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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
public class Solution {
public IList<IList<string>> SolveNQueens(int n) {
return this.Backtrack(n, 0, (x, y) => false).ToList();
}
private IEnumerable<IList<string>> Backtrack(int boardSize, int y, Func<int, int, bool> check) {
for (int x = 0; x < boardSize; x++) {
if (check(x, y)) {
continue;
}
string currentLine = $"{new string('.', x)}Q{new string('.', boardSize - x - 1)}";
if (y == boardSize - 1) {
yield return new List<string> { currentLine };
continue;
}
var results = this.Backtrack(boardSize, y + 1, (xx, yy) =>
check(xx, yy) ||
(xx == x) ||
(yy == (y - x) + xx) ||
(yy == (x + y) - xx)
);
foreach (var result in results) {
result.Add(currentLine);
yield return result;
}
}
}
}