深度优先遍历解决连通域求解问题-python实现

问题描述

在一个矩形网格中每一个格子的颜色或者为白色或者为黑色。任意或上、或下、或左、或右相邻同为黑色的格子组成一个家族。家族中所有格子的数量反映家族的大小。要求找出最大家族的家族大小（组成最大家族的格子的数量）并统计出哪些点属于哪一族。例如下图中最大家族的格子数量为 8。

求解思路

遍历矩形网格，找到一个没有被标记的黑块作为入口进行上下左右的搜索并不断的扩散，每找到一个就进行族标记，最后输出相应的族标记即可，使用深度优先算法来做搜索比较简单。

代码实现

#!/usr/bin/python
#encoding=utf8

table = [[0,0,1,0,1,1,1,0],
        [0,0,1,0,0,1,1,0],
        [0,1,1,0,1,1,1,0],
        [0,0,1,0,1,0,0,0],
        [0,0,0,0,0,1,1,0],
        [0,0,0,0,1,1,1,0]]

rows = len(table)
cols = len(table[0])

label_table = []
for i in range(rows):
    col = cols*[0]
    label_table.append(col)

def show(table):
    rows = len(table)
    cols = len(table[0])
    for i in range(rows):
        for j in range(cols):
            print(table[i][j], end=" ")
        print()

def dfs(i, j, mask):
    if i<0 or i>=rows or j<0 or j>=cols or 
        label_table[i][j]!=0 or 
        table[i][j]!=1:
        return 0
    label_table[i][j] = mask
    ret = 1
    #left right up down search
    ret+=dfs(i, j-1, mask)
    ret+=dfs(i, j+1, mask)
    ret+=dfs(i-1, j, mask)
    ret+=dfs(i+1, j, mask)

    return ret
    
if __name__ == "__main__":
    print("original table:")
    show(table)
    res={}
    print("++++++++++++++++++++")
    print("label table")
    mask = 1
    for i in range(rows):
        for j in range(cols):
            if table[i][j] == 1 and label_table[i][j] == 0:
                ret = dfs(i,j, mask)
                res[mask] = ret
                mask+=1
               
    show(label_table)
    print("++++++++++++++++++++")
    print("results:")
    
    sorted_res = [(k, res[k]) for k in sorted(res, key=res.get, reverse=True)]
    max_grp = sorted_res[0][0]
    print("max group num: %d"%sorted_res[0][1])

    for i in range(rows):
        for j in range(cols):
            if label_table[i][j] == max_grp:
                print("point (%d, %d) belongs to max group: %d"%(i,j,max_grp))


#output
# original table:
# 0 0 1 0 1 1 1 0
# 0 0 1 0 0 1 1 0
# 0 1 1 0 1 1 1 0
# 0 0 1 0 1 0 0 0
# 0 0 0 0 0 1 1 0
# 0 0 0 0 1 1 1 0
# ++++++++++++++++++++
# label table
# 0 0 1 0 2 2 2 0
# 0 0 1 0 0 2 2 0
# 0 1 1 0 2 2 2 0
# 0 0 1 0 2 0 0 0
# 0 0 0 0 0 3 3 0
# 0 0 0 0 3 3 3 0
# ++++++++++++++++++++
# results:
# max group num: 9
# point (0, 4) belongs to max group: 2
# point (0, 5) belongs to max group: 2
# point (0, 6) belongs to max group: 2
# point (1, 5) belongs to max group: 2
# point (1, 6) belongs to max group: 2
# point (2, 4) belongs to max group: 2
# point (2, 5) belongs to max group: 2
# point (2, 6) belongs to max group: 2
# point (3, 4) belongs to max group: 2