317. Shortest Distance from All Buildings

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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.
Example:
Input: [[1,0,2,0,1],[0,0,0,0,0],[0,0,1,0,0]]

1 - 0 - 2 - 0 - 1
|   |   |   |   |
0 - 0 - 0 - 0 - 0
|   |   |   |   |
0 - 0 - 1 - 0 - 0

Output: 7 

Explanation: Given three buildings at (0,0), (0,4), (2,2), and an obstacle at (0,2),
             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.
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Intuition
Compute Manhattan distance (along x, y axis) from one building to each empty land. 
We can use BFS to get the shortest distance from a particular building to land.
Run BFS from each building, and accumulate the shortest distances.
* Also track how many buildings can reach the empty land
In the end, return min distance from empty land if its reached by all buildings
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Time - O(m * n * number of buildings)
Space - O(m * n)
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Related problems
286-walls-and-gates
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