{

std::set<std::string> seen;

for (int i = 0; i < 9; ++i) {

for (int j = 0; j < 9; ++j) {

if (board[i][j] != '.') {

int num = board[i][j] - '0';

// k1 = "(row)num", k2 = "num(col)", k3 = "xnumy", x&y identify 3*3 grid

auto k1 = '('+ std::to_string(i) + ')' + std::to_string(num);

auto k2 = std::to_string(num) + '(' + std::to_string(j) + ')';

auto k3 = std::to_string(i / 3) + std::to_string(num) + std::to_string(j / 3);

// if set don't contain value, then insert occured and return true, otherwise return false

if (!seen.insert(k1).second ||

!seen.insert(k2).second ||

!seen.insert(k3).second) {

return false;

}

}

}

}

return true;

// 'num': {{x0, y0}, {x1, y1}, ..., {x9, y9}}