int maximalSquare(vector<vector<char>>& matrix) {

return maximalSquare_1(matrix);

}

int maximalSquare_1(vector<vector<char>>& matrix)

{

int size_row = matrix.size();

if(0 == size_row || 0 == matrix[0].size()) return 0;

int size_col = matrix[0].size();

// dp[row][col] represent the max-area from coordinate [row,col] to lower-right-corner of the matrix

vector<vector<int>> dp(size_row, vector<int>(size_col, 0));

for(int row = size_row - 1; row >= 0; --row)

dp[row][size_col-1] = matrix[row][size_col-1] == '0' ? 0 : 1;

for(int col = size_col - 1; col >= 0; --col)

dp[size_row-1][col] = matrix[size_row-1][col] == '0' ? 0 : 1;

for(int row = size_row - 2; row >= 0; --row)

{

for(int col = size_col - 2; col >= 0; --col)

{

if(matrix[row][col] == '1')

{

int min_area = std::min(dp[row+1][col+1], std::min(dp[row][col+1], dp[row+1][col]));

dp[row][col] = std::pow(std::sqrt(min_area) + 1, 2);

}

else

dp[row][col] = 0;

}

}

int result = 0;

for(auto &v : dp)

for(auto i : v)

result = std::max(result, i);

return result;

}