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354 lines (330 loc) · 11.6 KB
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/**
* There is a ball in a maze with empty spaces and walls. The ball can go
* through empty spaces by rolling up, down, left or right, but it won't stop
* rolling until hitting a wall. When the ball stops, it could choose the next
* direction.
*
* Given the ball's start position, the destination and the maze, find the
* shortest distance for the ball to stop at the destination. The distance is
* defined by the number of empty spaces traveled by the ball from the start
* position (excluded) to the destination (included). If the ball cannot stop
* at the destination, return -1.
*
* The maze is represented by a binary 2D array. 1 means the wall and 0 means
* the empty space. You may assume that the borders of the maze are all walls.
* The start and destination coordinates are represented by row and column
* indexes.
*
* Example 1
*
* Input 1: a maze represented by a 2D array
*
* 0 0 1 0 0
* 0 0 0 0 0
* 0 0 0 1 0
* 1 1 0 1 1
* 0 0 0 0 0
*
* Input 2: start coordinate (rowStart, colStart) = (0, 4)
* Input 3: destination coordinate (rowDest, colDest) = (4, 4)
*
* Output: 12
* Explanation: One shortest way is : left -> down -> left -> down -> right -> down -> right.
* The total distance is 1 + 1 + 3 + 1 + 2 + 2 + 2 = 12.
* https://leetcode.com/static/images/problemset/maze_1_example_1.png
*
*
* Example 2
*
* Input 1: a maze represented by a 2D array
*
* 0 0 1 0 0
* 0 0 0 0 0
* 0 0 0 1 0
* 1 1 0 1 1
* 0 0 0 0 0
*
* Input 2: start coordinate (rowStart, colStart) = (0, 4)
* Input 3: destination coordinate (rowDest, colDest) = (3, 2)
*
* Output: -1
* Explanation: There is no way for the ball to stop at the destination.
* https://leetcode.com/static/images/problemset/maze_1_example_2.png
*
* Note:
* There is only one ball and one destination in the maze.
* Both the ball and the destination exist on an empty space, and they will not
* be at the same position initially.
* The given maze does not contain border (like the red rectangle in the
* example pictures), but you could assume the border of the maze are all walls.
* The maze contains at least 2 empty spaces, and both the width and height of
* the maze won't exceed 100.
*/
public class TheMazeII505 {
private int[][] DIRECTIONS = new int[][]{{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
public int shortestDistance(int[][] maze, int[] start, int[] destination) {
int M = maze.length;
int N = maze[0].length;
if (isSame(start, destination)) return 0;
int[][] visited = new int[M][N];
for (int[] row: visited) {
Arrays.fill(row, -1);
}
Queue<Point> q = new LinkedList<>();
q.add(new Point(start, 0));
visited[start[0]][start[1]] = 0;
int min = Integer.MAX_VALUE;
while (!q.isEmpty()) {
int size = q.size();
Point curr = q.poll();
if (isSame(curr.pos, destination)) {
min = Math.min(min, curr.dist);
continue;
}
for (int[] d: DIRECTIONS) {
int x = curr.pos[0] + d[0];
int y = curr.pos[1] + d[1];
int more = 1;
while (x >= 0 && y >= 0 && x < M && y < N && maze[x][y] == 0) {
x += d[0];
y += d[1];
more++;
}
x -= d[0];
y -= d[1];
more--;
int[] newPos = new int[]{x, y};
if (visited[x][y] == -1 || visited[x][y] > curr.dist + more) {
q.add(new Point(newPos, curr.dist + more));
visited[x][y] = curr.dist + more;
}
}
}
return min == Integer.MAX_VALUE ? -1 : min;
}
private boolean isSame(int[] a, int[] b) {
return a[0] == b[0] && a[1] == b[1];
}
class Point {
int[] pos;
int dist;
Point(int[] p, int d) {
pos = p;
dist = d;
}
}
/**
* https://leetcode.com/problems/the-maze-ii/discuss/98418/Simple-Java-Solution-BFS
*/
public int shortestDistance2(int[][] maze, int[] start, int[] destination) {
Queue<int[]> q = new LinkedList<>();
int m = maze.length, n = maze[0].length;
int[][] dist = new int[m][n];
for (int i = 0; i < m; i++) {
Arrays.fill(dist[i], Integer.MAX_VALUE);
}
int[] dx = new int[] {-1, 0, 1, 0};
int[] dy = new int[] { 0, 1, 0, -1};
q.offer(start);
dist[start[0]][start[1]] = 0;
while (!q.isEmpty()) {
int[] p = q.poll();
for (int i = 0; i < 4; i++) {
int x = p[0] + dx[i], y = p[1] + dy[i];
int cnt = 1;
while (x >=0 && x < m && y >= 0 && y < n && maze[x][y] != 1) {
x += dx[i];
y += dy[i];
cnt++;
}
x -= dx[i];
y -= dy[i];
cnt--;
if (dist[p[0]][p[1]] + cnt < dist[x][y]) {
dist[x][y] = dist[p[0]][p[1]] + cnt;
q.offer(new int[] {x, y});
}
}
}
return dist[destination[0]][destination[1]] == Integer.MAX_VALUE ? -1 : dist[destination[0]][destination[1]];
}
public int shortestDistance3(int[][] maze, int[] start, int[] destination) {
