LeetCode-in-All
51. N-Queens
Hard
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.
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
#include <vector>
#include <string>
#include <algorithm>
class Solution {
public:
std::vector<std::vector<std::string>> solveNQueens(int n) {
std::vector<bool> pos(n + 2 * n - 1 + 2 * n - 1, false);
std::vector<int> pos2(n, 0);
std::vector<std::vector<std::string>> ans;
helper(n, 0, pos, pos2, ans);
return ans;
}
private:
void helper(int n, int row, std::vector<bool>& pos, std::vector<int>& pos2, std::vector<std::vector<std::string>>& ans) {
if (row == n) {
construct(n, pos2, ans);
return;
}
for (int i = 0; i < n; ++i) {
int index = n + 2 * n - 1 + n - 1 + i - row;
if (pos[i] || pos[n + i + row] || pos[index]) {
continue;
}
pos[i] = true;
pos[n + i + row] = true;
pos[index] = true;
pos2[row] = i;
helper(n, row + 1, pos, pos2, ans);
pos[i] = false;
pos[n + i + row] = false;
pos[index] = false;
}
}
void construct(int n, std::vector<int>& pos, std::vector<std::vector<std::string>>& ans) {
std::vector<std::string> sol;
for (int r = 0; r < n; ++r) {
std::string queenRow(n, '.');
queenRow[pos[r]] = 'Q';
sol.push_back(queenRow);
}
ans.push_back(sol);
}
};