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# Knight Shortest Path

## Knight Shortest Path

Given a knight in a chessboard (a binary matrix with`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 knight can not reached.

## Example

```
[[0,0,0],
 [0,0,0],
 [0,0,0]]
source = [2, 0] destination = [2, 2] return 2

[[0,1,0],
 [0,0,0],
 [0,0,0]]
source = [2, 0] destination = [2, 2] return 6

[[0,1,0],
 [0,0,1],
 [0,0,0]]
source = [2, 0] destination = [2, 2] return -1
```

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)
```

## Note

BFS最短路径——三层循环

## Code

```java
public class Solution {
    int n, m; // size of the chessboard
    int[] deltaX = {1, 1, 2, 2, -1, -1, -2, -2};
    int[] deltaY = {2, -2, 1, -1, 2, -2, 1, -1};
    /**
     * @param grid a chessboard included 0 (false) and 1 (true)
     * @param source, destination a point
     * @return the shortest path 
     */
    public int shortestPath(boolean[][] grid, Point source, Point destination) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return -1;
        }

        n = grid.length;
        m = grid[0].length;

        Queue<Point> queue = new LinkedList<>();
        queue.offer(source);

        int steps = 0;
        while (!queue.isEmpty()) {
            int size = queue.size();
            for (int i = 0; i < size; i++) {
                Point point = queue.poll();
                if (point.x == destination.x && point.y == destination.y) {
                    return steps;
                }

                for (int direction = 0; direction < 8; direction++) {
                    Point nextPoint = new Point(
                        point.x + deltaX[direction],
                        point.y + deltaY[direction]
                    );

                    if (!inBound(nextPoint, grid)) {
                        continue;
                    }

                    queue.offer(nextPoint);
                    // mark the point not accessible
                    grid[nextPoint.x][nextPoint.y] = true;
                }
            }
            steps++;
        }

        return -1;
    }

    private boolean inBound(Point point, boolean[][] grid) {
        if (point.x < 0 || point.x >= n) {
            return false;
        }
        if (point.y < 0 || point.y >= m) {
            return false;
        }
        return (grid[point.x][point.y] == false);
    }
}
```


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