算法：图论（一）邻接矩阵、邻接表

图类型的格式规定：Textual Presentation of Graph Object

1. U：undirected 无向图
2. D：directed 有向图
3. W：weighted 有权重的

示例：（无向无权重图）

U 4
1 3
0 2
1 0

该图的邻接矩阵表现形式：

该图的邻接表表现形式：

输入样例：

graph_string = """\
U 17
1 2
1 15
1 6
12 13
2 15
13 4
4 5
"""

1.将上述字符串转换为邻接矩阵

from math import inf
def adjacent_matrix(graph_str):
    lis = graph_str.split('\n')
    lis.pop()
    info = lis[0].split()#info[0]表示图的类型 info[1]表示点的个数
    n = int(info[1])
    ans = [[inf for i in range(n)] for j in range(n)]
    if len(info) == 2:   #无权重的图
        if info[0] == 'D':   #有向图
            for i in range(1, len(lis)):
                start, end = map(lambda x:int(x), lis[i].split())
                ans[start][end] = 1
        elif info[0] == 'U': #无向图
            for i in range(1, len(lis)):
                start, end = map(lambda x:int(x), lis[i].split())
                ans[start][end] = 1
                ans[end][start] = 1
    elif len(info) == 3: #有权重的图
        if info[0] == 'D':   #有向图
            for i in range(1, len(lis)):
                start, end, weight = map(lambda x:int(x), lis[i].split())
                ans[start][end] = weight
        elif info[0] == 'U': #无向图
            for i in range(1, len(lis)):
                start, end, weight= map(lambda x:int(x), lis[i].split())
                ans[start][end] = weight
                ans[end][start] = weight
    return ans

2. 将上述字符串转换为邻接表

def adjacency_list(graph_str):
    lis = graph_str.split('\n')
    lis.pop()
    info = lis[0].split()
    #info[0]表示图的类型 info[1]表示点的个数
    ans = [[] for i in range(int(info[1]))]
    if len(info) == 2:   #无权重的图
        if info[0] == 'D':   #有向图
            for i in range(1, len(lis)):
                start, end = map(lambda x:int(x), lis[i].split())
                tup = (end, None)
                ans[start].append(tup)
        elif info[0] == 'U': #无向图
            for i in range(1, len(lis)):
                start, end = map(lambda x:int(x), lis[i].split())
                tup1 = (end, None)
                tup2 = (start, None)
                ans[start].append(tup1)
                ans[end].append(tup2)
    elif len(info) == 3: #有权重的图
        if info[0] == 'D':   #有向图
            for i in range(1, len(lis)):
                start, end, weight = map(lambda x:int(x), lis[i].split())
                tup = (end, weight)
                ans[start].append(tup)
        elif info[0] == 'U': #无向图
            for i in range(1, len(lis)):
                start, end, weight= map(lambda x:int(x), lis[i].split())
                tup1 = (end, weight)
                tup2 = (start, weight)
                ans[start].append(tup1)
                ans[end].append(tup2)
    return ans

3. 从邻接表转换为矩阵

def adjacent_list_to_matrix(adj_list):
    n = len(adj_list)
    ans = [[inf for i in range(n)] for j in range(n)]
    for i, edges in enumerate(adj_list):
        ans[i][i] = 0
        for edge in edges:
            end = edge[0]
            weight = edge[1]
            ans[i][end] = weight
    return ans