Matrix: Best Meeting Point - mbhushan/codique GitHub Wiki
Best Meeting Point
A group of two or more people wants to meet and minimize the total travel distance. You are given a 2D grid of values 0 or 1, where each 1 marks the home of someone in the group. The distance is calculated using Manhattan Distance, where distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|.
For example, given three people living at (0,0), (0,4), and (2,2):
1 - 0 - 0 - 0 - 1
0 - 0 - 0 - 0 - 0
0 - 0 - 1 - 0 - 0
The point (0,2) is an ideal meeting point, as the total travel distance of 2+2+2=6 is minimal. So return 6.
High Level Solution:
Find the x and y coordinates of all people in the group and get the x-axis median and y-axis median say a & b respectively. Now get the manhattan distance from each person (Xi, Yi) to (a,b) points, which will be the required min distance.
- Time Complexity: O(n^2)
- Space Complexity: O(n^2)