxLen, dp[cur][j]); } } return maxLen * maxLen; } }
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