N-Queens
The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.
Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.
Each solution contains a distinct board configuration of the n-queens’ placement, where ‘Q’ and ‘.’ both indicate a queen and an empty space, respectively.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Example 1:
Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:
Input: n = 1
Output: [["Q"]]
Constraints:
1 <= n <= 9
Solution
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
class Solution {
private:
vector<vector<string>> res;
unordered_set<int> colSet;
unordered_set<int> diag1Set;
unordered_set<int> diag2Set;
public:
bool checkVec(int row, int col) {
// Check column conflicts
if (colSet.count(col) > 0) {
return false;
}
// Check diagonal conflicts
if (diag1Set.count(row + col) > 0 || diag2Set.count(row - col) > 0) {
return false;
}
return true;
}
void solveNQueensImpl(int row, int n, vector<int> board) {
if (row == n) {
vector<string> tmpVec;
for (int i = 0; i < n; i++) {
string tmp(n, '.');
tmp[board[i]] = 'Q';
tmpVec.push_back(tmp);
}
res.push_back(tmpVec);
return;
}
for (int col = 0; col < n; col++) {
if (checkVec(row, col)) {
board[row] = col;
colSet.insert(col);
diag1Set.insert(row + col);
diag2Set.insert(row - col);
solveNQueensImpl(row + 1, n, board);
colSet.erase(col);
diag1Set.erase(row + col);
diag2Set.erase(row - col);
}
}
}
vector<vector<string>> solveNQueens(int n) {
vector<int> board(n, 0);
solveNQueensImpl(0, n, board);
return res;
}
};
