6.5 已知有6个村子，相互间道路的距离如图所示，拟合建一所小学，现计划建造一所医院和一所小学，问医院应该建在哪个村庄才能使得最远村庄的人到医院看病所走的路最短？小学应该建在哪个村庄使得所有学生上学走

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：3004")