回溯法
class Solution { public List<List<String>> solveNQueens(int n) { List<List<String>> solutions = new ArrayList<List<String>>(); int[] queens = new int[n]; Arrays.fill(queens, -1); Set<Integer> columns = new HashSet<Integer>(); Set<Integer> diagonals1 = new HashSet<Integer>(); Set<Integer> diagonals2 = new HashSet<Integer>(); backtrack(solutions, queens, n, 0, columns, diagonals1, diagonals2); return solutions; } public void backtrack(List<List<String>> solutions, int[] queens, int n, int row, Set<Integer> columns, Set<Integer> diagonals1, Set<Integer> diagonals2) { if (row == n) { List<String> board = generateBoard(queens, n); solutions.add(board); } else { for (int i = 0; i < n; i++) { if (columns.contains(i)) { continue; } int diagonal1 = row - i; if (diagonals1.contains(diagonal1)) { continue; } int diagonal2 = row + i; if (diagonals2.contains(diagonal2)) { continue; } queens[row] = i; columns.add(i); diagonals1.add(diagonal1); diagonals2.add(diagonal2); backtrack(solutions, queens, n, row + 1, columns, diagonals1, diagonals2); queens[row] = -1; columns.remove(i); diagonals1.remove(diagonal1); diagonals2.remove(diagonal2); } } } public List<String> generateBoard(int[] queens, int n) { List<String> board = new ArrayList<String>(); for (int i = 0; i < n; i++) { char[] row = new char[n]; Arrays.fill(row, '.'); row[queens[i]] = 'Q'; board.add(new String(row)); } return board; } }