LeetCode Q317: Shortest Distance from All Buildings (hard)

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.

Solution:

Use BFS, and only expand to empty land which can be reached by all previous tested buildings.

	class Solution {
	public:
	int shortestDistance(vector<vector<int>>& grid) {
	if(grid.empty())
	return -1;
	int rows = grid.size();
	int cols = grid[0].size();
	vector<vector<int> > sumDist(rows, vector<int>(cols, 0));
	for(int i=0; i<rows; i++){
	for(int j=0; j<cols; j++){
	if(grid[i][j]!=1)
	continue;
	vector<vector<int> > dist(rows, vector<int>(cols, -1));
	dist[i][j]=0;
	queue<vector<int> > myQ;
	vector<int> tmp={i, j, 0};
	myQ.push(tmp);
	while(!myQ.empty()){
	vector<int> front = myQ.front();
	myQ.pop();
	int r=front[0];
	int c=front[1];
	int s=front[2];
	if(r!=0 && grid[r-1][c]!=2 && grid[r-1][c]!=1 && (s+1<dist[r-1][c] || dist[r-1][c]==-1) && sumDist[r-1][c]!=-1){
	vector<int> tmp={r-1, c, s+1};
	dist[r-1][c]=s+1;
	myQ.push(tmp);
	}
	if(r!=rows-1 && grid[r+1][c]!=2 && grid[r+1][c]!=1 && (s+1<dist[r+1][c] || dist[r+1][c]==-1) && sumDist[r+1][c]!=-1){
	vector<int> tmp={r+1, c, s+1};
	dist[r+1][c]=s+1;
	myQ.push(tmp);
	}
	if(c!=0 && grid[r][c-1]!=2 && grid[r][c-1]!=1 && (s+1<dist[r][c-1] || dist[r][c-1]==-1) && sumDist[r][c-1]!=-1){
	vector<int> tmp={r, c-1, s+1};
	dist[r][c-1]=s+1;
	myQ.push(tmp);
	}
	if(c!=cols-1 && grid[r][c+1]!=2 && grid[r][c+1]!=1 && (s+1<dist[r][c+1] || dist[r][c+1]==-1) && sumDist[r][c+1]!=-1){
	vector<int> tmp={r, c+1, s+1};
	dist[r][c+1]=s+1;
	myQ.push(tmp);
	}
	}
	for(int r=0; r<rows; r++){
	for(int c=0; c<cols; c++){
	if((grid[r][c]==0&&dist[r][c]==-1)||(sumDist[r][c]==-1)){
	sumDist[r][c]=-1;
	continue;
	}
	sumDist[r][c]+=dist[r][c]; }
	}
	}
	}
	int minv=INT_MAX;
	for(int i=0; i<rows; i++){
	for(int j=0; j<cols; j++){
	if(grid[i][j]!=0||sumDist[i][j]==-1)
	continue;
	minv = min(minv, sumDist[i][j]);
	}
	}
	return minv==INT_MAX? -1:minv;
	}
	};

view raw Q317.cpp hosted with ❤ by GitHub