在2D二进制矩阵中找到孤岛的数量 [英] In 2D binary matrix find the number of islands
问题描述
我正在尝试计算2D二进制矩阵中的孤岛(一组相连的1组成一个孤岛)的数量.
I am trying to count the number of islands (a group of connected 1s forms an island) in a 2D binary matrix.
示例:
[
[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]
]
在上面的矩阵中,有5个岛,分别是:
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)
要计算2D矩阵中的孤岛数量,我假设矩阵为图,然后使用DFS类型的算法对孤岛进行计数.
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.
我一直在跟踪DFS(递归函数)调用的次数,因为在图中有很多组件.
I am keeping track for the number of DFS (a recursive function) calls, because that many components would be there in the Graph.
下面是我为此目的编写的代码:
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(i-1, i+2, 1):
for c in xrange(j-1, 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)
我传入参数的矩阵输出错误.我得到7
,但是有5
个群集.
I get a wrong output for the matrix I have passed in argument. I get 7
but there are 5
clusters.
我尝试调试任何逻辑错误的代码.但是我找不到问题所在.
I tried debugging the code for any logical errors. But I couldn't find out where is the problem.
推荐答案
除了第21行之外,您的算法几乎是正确的:
Your algorithm is almost correct except for the line 21:
if r != i and c != j:
cnt += count_houses(mat, visited, r, c)
相反,您要使用or
来继续计数,前提是至少有一个坐标与中心不同.
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)
下面是另一种更直观的书写方式
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)
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