In 2D binary matrix find the number of islands
I am trying to count the number of islands (a group of connected 1s forms an island) in a 2D binary matrix.
Example:
[
[1, 1, 0, 0, 0],
[0, 1, 0, 0, 1],
[1, 0, 0, 1, 1],
[0, 0, 0, 0, 0],
[1, 0, 1, 0, 1]
]
In the above matrix there are 5 islands, which are:
First: (0,0), (0,1), (1,1), (2,0)
Second: (1,4), (2,3), (2,4)
Third: (4,0)
Fourth: (4,2)
Fifth: (4,4)
To count the number of island in the 2D matrix, I am assuming the matrix as a Graph and then I am using DFS kind of algorithm to count the islands.
I am keeping track for the number of DFS (a recursive function) calls, because that many components would be there in the Graph.
Below is the code I wrote for this purpose:
# count the 1's in the island
def count_houses(mat, visited, i, j):
# base case
if i < 0 or i >= len(mat) or j < 0 or j >= len(mat[0]) or\
visited[i][j] is True or mat[i][j] == 0:
return 0
# marking visited at i, j
visited[i][j] = True
# cnt is initialized to 1 coz 1 is found
cnt = 1
# now go in all possible directions (i.e. form 8 branches)
# starting from the left upper corner of i,j and going down to right bottom
# corner of i,j
for r in xrange(i1, i+2, 1):
for c in xrange(j1, j+2, 1):
# print 'r:', r
# print 'c:', c
# don't call for i, j
if r != i and c != j:
cnt += count_houses(mat, visited, r, c)
return cnt
def island_count(mat):
houses = list()
clusters = 0
row = len(mat)
col = len(mat[0])
# initialize the visited matrix
visited = [[False for i in xrange(col)] for j in xrange(row)]
# run over matrix, search for 1 and then do dfs when found 1
for i in xrange(row):
for j in xrange(col):
# see if value at i, j is 1 in mat and val at i, j is False in
# visited
if mat[i][j] == 1 and visited[i][j] is False:
clusters += 1
h = count_houses(mat, visited, i, j)
houses.append(h)
print 'clusters:', clusters
return houses
if __name__ == '__main__':
mat = [
[1, 1, 0, 0, 0],
[0, 1, 0, 0, 1],
[1, 0, 0, 1, 1],
[0, 0, 0, 0, 0],
[1, 0, 1, 0, 1]
]
houses = island_count(mat)
print houses
# print 'maximum houses:', max(houses)
I get a wrong output for the matrix I have passed in argument. I get 7
but there are 5
clusters.
I tried debugging the code for any logical errors. But I couldn't find out where is the problem.
2 answers

big hammer approach, for reference
had to add
structure
argumentnp.ones((3,3))
to add diagonal connectivityimport numpy as np from scipy import ndimage ary = np.array([ [1, 1, 0, 0, 0], [0, 1, 0, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 0], [1, 0, 1, 0, 1] ]) labeled_array, num_features = ndimage.label(ary, np.ones((3,3))) labeled_array, num_features Out[183]: (array([[1, 1, 0, 0, 0], [0, 1, 0, 0, 2], [1, 0, 0, 2, 2], [0, 0, 0, 0, 0], [3, 0, 4, 0, 5]]), 5)

Your algorithm is almost correct except for the line 21:
if r != i and c != j: cnt += count_houses(mat, visited, r, c)
Instead you want to use
or
as you want to continue counting provided at least one of the coordinate is not the same as your center.if r != i or c != j: cnt += count_houses(mat, visited, r, c)
An alternate and more intuitive way to write this would be the following
if (r, c) != (i, j): cnt += count_houses(mat, visited, r, c)