221. Maximal Square

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

For example, given the following matrix:

1 0 1 0 01 0 1 1 11 1 1 1 11 0 0 1 0

Return 4.

思路：还是典型的DP问题，递推式为d[i][j]=min(d[i−1][j−1],d[i−1][j],d[i][j−1])+1，当d[i][j]==1时，这题的关键是对边界的处理，如果面试官要求不能修改原数组，则需要重新开一个空间，这题可以开一个长宽比原数组大一的数组来方便求解；如果允许修改原数组的话，只需要常数额外空间就够了，见代码：

class Solution {public:    int maximalSquare(vector<vector<char>>& matrix) {        int res = 0;        for (int i=0;i<matrix.size();i++){            for(int j=0;j<matrix[0].size();j++){                int a = (i&&j)?matrix[i-1][j-1]:0;                int b = i?matrix[i-1][j]:0;                int c = j?matrix[i][j-1]:0;                matrix[i][j] = matrix[i][j]=='1'?(min(a,min(b,c))+1):0;                res = max(res,matrix[i][j]*matrix[i][j]);            }        }        return res;    }};