Given a knight in a chessboard (a binary matrix with
Return
0
as empty and 1
as barrier) with a source
position, find the shortest path to a destination
position, return the length of the route.Return
-1
if destination cannot be reached.Example
Example 1:
Input:
[[0,0,0],
[0,0,0],
[0,0,0]]
source = [2, 0] destination = [2, 2]
Output: 2
Explanation:
[2,0]->[0,1]->[2,2]
Example 2:
Input:
[[0,1,0],
[0,0,1],
[0,0,0]]
source = [2, 0] destination = [2, 2]
Output:-1
Clarification
If the knight is at (x, y), he can get to the following positions in one step:
(x + 1, y + 2)
(x + 1, y - 2)
(x - 1, y + 2)
(x - 1, y - 2)
(x + 2, y + 1)
(x + 2, y - 1)
(x - 2, y + 1)
(x - 2, y - 1)
Notice
source and destination must be empty.
Knight can not enter the barrier.
Knight can not enter the barrier.
/** * Definition for a point. * class Point { * int x; * int y; * Point() { x = 0; y = 0; } * Point(int a, int b) { x = a; y = b; } * } */ public class Solution { /** * @param grid: a chessboard included 0 (false) and 1 (true) * @param source: a point * @param destination: a point * @return: the shortest path */ public int shortestPath(boolean[][] grid, Point source, Point destination) { // write your code here if (grid == null || grid.length == 0) { return 0; } int nRows = grid.length; int nCols = grid[0].length; Queue<Point> queue = new LinkedList<>(); boolean[][] visited = new boolean[nRows][nCols]; queue.offer(source); visited[source.x][source.y] = true; int level = 0; int[][] dirs = {{1, 2}, {1, -2}, {-1, 2}, {-1, -2}, {2, 1}, {2, -1}, {-2, 1}, {-2, -1}}; while (!queue.isEmpty()) { int size = queue.size(); for (int i = 0; i < size; i++) { Point curPoint = queue.poll(); if (curPoint.x == destination.x && curPoint.y == destination.y) { return level; } for (int[] dir : dirs) { int nx = curPoint.x + dir[0]; int ny = curPoint.y + dir[1]; if (isInBound(grid, nx, ny, visited)) { queue.offer(new Point(nx, ny)); visited[nx][ny] = true; } } } level++; } return -1; } private boolean isInBound(boolean[][] grid, int x, int y, boolean[][] visited) { int nRows = grid.length; int nCols = grid[0].length; return x >= 0 && x < nRows && y >= 0 && y < nCols && !grid[x][y] && !visited[x][y]; } }
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