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Rohit Agrawal
Rohit Agrawal

Reputation: 161

SPOJ WATER : Developing a BFS algorithm

I am attempting to solve the following question from SPOJ :

On a rectangular mesh comprising nm fields, nm cuboids were put, one cuboid on each field. A base of each cuboid covers one field and its surface equals to one square inch. Cuboids on adjacent fields adhere one to another so close that there are no gaps between them. A heavy rain pelted on a construction so that in some areas puddles of water appeared.

Task

Write a program which:

  • reads from the standard input a size of the chessboard and heights of cuboids put on the fields
  • computes maximal water volume, which may gather in puddles after the rain
  • writes results in the standard output.

Input

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case two positive integers 1 <= n <= 100, 1 <= m <= 100 are written. They are the size of the mesh. In each of the following n lines there are m integers from the interval [1..10000]; i-th number in j-th line denotes a height of a cuboid given in inches put on the field in the i-th column and j-th raw of the chessboard.

Output

Your program should write for each tes case one integer equal to the maximal volume of water (given in cubic inches), which may gather in puddles on the construction. 

Example

Sample input:
1
3 6
3 3 4 4 4 2
3 1 3 2 1 4
7 3 1 6 4 1

Sample output:
5

I am using a BFS to add how much water will flow from the border elements into the puddle(if theres any path found). But I am unable to handle cases where a puddle maybe like two consecutive cuboids. Can anyone help me with that case?

Upvotes: 1

Views: 3473

Answers (1)

GBrean Nguyen
GBrean Nguyen

Reputation: 21

Here is my answer for the problem. For speaking convenience, I assume the index start from (1,1) to (M,N)

As you can imagine as the flow of water, the water can only travel from the higher cuboid to the lower cuboid ( there is no revert direction i.e. the water from lower cuboid will hit the wall of higher cuboid and stop there).

So we build the graph G = (V,E) such that V are M x N vertices i.e. the cuboid on the matrix. The edge are connected (1-way ONLY) that connected cuboid i(th) to cuboid j(th) when height(i) >= height(j) and (i and j are physically CONNECTED)

So the problem are just a simple BFS.

By the way, I found another one solve this problem as well. Please take a look

http://www.spojsolutions.com/212-water-among-cubes/

Upvotes: 2

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