/**
* Get all distinct N-Queen solutions
* @param n: The number of queens
* @return: All distinct solutions
* For example, A string '...Q' shows a queen on forth position
*/
vector<vector<string> > solveNQueens(int n) {
vector<vector<string> > m_res;
if (n < 1)
return m_res;
int *columns = new int[n];
memset(columns, -1, sizeof(columns));
vector<string> m_path;
solveNQueensHelper(m_res, m_path, columns, 0, n);
delete columns;
return m_res;
}
// dfs row by row
void solveNQueensHelper(vector<vector<string> > &m_res, vector<string> m_path,
int *columns, int row, int n) {
if (row == n) {
m_res.push_back(m_path);
}
else {
// check from col 1 to col n-1
for (int i = 0; i < n; i++) {
if (checkValid(columns, row, i)) {
string curr_row(n, '.');
curr_row[i] = 'Q';
columns[row] = i;
m_path.push_back(curr_row);
solveNQueensHelper(m_res, m_path, columns, row + 1, n);
m_path.pop_back();
columns[row] = -1;
curr_row[i] = '.';
}
}
}
return;
}
void solveNQueensHelper(vector<vector<string>>& res, vector<string>& state, int n, int l) {
if(l<n){
for(int j=0;j<n;++j){
bool b = 1;
for(int i=0;i<l;++i){
b = b&&(state[i][j]=='.');
}
if(!b) continue;
for(int l1=l-1,j1=j-1;j1>=0&&l1>=0;--l1,--j1){
b = b&&(state[l1][j1]=='.');
}
if(!b) continue;
for(int l1=l-1,j1=j+1;j1<n&&l1>=0;--l1,++j1){
b = b&&(state[l1][j1]=='.');
}
if(!b) continue;
state[l][j] = 'Q';
solveNQueensHelper(res,state,n,l+1);
state[l][j] = '.';
}
}else{
res.push_back(state);
}
}
vector<vector<string>> solveNQueens(int n) {
vector<vector<string>> res;
vector<string> state(n,string(n,'.'));
solveNQueensHelper(res,state,n,0);
return res;
}
