I'm really struggling to solve problem #5 from the South African Programming Olympiad 2007. please help by sharing an approach, algorithm or program.

Q5. Rooms

Proposed & Prepared by Marco Gallotta

Description

Fred the manic store-keeper can't keep up with the growing size of his store. He wants to know how many rooms he has and the size of the smallest and largest ones. However, his store is too large for him to work out on his own, so he has asked for your help.

Task

Fred has given you the plans of his store. In the plans, a wall is represented by a '1' and a floor tile by a '0'. Your task is to write a program to group neighbouring floor tiles into rooms. A tile can be grouped together with all tiles one space directly to its left, right, top and bottom. Note that this does *not* include diagonals. A room is defined as a group of floor tiles that cannot be grouped together with any further floor tiles.

Given the plans your task is to work out:

- The total number of rooms
- The size of the smallest room
- The size of the largest room.

Constraints

1 <= width, height <= 20.

Sample run

Input:

Enter width: 3

Enter height: 2

Enter row: 001

Enter row: 010

Output:

Number of rooms: 2

Smallest room: 1

Largest room: 3

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## Comments

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TopNewestPerhaps you could reduce this to a graph theory problem. Make an adjacency matrix where each zero in the original data corresponds to a row and column, with 1's in entries corresponding to adjacent zeroes (you could do this in one pass through the given data). Perform matrix operations to order the adjacency matrix into connected components. Each component is one room, and then you just have to pass through the components to find the smallest and largest.

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I am not sure I understand.

Also, the adjacency matrix takes up a lot of space.

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Another example to ensure that you fully understand the problem:

Suppose the plan looks like this:

Number of rooms: 3

Smallest room: 2

Largest room:4

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