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1 | 1 | package g0001_0100.s0051_n_queens;
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2 | 2 |
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3 | 3 | // #Hard #Top_100_Liked_Questions #Array #Backtracking #Big_O_Time_O(N!)_Space_O(N)
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4 |
| -// #2023_08_11_Time_1_ms_(100.00%)_Space_43.6_MB_(97.17%) |
| 4 | +// #2024_11_11_Time_1_ms_(99.77%)_Space_44.8_MB_(61.16%) |
5 | 5 |
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6 | 6 | import java.util.ArrayList;
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7 |
| -import java.util.Arrays; |
| 7 | +import java.util.LinkedList; |
8 | 8 | import java.util.List;
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9 | 9 |
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10 | 10 | public class Solution {
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11 | 11 | public List<List<String>> solveNQueens(int n) {
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12 |
| - boolean[] pos = new boolean[n + 2 * n - 1 + 2 * n - 1]; |
13 |
| - int[] pos2 = new int[n]; |
14 |
| - List<List<String>> ans = new ArrayList<>(); |
15 |
| - helper(n, 0, pos, pos2, ans); |
16 |
| - return ans; |
| 12 | + char[][] board = new char[n][n]; |
| 13 | + for (int i = 0; i < n; i++) { |
| 14 | + for (int j = 0; j < n; j++) { |
| 15 | + board[i][j] = '.'; |
| 16 | + } |
| 17 | + } |
| 18 | + List<List<String>> res = new ArrayList<>(); |
| 19 | + int[] leftRow = new int[n]; |
| 20 | + int[] upperDiagonal = new int[2 * n - 1]; |
| 21 | + int[] lowerDiagonal = new int[2 * n - 1]; |
| 22 | + solve(0, board, res, leftRow, lowerDiagonal, upperDiagonal); |
| 23 | + return res; |
17 | 24 | }
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18 | 25 |
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19 |
| - private void helper(int n, int row, boolean[] pos, int[] pos2, List<List<String>> ans) { |
20 |
| - if (row == n) { |
21 |
| - construct(n, pos2, ans); |
| 26 | + void solve( |
| 27 | + int col, |
| 28 | + char[][] board, |
| 29 | + List<List<String>> res, |
| 30 | + int[] leftRow, |
| 31 | + int[] lowerDiagonal, |
| 32 | + int[] upperDiagonal) { |
| 33 | + if (col == board.length) { |
| 34 | + res.add(construct(board)); |
22 | 35 | return;
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23 | 36 | }
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24 |
| - for (int i = 0; i < n; i++) { |
25 |
| - int index = n + 2 * n - 1 + n - 1 + i - row; |
26 |
| - if (pos[i] || pos[n + i + row] || pos[index]) { |
27 |
| - continue; |
| 37 | + for (int row = 0; row < board.length; row++) { |
| 38 | + if (leftRow[row] == 0 |
| 39 | + && lowerDiagonal[row + col] == 0 |
| 40 | + && upperDiagonal[board.length - 1 + col - row] == 0) { |
| 41 | + board[row][col] = 'Q'; |
| 42 | + leftRow[row] = 1; |
| 43 | + lowerDiagonal[row + col] = 1; |
| 44 | + upperDiagonal[board.length - 1 + col - row] = 1; |
| 45 | + solve(col + 1, board, res, leftRow, lowerDiagonal, upperDiagonal); |
| 46 | + board[row][col] = '.'; |
| 47 | + leftRow[row] = 0; |
| 48 | + lowerDiagonal[row + col] = 0; |
| 49 | + upperDiagonal[board.length - 1 + col - row] = 0; |
28 | 50 | }
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29 |
| - pos[i] = true; |
30 |
| - pos[n + i + row] = true; |
31 |
| - pos[index] = true; |
32 |
| - pos2[row] = i; |
33 |
| - helper(n, row + 1, pos, pos2, ans); |
34 |
| - pos[i] = false; |
35 |
| - pos[n + i + row] = false; |
36 |
| - pos[index] = false; |
37 | 51 | }
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38 | 52 | }
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39 | 53 |
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40 |
| - private void construct(int n, int[] pos, List<List<String>> ans) { |
41 |
| - List<String> sol = new ArrayList<>(); |
42 |
| - for (int r = 0; r < n; r++) { |
43 |
| - char[] queenRow = new char[n]; |
44 |
| - Arrays.fill(queenRow, '.'); |
45 |
| - queenRow[pos[r]] = 'Q'; |
46 |
| - sol.add(new String(queenRow)); |
| 54 | + List<String> construct(char[][] board) { |
| 55 | + List<String> res = new LinkedList<>(); |
| 56 | + for (char[] chars : board) { |
| 57 | + String s = new String(chars); |
| 58 | + res.add(s); |
47 | 59 | }
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48 |
| - ans.add(sol); |
| 60 | + return res; |
49 | 61 | }
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50 | 62 | }
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