Tips on finding the volume of water in a 3d chess board

Question

So I have an assignment where I have to recreate a 3d chessboard that is a RxC grid of squares each being a different height. If the chessboard is water tight, and someone pours

Answer 1

This is python(2.7) version of the pseudocode by @paddy .Hope this will help someone .

import heapq
block =[
1, 2, 3,
4 ,2,6,
7, 0,5,
11,15, 13,
14,15,16,
1,0,1,
1,1,1]
cmax =3; 
rmax =7;
items =[]
fence = []
flood = []
waterlevel = 0
total = 0
class Item(object):
    visited = False
    fenced = False
    flooding = False
    height= 0
    index = 0
i=0
## initializing blocks
for val in block:    
    item =  Item();
    item.height = val
    item.index = i
    i+=1
    items.append((item.height,item))
## find out the edges  
for i in range (cmax):
    heapq.heappush(fence, items[i])
    heapq.heappush(fence, items[i+(rmax-1)*cmax])
    print items[i][1].height,items[i+(rmax-1)*cmax][1].height

for i in range(1,rmax-1):
    heapq.heappush(fence, items[cmax*i])
    heapq.heappush(fence, items[cmax*i+(cmax-1)])
    print items[cmax*i][1].height,items[cmax*i+(cmax-1)][1].height

## get neighbour
def get_neighbour(i):
    c= i%cmax
    r= i//cmax
    neighbour = []
    if (c != 0):
        neighbour.append(items[r*cmax+c-1])
    if (c != (cmax -1)):
        neighbour.append(items[r*cmax+c+1])
    if (r != 0):
        neighbour.append(items[(r-1)*cmax+c])
    if (r != (rmax -1)):    
        neighbour.append(items[(r+1)*cmax+c])
    return neighbour



while (len(fence)>0):
    item = heapq.heappop(fence)
    if(item[1].visited):
        continue
    if (item[1].height > waterlevel):
        waterlevel = item[1].height
    heapq.heappush(flood,item)
    item[1].flooding = True
    while(len(flood)>0):
        fitem = heapq.heappop(flood)
        depth = waterlevel - fitem[1].height
        if (depth >= 0):
            total += depth
            fitem[1].visited = True
            neighbour = get_neighbour(fitem[1].index)
            for nitem in neighbour:
                if nitem[1].visited == False :
                    if nitem[1].flooding == False :
                        heapq.heappush(flood,nitem)
                        nitem[1].flooding = True
        else:
            fitem[1].flooding = False
            if fitem[1].fenced == False:
                heapq.heappush(fence,fitem)
                fitem[1].fenced = True
print total