|
1 | 1 | // https://leetcode.com/problems/snakes-and-ladders |
2 | | -// T: O() |
3 | | -// S: O() |
| 2 | +// T: O(n^2) |
| 3 | +// S: O(n^2) |
| 4 | + |
| 5 | +import java.util.ArrayList; |
| 6 | +import java.util.Arrays; |
| 7 | +import java.util.HashMap; |
| 8 | +import java.util.LinkedList; |
| 9 | +import java.util.List; |
| 10 | +import java.util.Map; |
| 11 | +import java.util.Queue; |
4 | 12 |
|
5 | 13 | public class SnakesAndLadders { |
| 14 | + private record Position(int row, int column) {} |
| 15 | + |
| 16 | + private record Info(int square, int cost) {} |
| 17 | + |
| 18 | + // BFS: T: O(V + E), V = n^2, E = 6n^2 T: O(n^2), S: O(V) = O(n^2) |
| 19 | + public int snakesAndLadders(int[][] board) { |
| 20 | + final int n = board.length; |
| 21 | + final Map<Integer, Position> squareToPosition = createSquaresToPositions(n); |
| 22 | + final Queue<Info> queue = new LinkedList<>() {{ add(new Info(1, 0)); }}; |
| 23 | + final int[] distances = initializeDistances(n); |
| 24 | + |
| 25 | + while (!queue.isEmpty()) { |
| 26 | + final Info info = queue.poll(); |
| 27 | + if (distances[info.square] <= info.cost) { |
| 28 | + continue; |
| 29 | + } |
| 30 | + |
| 31 | + distances[info.square] = info.cost; |
| 32 | + |
| 33 | + for (int nextSquare : validPositions(board, info.square, squareToPosition)) { |
| 34 | + queue.add(new Info(nextSquare, info.cost + 1)); |
| 35 | + } |
| 36 | + } |
| 37 | + |
| 38 | + return distances[n * n] == Integer.MAX_VALUE ? -1 : distances[n * n]; |
| 39 | + } |
| 40 | + |
| 41 | + // T: O(1), S: O(1) |
| 42 | + private static List<Integer> validPositions(int[][] grid, int square, Map<Integer, Position> positions) { |
| 43 | + final int n = grid.length; |
| 44 | + final List<Integer> result = new ArrayList<>(); |
| 45 | + for (int i = 1 ; i <= 6 ; i++) { |
| 46 | + final int nextSquare = square + i; |
| 47 | + if (nextSquare > n * n) { |
| 48 | + break; |
| 49 | + } |
| 50 | + final Position position = positions.get(nextSquare); |
| 51 | + if (grid[position.row][position.column] == -1) { |
| 52 | + result.add(nextSquare); |
| 53 | + } else { |
| 54 | + result.add(grid[position.row][position.column]); |
| 55 | + } |
| 56 | + } |
| 57 | + return result; |
| 58 | + } |
| 59 | + |
| 60 | + // T: O(n^2), S: O(n^2) |
| 61 | + private static int[] initializeDistances(int n) { |
| 62 | + final int[] distances = new int[n * n + 1]; |
| 63 | + Arrays.fill(distances, Integer.MAX_VALUE); |
| 64 | + return distances; |
| 65 | + } |
| 66 | + |
| 67 | + // T: O(n^2), S: O(n^2) |
| 68 | + private static Map<Integer, Position> createSquaresToPositions(int n) { |
| 69 | + final Map<Integer, Position> result = new HashMap<>(); |
| 70 | + for (int i = 1 ; i <= n * n ; i++) { |
| 71 | + final int row = n - ((i - 1) / n) - 1; |
| 72 | + final int column = (n - 1 - row) % 2 == 0 ? (i - 1) % n : n - 1 - ((i - 1) % n); |
| 73 | + result.put(i, new Position(row, column)); |
| 74 | + } |
| 75 | + return result; |
| 76 | + } |
6 | 77 | } |
0 commit comments