Trapping Rain Water II

In two dimensions, a cell's water level is controlled by the lowest escape path to the boundary, so process the terrain from outside inward. Put all boundary cells in a min-heap and mark them visited. Repeatedly pop the lowest current boundary cell. For each unvisited neighbor, any water trapped there is max(0, boundaryHeight-neighborHeight); then push it with effective height max(boundaryHeight, neighborHeight). That effective height is the crucial flood level carried forward. Each cell enters the heap once, giving O(mn log(mn)) time and O(mn) space. Reject grids with fewer than three rows or columns because they cannot enclose water. Test a central basin, several basins connected by a low channel, and equal-height plateaus.