int M = maze.length;
int N = maze[0].length;
int[][] memo = new int[M][N];
for (int[] row: memo) Arrays.fill(row, Integer.MAX_VALUE);
memo[start[0]][start[1]] = 0;
roll(maze, start[0], start[1], memo, M, N);
return memo[destination[0]][destination[1]] == Integer.MAX_VALUE ? -1 : memo[destination[0]][destination[1]];
}
private void roll(int[][] maze, int i, int j, int[][] memo, int M, int N) {
// top
int t = i - 1;
int rt = 1;
while (t >= 0 && maze[t][j] == 0) {
t--;
rt++;
}
t++;
rt--;
if (memo[i][j] + rt < memo[t][j]) {
memo[t][j] = memo[i][j] + rt;
roll(maze, t, j, memo, M, N);
}
// bottom
int b = i + 1;
int rb = 1;
while (b < M && maze[b][j] == 0) {
b++;
rb++;
}
b--;
rb--;
if (memo[i][j] + rb < memo[b][j]) {
memo[b][j] = memo[i][j] + rb;
roll(maze, b, j, memo, M, N);
}
// left
int l = j - 1;
int rl = 1;
while (l >= 0 && maze[i][l] == 0) {
l--;
rl++;
}
l++;
rl--;
if (memo[i][j] + rl < memo[i][l]) {
memo[i][l] = memo[i][j] + rl;
roll(maze, i, l, memo, M, N);
}
// right
int r = j + 1;
int rr = 1;
while (r < N && maze[i][r] == 0) {
r++;
rr++;
}
r--;
rr--;
if (memo[i][j] + rr < memo[i][r]) {
memo[i][r] = memo[i][j] + rr;
roll(maze, i, r, memo, M, N);
}
}
/**
* https://leetcode.com/problems/the-maze-ii/solution/
*/
public int shortestDistance4(int[][] maze, int[] start, int[] dest) {
int[][] distance = new int[maze.length][maze[0].length];
for (int[] row: distance)
Arrays.fill(row, Integer.MAX_VALUE);
distance[start[0]][start[1]] = 0;
dfs(maze, start, distance);
return distance[dest[0]][dest[1]] == Integer.MAX_VALUE ? -1 : distance[dest[0]][dest[1]];
}
public void dfs(int[][] maze, int[] start, int[][] distance) {
int[][] dirs={{0,1}, {0,-1}, {-1,0}, {1,0}};
for (int[] dir: dirs) {
int x = start[0] + dir[0];
int y = start[1] + dir[1];
int count = 0;
while (x >= 0 && y >= 0 && x < maze.length && y < maze[0].length && maze[x][y] == 0) {
x += dir[0];
y += dir[1];
count++;
}
if (distance[start[0]][start[1]] + count < distance[x - dir[0]][y - dir[1]]) {
distance[x - dir[0]][y - dir[1]] = distance[start[0]][start[1]] + count;
dfs(maze, new int[]{x - dir[0],y - dir[1]}, distance);
}
}
}
/**
* https://leetcode.com/problems/the-maze-ii/solution/
*/
public int shortestDistance5(int[][] maze, int[] start, int[] destination) {
int M = maze.length;
int N = maze[0].length;
int[][] distances = new int[M][N];
for (int[] row: distances) Arrays.fill(row, Integer.MAX_VALUE);
distances[start[0]][start[1]] = 0;
boolean[][] visited = new boolean[M][N];
roll(maze, distances, visited, M, N);
int res = distances[destination[0]][destination[1]];
return res == Integer.MAX_VALUE ? -1 : res;
}
private void roll(int[][] maze, int[][] distances, boolean[][] visited, int M, int N) {
while (true) {
int[] m = minDistance(distances, visited, M, N);
if (m == null) return;
visited[m[0]][m[1]] = true;
for (int[] dir: DIRECTIONS) {
int x = m[0] + dir[0];
int y = m[1] + dir[1];
int dis = 0;
while (x >= 0 && y >= 0 && x < M && y < N && maze[x][y] == 0) {
x += dir[0];
y += dir[1];
dis++;
}
x -= dir[0];
y -= dir[1];
int d = distances[m[0]][m[1]] + dis;
if (d < distances[x][y]) {
distances[x][y] = d;
}
}
}
}
private int[] minDistance(int[][] distances, boolean[][] visited, int M, int N) {
int[] res = null;
int min = Integer.MAX_VALUE;
for (int i=0; i<M; i++) {
for (int j=0; j<N; j++) {
if (!visited[i][j] && distances[i][j] < min) {
res = new int[]{i, j};
min = distances[i][j];
}
}
}
return res;
}
/**
* https://leetcode.com/problems/the-maze-ii/solution/
*/
public int shortestDistance6(int[][] maze, int[] start, int[] destination) {
int M = maze.length;
int N = maze[0].length;
int[][] distances = new int[M][N];
for (int[] row: distances) Arrays.fill(row, Integer.MAX_VALUE);
distances[start[0]][start[1]] = 0;
roll(maze, distances, start, M, N);
int res = distances[destination[0]][destination[1]];
return res == Integer.MAX_VALUE ? -1 : res;
}
private void roll(int[][] maze, int[][] distances, int[] start, int M, int N) {
PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[2] - b[2]);
pq.add(new int[]{start[0], start[1], 0});
while (!pq.isEmpty()) {
int[] md = pq.poll();
if (distances[md[0]][md[1]] < md[2]) continue;
for (int[] dir: DIRECTIONS) {
int x = md[0] + dir[0];
int y = md[1] + dir[1];
int dis = 0;
while (x >= 0 && y >= 0 && x < M && y < N && maze[x][y] == 0) {
x += dir[0];
y += dir[1];
dis++;
}
x -= dir[0];
y -= dir[1];
int d = distances[md[0]][md[1]] + dis;
if (d < distances[x][y]) {
distances[x][y] = d;
pq.add(new int[]{x, y, d});
}
}
}
}
}
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