296. Best meeting Point

A Group of people wants to meet and minimize the total travel distance. You is 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 a ideal meeting point, as the all travel distance of 2+2+2=6 is minimal. So return 6.

Solution 1. Median in Math. Collect coordinates in sorted order.

1  Public classSolution {2      Public intMintotaldistance (int[] grid) {3             intm = grid.length, n = grid[0].length;4         intTotal = 0, z[] =New int[m*n];5          for(intdim=0; dim<2; ++Dim) {6             inti = 0, j = 0;7             if(Dim = = 0) {8                  for(intx=0; x<n; ++x)9                      for(inty=0; y<m; ++y)Ten                         if(Grid[y][x] = = 1) OneZ[j++] =x; A}Else { -                  for(inty=0; y<m; ++y) -                      for(intG:grid[y]) the                         if(g = = 1) -Z[j++] =y; -             } -              while(I <--j) +Total + = Z[j]-z[i++]; -         } +         returnTotal ; A     } at}

Solution 2. Count How many people live with each row and each column. Only O (m+n) space.

1  Public classSolution {2      Public intMintotaldistance (int[] grid) {3         intm = grid.length, n = grid[0].length;4         int[] I =New int[M], J =New int[n];5          for(inti=0; i<m; ++i)6              for(intj=0; j<n; ++j)7                 if(Grid[i][j] = = 1) {8++I[i];9++J[j];Ten                 } One          A         intTotal = 0; -          for(int[] K:New int[][]{I, J}] { -             inti = 0, j = k.length-1; the              while(I <j) { -                 intK =math.min (K[i], k[j]); -Total + = k * (J-i); -                 if((k[i]-= K) = = 0) + +i; +                 if((k[j]-= K) = = 0)--J; -             } +         } A         returnTotal ; at     } -}

296. Best meeting Point