solves #499: The maze III in java

Author: anishLearnsToCode

README.md

@@ -334,6 +334,7 @@
 | 492  | [Construct the Rectangle](https://leetcode.com/problems/construct-the-rectangle)                                                                                       |                                                   [![Java](assets/java.png)](src/ConstructTheRectangle.java) [![Python](assets/python.png)](python/construct_the_rectangle.py)                                                   |                                                                                                                                   |
 | 495  | [Teemo Attacking](https://leetcode.com/problems/teemo-attacking/)                                                                                                      |                                                          [![Java](assets/java.png)](src/TeemoAttacking.java) [![Python](assets/python.png)](python/teemo_attacking.py)                                                           |                                                                                                                                   |
 | 496  | [Next Greater Element I](https://leetcode.com/problems/next-greater-element-i)                                                                                         |                                                    [![Java](assets/java.png)](src/NextGreaterElementI.java) [![Python](assets/python.png)](python/next_greater_element_i.py)                                                     |                                                                                                                                   |
+| 499  | [The Maze III](https://leetcode.com/problems/the-maze-iii)                                                                                                             |                                                                                         [![Java](assets/java.png)](src/TheMazeIII.java)                                                                                          |                                                                                                                                   |
 | 500  | [Keyboard Row](https://leetcode.com/problems/keyboard-row)                                                                                                             |                                                             [![Java](assets/java.png)](src/KeyBoardRow.java) [![Python](assets/python.png)](python/keyboard_row.py)                                                              |                                                                                                                                   |
 | 501  | [Find Mode in Binary Search Tree](https://leetcode.com/problems/find-mode-in-binary-search-tree)                                                                       |                                            [![Java](assets/java.png)](src/FindModeInBinarySearchTree.java) [![Python](assets/python.png)](python/find_mode_in_binary_search_tree.py)                                             |                                                                                                                                   |
 | 504  | [Base 7](https://leetcode.com/problems/base-7)                                                                                                                         |                                                                   [![Java](assets/java.png)](src/Base7.java) [![Python](assets/python.png)](python/base_7.py)                                                                    |                                                                                                                                   |

src/TheMazeIII.java

@@ -0,0 +1,98 @@
+// https://leetcode.com/problems/the-maze-iii
+// T: O(m * n log(m * n))
+// S: O(m * n)
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+import java.util.PriorityQueue;
+import java.util.Queue;
+
+public class TheMazeIII {
+    private record Info(int[] position, int distance, String path) {}
+
+    private record Position(int[] position, String direction) {}
+
+    private static final Position[] DIRECTIONS = new Position[] {
+            new Position(new int[] { 1, 0 }, "d"),
+            new Position(new int[] { 0, -1 }, "l"),
+            new Position(new int[] { 0, 1 }, "r"),
+            new Position(new int[] { -1, 0 }, "u")
+    };
+
+    // T: O(m * n * log(m * n)), S: O(m * n)
+    public String findShortestWay(int[][] maze, int[] ball, int[] hole) {
+        final int[][] distances = getDistances(maze.length, maze[0].length);
+        final Queue<Info> queue = new PriorityQueue<>((a, b) -> {
+            if (a.distance == b.distance) {
+                return a.path.compareTo(b.path);
+            }
+            return Integer.compare(a.distance, b.distance);
+        });
+        queue.add(new Info(ball, 0, ""));
+        String path = null;
+
+        while (!queue.isEmpty()) {
+            final Info info = queue.poll();
+
+            if (distances[info.position[0]][info.position[1]] <= info.distance) {
+                continue;
+            }
+
+            distances[info.position[0]][info.position[1]] = info.distance;
+
+            if (info.position[0] == hole[0] && info.position[1] == hole[1]) {
+                if (path == null) {
+                    path = info.path;
+                } else {
+                    path = path.compareTo(info.path) > 0 ? info.path : path;
+                }
+            }
+
+            for (Position position : validPositions(maze, info.position, hole)) {
+                queue.add(new Info(
+                        position.position,
+                        info.distance + manhattanDistance(position.position, info.position),
+                        info.path + position.direction
+                ));
+            }
+        }
+
+        final int minDistance = distances[hole[0]][hole[1]];
+        return minDistance == Integer.MAX_VALUE ? "impossible" : path;
+    }
+
+    // T: O(1), S:O(1)
+    private static int manhattanDistance(int[] p1, int[] p2) {
+        return Math.abs(p1[0] - p2[0]) + Math.abs(p1[1] - p2[1]);
+    }
+
+    // T: O(m + n), S: O(1)
+    private static List<Position> validPositions(int[][] grid, int[] position, int[] target) {
+        final List<Position> result = new ArrayList<>();
+        for (Position p : DIRECTIONS) {
+            int row = position[0], column = position[1];
+            while (row >= 0 && row < grid.length
+                    && column >= 0 && column < grid[0].length && grid[row][column] == 0 &&
+                    (row != target[0] || column != target[1])) {
+                row += p.position[0];
+                column += p.position[1];
+            }
+            if (row == target[0] && column == target[1]) {
+                result.add(new Position(new int[] { row, column}, p.direction));
+            } else {
+                result.add(new Position(new int[]{row - p.position[0], column - p.position[1]}, p.direction));
+            }
+        }
+        return result;
+    }
+
+    // T: O(m * n), S: O(m * n)
+    private static int[][] getDistances(int rows, int columns) {
+        final int[][] distances = new int[rows][columns];
+        for (int[] row : distances) {
+            Arrays.fill(row, Integer.MAX_VALUE);
+        }
+        return distances;
+    }
+}