代码随想录算法训练营第55天 | 图论岛屿+水流

101.孤岛的总面积
https://kamacoder.com/problempage.php?pid=1173
代码随想录
https://www.programmercarl.com/kamacoder/0102.沉没孤岛.html
102.沉没孤岛
https://kamacoder.com/problempage.php?pid=1174
代码随想录
https://www.programmercarl.com/kamacoder/0102.沉没孤岛.html
103.水流问题
https://kamacoder.com/problempage.php?pid=1175
代码随想录
https://www.programmercarl.com/kamacoder/0103.水流问题.html
104.建造最大岛屿
https://www.programmercarl.com/kamacoder/0104.建造最大岛屿.html
代码随想录
https://www.programmercarl.com/kamacoder/0104.建造最大岛屿.html

101. 孤岛的总面积

• 孤岛：不和边缘相连的岛屿称为孤岛

• 将所有和边缘相连的岛屿变为平地然后统计孤岛的总面积

  深度优先搜索

  def dfs(graph,x,y):
  	direction = [[0,-1],[0,1],[1,0],[-1,0]]
  	graph[x][y] = 0
  	for dir_ in direction:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  			continue
  		if graph[nextx][nexty]==1:
  			graph[nextx][nexty]=0
  			dfs(graph,nextx,nexty)
  def main():
  	n,m = map(int,input().split())
  	graph = [[0]*m for _ in range(n)]
  	visited = [[False]*m for _ in range(n)]
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	# 将边界所有岛屿变为平地
  	for i in range(n):
  		if graph[i][0]==1:
  			dfs(graph,i,0)
  		if graph[i][m-1]==1:
  			dfs(graph,i,m-1)
  	for j in range(m):
  		if graph[0][j]==1:
  			dfs(graph,0,j)
  		if graph[n-1][j]==1:
  			dfs(graph,n-1,j)
  	#统计剩余孤岛
  	res = 0
  	for i in range(n):
  		for j in range(m):
  			if graph[i][j]==1:
  				res+=1
  	print(res)
  if __name__ == '__main__':
  	main()
  

  广度优先搜索

  def dfs(graph,x,y):
  	direction = [[0,-1],[0,1],[1,0],[-1,0]]
  	graph[x][y] = 0
  	queue = [[x,y]]
  	while queue:
  		curr = queue.pop()
  		x = curr[0]
  		y = curr[1]
  		graph[x][y] = 0
  		for dir_ in direction:
  			nextx = x+dir_[0]
  			nexty = y+dir_[1]
  			if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  				continue
  			if graph[nextx][nexty]==1:
  				graph[nextx][nexty] = 0
  				queue.append([nextx,nexty])
  

102. 沉没孤岛

• 将不是孤岛的岛变为2

• 最后处理的：2->1 1->0 0->0

  深度优先搜索

  def dfs(graph,x,y):
  	direction = [[0,-1],[0,1],[1,0],[-1,0]]
  	graph[x][y] = 2
  	for dir_ in direction:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  			continue
  		if graph[nextx][nexty]==1:
  			graph[nextx][nexty]=2
  			dfs(graph,nextx,nexty)
  

  广度优先搜索

  
  def dfs(graph,x,y):
  	direction = [[0,-1],[0,1],[1,0],[-1,0]]
  	graph[x][y] = 0
  	queue = [[x,y]]
  	while queue:
  		curr = queue.pop()
  		x = curr[0]
  		y = curr[1]
  		graph[x][y] = 2
  		for dir_ in direction:
  			nextx = x+dir_[0]
  			nexty = y+dir_[1]
  			if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  				continue
  			if graph[nextx][nexty]==1:
  				graph[nextx][nexty] = 2
  				queue.append([nextx,nexty])
  
  def main():
  	n,m = map(int,input().split())
  	graph = [[0]*m for _ in range(n)]
  	visited = [[False]*m for _ in range(n)]
  
