graph - Algorithm to find the total number of connected sets in a matrix

Question

i wanted to know which algorithm should i apply here. Would a DFS do?

Given a 2–d matrix. Find the total number of connected sets in that matrix.

Connected set can be defined as group of cell(s) which has 1 mentioned on it and have at least one other cell in that set with which they share the neighbor relationship. A cell with 1 in it and no surrounding neighbor having 1 in it can be considered as a set with one cell in it. Neighbors can be defined as all the cells adjacent to the given cell in 8 possible directions (i.e. N, W, E, S, NE, NW, SE, SW direction). A cell is not a neighbor of itself.

For example:

1 0 0 1

0 0 1 0

0 0 1 0

1 0 0 1

number of connected sets is 3

0 0 1 0 0 1 0 0

1 0 0 0 0 0 0 1

0 0 1 0 0 1 0 1

0 1 0 0 0 1 0 0

1 0 0 0 0 0 0 0

0 0 1 1 0 1 1 0

1 0 1 1 0 1 1 0

0 0 0 0 0 0 0 0

number of connected set is 9.

Answer 1

I don't think you will need to think of it as a general graph problem and apply any algorithm such as BFS or DFS.

You will need to do three scans of the matrix.

scan 1:

start from the top

1. give every number each 1 with 1..n, in you example the first row would after that step would look like

   1 0 0 2

2. go to the next line and for every 1 in the row check if the neighbor to your left is non-0
   • if non-0 take on the value to the left
   • if 0 check for non-0 neighbors in the previous line and take on the value of the left most one
   • if all of those are 0 that simply add 1 to the maximum number given so far
3. repeat 2 until last line has been processed

and your example should look like follows

1 0 0 2
0 0 2 0
0 0 2 0
3 0 0 2

scan 2:

start from the bottom check if each neighbor has the same number as the left most neighbor as well as the same number as the neighbor in the row below it

basically if you have a matrix like this

1 0 2

1 0 2

0 1 0

to check ensure that a set has really the same number

scan 3:

count the number of unique non-0 entries in the matrix