6.5 6.6

6.5

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import numpy as np  
   
distances = np.array([  
    [0, 2, 7, np.inf, np.inf, np.inf],  
    [2, 0, 4, 6, 8, np.inf],           
    [7, 4, 0, 1, 3, np.inf],          
    [np.inf, 6, 1, 0, 1, 6],           
    [np.inf, 8, 3, 1, 0, 3],          
    [np.inf, np.inf, np.inf, 6, 3, 0]  
], dtype=float)  
 
students = np.array([50, 40, 60, 20, 70, 90])  
  
hospital_distances_sum = np.zeros(6)  
for i in range(6):   
    connected_distances = distances[i, :i+1].copy()  
    connected_distances = connected_distances[connected_distances != np.inf]  
    hospital_distances_sum[i] = np.sum(connected_distances)  
hospital_location = np.argmin(hospital_distances_sum)  
print(f"医院应该建在村庄 {chr(65 + hospital_location)} 处，使得最远村庄的人到医院看病所走的路最短。")  
  
school_total_distances = np.zeros(6)  
for i in range(6):  
   
    weighted_distances = 0  
    for j in range(6):  
        if distances[j, i] != np.inf:  
            weighted_distances += students[j] * distances[j, i]  
    school_total_distances[i] = weighted_distances  
  
school_location = np.argmin(school_total_distances)  
print(f"小学应该建在村庄 {chr(65 + school_location)} 处，使得所有学生上学走的总路程最短。")
 
print("学号：3010")

6.6

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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, 3), (1, 4), (1, 5),           
    (2, 0), (2, 1), (2, 3),          
    (3, 4), (3, 5),                 
    (4, 2), (4, 5),                   
    (5, 2)                           
]  
  
 
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：3010")