6.6 1队战胜了2、4、5、6队，输给了3队；2队战胜了4、5、6队，输给了1、3队；3队战胜了1、2、4队，输给了5、6队；4队战胜了5、6队，输给了1、2、3队；5队战胜了3、6队，输给了1、2、4队；6队战胜了3队，输给了1、2、4、5队。（1）利用竞赛图的适当方法，给出6支球队的一个排名顺序，（2）利用pagerank算法，再次给出6支球队的排名顺序

点击查看代码

import numpy as np  
  
matches = np.array([  
    [0, 1, 0, 1, 1, 1],  # 1队  
    [0, 0, 0, 1, 1, 1],  # 2队  
    [1, 1, 0, 1, 0, 0],  # 3队  
    [0, 0, 0, 0, 1, 1],  # 4队  
    [0, 0, 1, 0, 0, 1],  # 5队  
    [0, 0, 1, 0, 0, 0]   # 6队  
], dtype=int)  
  
n = matches.shape[0]  
closure = matches.copy()  
for k in range(n):  
    for i in range(n):  
        for j in range(n):  
            closure[i, j] = closure[i, j] or (closure[i, k] and closure[k, j])  
  
strength = closure.sum(axis=1)  
   
ranking = np.argsort(-strength) 
  
for i, rank in enumerate(ranking):  
    print(f"{chr(65 + rank)}队 排名 {i + 1}")
    
    
import numpy as np  
from scipy.sparse import csr_matrix  
  
edges = [  
    (0, 1), (0, 3), (0, 4), (0, 5),  # 1队胜  
    (1, 3), (1, 4), (1, 5),          # 2队胜  
    (2, 0), (2, 1), (2, 3),          # 3队胜  
    (3, 4), (3, 5),                  # 4队胜  
    (4, 2), (4, 5),                  # 5队胜  
    (5, 2)                           # 6队胜  
]  
  

num_teams = 6  
  

row_ind = []  
col_ind = []  
data = []  
for u, v in edges:  
    row_ind.append(u)  
    col_ind.append(v)  
    data.append(1)  
adj_matrix = csr_matrix((data, (row_ind, col_ind)), shape=(num_teams, num_teams))  
  

adj_matrix_T = adj_matrix.T  
  

d = 0.85  
out_degree = np.array(adj_matrix_T.sum(axis=1)).flatten()  
out_degree[out_degree == 0] = 1  
M = adj_matrix_T.multiply(1.0 / out_degree).tocsr()  
M = M + (1 - d) / num_teams * csr_matrix(np.ones((num_teams, num_teams)))  
  

R = np.ones(num_teams) / num_teams  
  

num_iterations = 100  
for _ in range(num_iterations):  
    R = R.dot(M.toarray())  
  

pagerank_ranking = np.argsort(-R) 
  

for i, rank in enumerate(pagerank_ranking):  
    print(f"{chr(65 + rank)}队 PageRank排名 {i + 1}")

print("学号：3004")