Shortest Distance from All Buildings
You want to build a house on an empty land which reaches all buildings in the shortest amount of distance. You can only move up, down, left and right. You are given a 2D grid of values 0, 1 or 2, where:
- Each 0 marks an empty land which you can pass by freely.
- Each 1 marks a building which you cannot pass through.
- Each 2 marks an obstacle which you cannot pass through.
For example, given three buildings at (0,0)
, (0,4)
, (2,2)
, and an obstacle at (0,2)
:
1 - 0 - 2 - 0 - 1
| | | | |
0 - 0 - 0 - 0 - 0
| | | | |
0 - 0 - 1 - 0 - 0
The point (1,2)
is an ideal empty land to build a house, as the total travel distance of 3+3+1=7
is minimal. So return 7
.
Note:
There will be at least one building. If it is not possible to build such house according to the above rules, return -1.