图论基础

98. 所有可达路径

result = []
path = []
def dfs(graph,x,n):
    if x == n:
        result.append(path[:])
        return
    for i in range(1,n+1):
        if graph[x][i] == 1:
            path.append(i)
            dfs(graph,i,n)
            path.pop()
def main():
    n,m = map(int,input().split())
    # 邻接矩阵
    graph = [[0]*(n+1) for _ in range(n+1)]
    for _ in range(m):
        s,t = map(int,input().split())
        graph[s][t] = 1
    path.append(1)
    dfs(graph,1,n)
    if len(result) == 0:
        print(-1)
    for x in result:
        print(' '.join(map(str,x)))
if __name__ == "__main__":
    main()
        

岛屿问题

200. 岛屿数量

class Solution:
    def numIslands(self, grid: List[List[str]]) -> int:
        res = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == "1":
                    res += 1
                    self.dfs(grid,i,j)
        return res
    
    def dfs(self,grid,x,y):
        # 判断(x,y)是否在网格范围内
        if not (x >= 0 and y >=0 and x <len(grid) and y<len(grid[0])):
            return
        if grid[x][y] != "1": # 海洋格子以及遍历过的陆地格子直接返回
            return 
        grid[x][y] = "2"
        self.dfs(grid,x-1,y) # 上
        self.dfs(grid,x+1,y) # 下
        self.dfs(grid,x,y-1) # 左
        self.dfs(grid,x,y+1) # 右

695. 岛屿的最大面积

class Solution:
    def dfs(self,grid,x,y,i):
        if not (x >= 0 and x < len(grid) and y >= 0 and y < len(grid[0])):
            return 0
        if grid[x][y] == 0:
            return 0
        grid[x][y] = i
        s1 = self.dfs(grid,x-1,y,i)
        s2 = self.dfs(grid,x+1,y,i)
        s3 = self.dfs(grid,x,y-1,i)
        s4 = self.dfs(grid,x,y+1,i)
        return 1 + s1 + s2 + s3 + s4

    def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
        maxarea = 0
        num = 2
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    res = self.dfs(grid,i,j,num)
                    maxarea = max(maxarea,res)
                    num += 1
        return maxarea

827. 最大人工岛

class Solution:
    def dfs(self,grid,x,y,i):
        if not (x >= 0 and x < len(grid) and y >= 0 and y < len(grid[0])):
            return 0
        # grid == 0 : 海洋 grid == 1 : 陆地但没被遍历过 grid == i 陆地但遍历过
        if grid[x][y] != 1:
            return 0
        grid[x][y] = i 
        s1 = self.dfs(grid,x-1,y,i)
        s2 = self.dfs(grid,x+1,y,i)
        s3 = self.dfs(grid,x,y-1,i)
        s4 = self.dfs(grid,x,y+1,i)
        return 1 + s1 + s2 + s3 + s4
    
    def dfs2(self,grid,x,y,island_area):
        if not (x >= 0 and x < len(grid) and y >= 0 and y < len(grid[0])):
            return 0
        # grid == 0 : 海洋（没被遍历） grid == 1 : 海洋（被遍历） grid == i 陆地面积
        if grid[x][y] == 1:
            return 0
        if grid[x][y] != 0:
            return island_area[grid[x][y]]
        grid[x][y] = 1
        s1 = self.dfs2(grid,x-1,y,island_area)
        s2 = self.dfs2(grid,x+1,y,island_area)
        s3 = self.dfs2(grid,x,y-1,island_area)
        s4 = self.dfs2(grid,x,y+1,island_area)
        s = set(grid[x-1][y],grid[x+1][y],grid[x][y-1],grid[x][y+1])


        return s1 + s2 + s3 + s4


    def largestIsland(self, grid: List[List[int]]) -> int:
        island_area = {}
        num = 2
        res = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1:
                    area = self.dfs(grid,i,j,num)
                    island_area[num] = area
                    num += 1
        print(grid)
        print(island_area)
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 0:
                    sea_area = self.dfs2(grid,i,j,island_area)
                    res = max(res,1+sea_area)
        return res