Problem
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|.
ExampleGiven 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.
Solutionpublic class Solution { /** * @param grid: a 2D grid * @return: the minimize travel distance */ public int minTotalDistance(int[][] grid) { // Write your code here Listx = new ArrayList<>(); List y = new ArrayList<>(); for (int i = 0; i < grid.length; i++) { for (int j = 0; j < grid[0].length; j++) { if (grid[i][j] == 1) { x.add(i); y.add(j); } } } return getMD(x) + getMD(y); } public int getMD(List nums) { // zhong dian is here Collections.sort(nums); int i = 0, j = nums.size()-1; int distance = 0; while (i < j) { distance += nums.get(j--) - nums.get(i++); } return distance; } }
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