Given a 2D binary matrix filled with 0’s and 1’s, find the largest square containing only 1’s and return its area.

Example:

Input: 
1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0
Output: 4

难度：medium

题目：给定由0,1组成的矩阵，找出由1组成的最大方块并返回其面积。

思路：动态规划
转换方程
grid[i][j] = Math.min(grid[i][j – 1], grid[i – 1][j], grid[i – 1][j – 1]) + 1 (matrix[i][j] = ‘1’)

Runtime: 7 ms, faster than 97.80% of Java online submissions for Maximal Square.
Memory Usage: 40.8 MB, less than 70.46% of Java online submissions for Maximal Square.

class Solution {
    public int maximalSquare(char[][] matrix) {
        if (null == matrix || matrix.length < 1) {
            return 0;
        }
        int maxSquare = 0, m = matrix.length, n = matrix[0].length;
        int[][] grid = new int[m][n];
        for (int i = 0; i < m; i++) {
            if ('1' == matrix[i][0]) {
                grid[i][0] = 1;
                maxSquare = 1;
            }
        }
        for (int i = 0; i < n; i++) {
            if ('1' == matrix[0][i]) {
                grid[0][i] = 1;
                maxSquare = 1;
            }
        }
        
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if ('1' == matrix[i][j]) {
                    grid[i][j] = Math.min(grid[i - 1][j - 1], 
                                             Math.min(grid[i - 1][j], grid[i][j - 1])) + 1;
                    maxSquare = Math.max(maxSquare, grid[i][j]);
                }
            }
        }
        
        return maxSquare * maxSquare;
    }
}