代码随想录算法训练营第53天 | 图论2：岛屿数量相关问题

99.岛屿数量
https://kamacoder.com/problempage.php?pid=1171
岛屿深搜
https://www.programmercarl.com/kamacoder/0099.岛屿的数量深搜.html
岛屿广搜
https://www.programmercarl.com/kamacoder/0099.岛屿的数量广搜.html#思路
100.岛屿的最大面积
https://www.programmercarl.com/kamacoder/0100.岛屿的最大面积.html
代码随想录
https://www.programmercarl.com/kamacoder/0100.岛屿的最大面积.html

岛屿数量

岛屿深搜

• 两种写法：可以把终止条件写在前面 也可以写在循环内；

  • 区别：把判断条件写在main函数或写在dfs函数中

• 采用递归

  深搜方法1：停止条件在主函数中

  def dfs(graph,visited,x,y,count):
  	directions = [[0,-1],[0,1],[1,0],[-1,0]]
  	for dir_ in directions:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nexty<0 or nexty>=len(graph[0]) or nextx<0 or nextx>=len(graph):
  			continue
  		if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
  			visited[nextx][nexty] = 1 ##执行访问
  			dfs(graph,visited,nextx,nexty,count)
  def main():
  	## 初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	visited = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	#分别统计
  	count = 0
  	for i in range(n):
  		for j in range(m):
  			##停止条件
  			if graph[i][j]==1 and visited[i][j]==0:
  				count+=1
  				dfs(graph,visited,i,j,count)
  	print(count)
  if __name__ == '__main__':
  	main()
  

  深搜方法2：停止条件在递归函数中

  def dfs(graph,visited,x,y):
  	if visited[x][y] or graph[x][y]==0:
  		return
  	visited[x][y] = True
  	dirs = [[0,-1],[0,1],[1,0],[-1,0]]
  	for i in range(4):
  		nextx = x+dirs[i][0]
  		nexty = y+dirs[i][1]
  		if (nextx)<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  			continue
  		dfs(graph,visited,nextx,nexty)
  def main():
  	##初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	visited = [[False]*(m) for _ in range(n)]
  	##递归计数
  	count = 0
  	for i in range(n):
  		for  j in range(m):
  			if not visited[i][j] and graph[i][j]==1:
  				count+=1
  				dfs(graph,visited,i,j)
  	print(count)
  if __name__ == '__main__':
  	main()
  

岛屿广搜

• 不需要递归

• 加入队列即为访问过了

  广度搜索代码

  def dfs(graph,visited,x,y,count):
  	directions = [[0,-1],[0,1],[1,0],[-1,0]]
  	queue = [[x,y]]
  	while queue:
  		curr = queue.pop()
  		x = curr[0]
  		y = curr[1]
  		visited[x][y] = 1
  		for dir_ in directions:
  			nextx = x+dir_[0]
  			nexty = y+dir_[1]
  			if nexty<0 or nexty>=len(graph[0]) or nextx<0 or nextx>=len(graph):
  				continue
  			if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
  				visited[nextx][nexty] = 1
  				dfs(graph,visited,nextx,nexty,count)
  
  def main():
  	## 初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	visited = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  
  	#分别统计
  	count = 0
  	for i in range(n):
  		for j in range(m):
  			if graph[i][j]==1 and visited[i][j]==0:
  				count+=1
  				dfs(graph,visited,i,j,count)
  	print(count)
  

岛屿最大面积

• 和岛屿广搜一样的

  深度优先搜索1

  def dfs(graph,visited,x,y):
  	if graph[x][y]==0 or visited[x][y]==1:
  		return 0
  	count = 1
  	visited[x][y] = 1
  	directions = [[0,1],[0,-1],[1,0],[-1,0]]
  	for dir_ in directions:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nexty<0 or nexty>=len(graph[0]) or nextx<0 or nextx>=len(graph):
  			continue
  		if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
  			count += dfs(graph,visited,nextx,nexty)
  	return count
  def main():
  	## 初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	visited = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	#分别统计
  	res = 0
  	for i in range(n):
  		for j in range(m):
  			##停止条件
  			if graph[i][j]==1 and visited[i][j]==0:
  			 #   visited[i][j] = 1
  			 #   count = 0
  				count = dfs(graph,visited,i,j)
  				res = max(res,count)
  	print(res)
  
  if __name__ == '__main__':
  	main()
  

  深度优先搜索2

  def dfs(graph,visited,x,y,count):
  	directions = [[0,1],[0,-1],[1,0],[-1,0]]
  	for dir_ in directions:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nexty<0 or nexty>=len(graph[0]) or nextx<0 or nextx>=len(graph):
  			continue
  		if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
  			visited[nextx][nexty] = 1 ##执行访
  			count+=1
  			count = dfs(graph,visited,nextx,nexty,count)
  	return count
  
  def main():
  	## 初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	visited = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	#分别统计
  	res = 0
  	for i in range(n):
  		for j in range(m):
  			##停止条件
  			if graph[i][j]==1 and visited[i][j]==0:
  				visited[i][j] = 1
  				count = 1
  				count = dfs(graph,visited,i,j,count)
  				res = max(res,count)
  	print(res)
  
  if __name__ == '__main__':
  	main()
  

  广度优先搜索

  def dfs(graph,visited,x,y):
  	queue = [[x,y]]
  	directions = [[0,1],[0,-1],[1,0],[-1,0]]
  	count = 1
  	visited[x][y] = 1
  	while queue:
  		curr = queue.pop()
  		x = curr[0]
  		y = curr[1]
  		for dir_ in directions:
  			nextx = x+dir_[0]
  			nexty = y+dir_[1]
  			if nexty<0 or nexty>=len(graph[0]) or nextx<0 or nextx>=len(graph):
  				continue
  			if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
  				visited[nextx][nexty]=1
  				count+=1
  				queue.append([nextx,nexty])
  	return count
  
  def main():
  	## 初始化
  	n,m = map(int,input().split())
  	graph = [[0]*(m) for _ in range(n)]
  	visited = [[0]*(m) for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	#分别统计
  	res = 0 
  	for i in range(n):
  		for j in range(m):
  			##停止条件
  			if graph[i][j]==1 and visited[i][j]==0:
  				count = dfs(graph,visited,i,j)
  				res = max(res,count)
  	print(res)
  
  if __name__ == '__main__':
  	main()