day50 第十一章：图论part01

ACM模式，自己控制输入输出

图论理论基础

连通性：

连通图（无向），强连通图（有向）----- 任意两个节点之间都可相互到达

连通分量（极大连通子图），强连通分量

图的构造：

邻接矩阵

优点：

表达简单

易于查找任意2个顶点之间的连接

适合稠密图

缺点：

n*n，不适合稀疏图

邻接表

优点：

空间利用率高

缺点：

不好搜索任意2点之间是否存在

回溯就是深度优先搜索

邻接表和邻接矩阵dfs写法上没有太大差异

深搜理论基础

98. 所有可达路径

邻接矩阵：n*n的矩阵

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

邻接表：defaultdict

from collections import defaultdict

def main():
    n, m = map(int, input().split())
    graph = defaultdict(list)
    
    for i in range(m):
        s, t = map(int, input().split())
        graph[s].append(t)
    
    result = []
    path = [1]
    dfs(graph, 1, n, path, result)
    
    if not result:
        print(-1)
    else:
        for path in result:
            print(' '.join(map(str, path)))
    
def dfs(graph, x, n, path, result):
    if x == n:
        result.append(path.copy())
        return
    for i in graph[x]:
        # if graph[x][i] == 1:
        path.append(i)
        dfs(graph, i, n, path, result)
        path.pop()
    
if __name__ == "__main__":
    main()
    

广搜理论基础