  	for i in range(n):
  		data = input().split()
  		for j in range(m):
  			graph[i][j] = int(data[j])
  	# print(graph)
  	for i in range(n):
  		if graph[i][0]==1:
  			dfs(graph,i,0)
  		if graph[i][m-1]==1:
  			dfs(graph,i,m-1)
  
  	for j in range(m):
  		if graph[0][j]==1:
  			dfs(graph,0,j)
  		if graph[n-1][j]==1:
  			dfs(graph,n-1,j)
  
  	res = 0
  	for i in range(n):
  		for j in range(m):
  			if graph[i][j]==1:
  				graph[i][j] = 0
  			if graph[i][j] ==2:
  				graph[i][j] = 1
  
  	for i in range(n):
  		print(" ".join(map(str,graph[i])))
  
  if __name__ == '__main__':
  	main()
  

103. 水流问题

• 从两个边界开始向上找重合点；

• 最终把两个边界的重合点作为结果输出；

  点击查看代码

  def dfs(graph,x,y,bound_res):
  	directions = [[0,-1],[0,1],[1,0],[-1,0]]
  	if not bound_res[x][y]:
  		bound_res[x][y] = True
  	for dir_ in directions:
  		nextx = x+dir_[0]
  		nexty = y+dir_[1]
  		if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>=len(graph[0]):
  			continue
  		if graph[nextx][nexty]>=graph[x][y] and not bound_res[nextx][nexty]:
  			bound_res[nextx][nexty] = True
  			dfs(graph,nextx,nexty,bound_res)
  
  def main():
  	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])
  
  	bound_1 = [[False]*m for _ in range(n)]
  	bound_2 = [[False]*m for _ in range(n)]
  	for i in range(n):
  		dfs(graph,i,0,bound_1)
  		dfs(graph,i,m-1,bound_2)
  	for j in range(m):
  		dfs(graph,0,j,bound_1)
  		dfs(graph,n-1,j,bound_2)
  	for i in range(n):
  		for j in range(m):
  			if bound_1[i][j] and bound_2[i][j]:
  				print(" ".join([str(i),str(j)]))
  
  if __name__ == '__main__':
  	main()
  

104.建造最大岛屿

• 首先分别标记不同岛屿的大小、修改graph上岛屿为index；
• 分别统计水变成陆地后附近岛屿大小和；

点击查看代码

def dfs(graph,visited,x,y,mark,count):
    directions = [[0,-1],[0,1],[1,0],[-1,0]]
    for dir_ in directions:
        nextx = x+dir_[0]
        nexty = y+dir_[1]
        if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>= len(graph[0]):
            continue
        if graph[nextx][nexty]==1 and visited[nextx][nexty]==0:
            count = count+1
            visited[nextx][nexty] = 1
            graph[nextx][nexty] = mark
            count = dfs(graph,visited,nextx,nexty,mark,count)
    return count
    

def main():
    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 = [[0]*m for _ in range(n)]
    map_ = {}
    isgrid = True
    mark = 2
    for i in range(n):
        for j in range(m):
            if graph[i][j] == 0:
                isgrid = False
            if visited[i][j]==0 and graph[i][j]==1:
                count = 1
                visited[i][j] = 1
                graph[i][j] = mark
                count = dfs(graph,visited,i,j,mark,count)
                map_[mark] = count
                mark = mark+1
    # print(graph)
    if isgrid:
        print(str(n*m))
        return
    directions = [[0,-1],[0,1],[1,0],[-1,0]]
    res = 0
    # visited_grid = []
    for i in range(n):
        for j in range(m):
            count = 1
            visited_grid = []
            if graph[i][j]==0:
                for dir_ in directions:
                    nextx = i+dir_[0]
                    nexty = j+dir_[1]
                    if nextx<0 or nextx>=len(graph) or nexty<0 or nexty>= len(graph[0]):
                        continue
                    if graph[nextx][nexty] in visited_grid:
                        continue
                    if graph[nextx][nexty]>0:
                        count+= map_[graph[nextx][nexty]]
                    visited_grid.append(graph[nextx][nexty])
            res = max(res,count)
    print(str(res))
if __name__ == '__main__':
    main()