算法导论 第三版 9.3-8

 1 # -*- coding: utf-8 -*-
 2 import math
 3 
 4 def merge(l1, l2):
 5     list_merge = []
 6     i = j = 0
 7     while i < len(l1) and j < len(l2):
 8         if l1[i] < l2[j]:
 9             list_merge.append(l1[i])
10             i += 1
11         else:
12             list_merge.append(l2[j])
13             j += 1
14     if i == len(l1):
15         while j < len(l2):
16             list_merge.append(l2[j])
17             j += 1
18     else:
19         while i < len(l1):
20             list_merge.append(l1[i])
21             i += 1
22     return list_merge
23 
24 def problem_9_3_8(list1, list2, l1, r1, l2, r2):
25     if l1 == r1:
26         if list1[l1] < list2[l2]:
27             return list1[l1], list2[l2]
28         else:
29             return list2[l2], list1[l1]
30 
31     if (r1 - l1 + 1) % 2:  # 每个数组中元素是奇数，分别只有一个中位数
32         l1_m = (r1 + l1) // 2
33         l2_m = (r2 + l2) // 2
34         if list1[l1_m] < list2[l2_m]:
35             return problem_9_3_8(list1, list2, l1_m, r1, l2, l2_m)
36         elif list1[l1_m] > list2[l2_m]:
37             return problem_9_3_8(list1, list2, l1, l1_m, l2_m, r2)
38         else:
39             return list1[l1_m], list2[l2_m]
40     else :                  # 每个数组中元素是偶数，则分别有两个中位数  此时有C(3,1)+C(3,2) = 6种情况
41         l1_m1 = math.floor((r1 + l1) / 2)
42         l1_m2 = math.ceil((r1 + l1) / 2)
43 
44         l2_m1 = math.floor((r2 + l2) / 2)
45         l2_m2 = math.ceil((r2 + l2) / 2)
46 
47         if (list1[l1_m2] <= list2[l2_m1]) :   # L1下 <= L1上 <= L2下 <= L2上
48             return problem_9_3_8(list1, list2, l1_m2, r1, l2, l2_m1)
49         elif list2[l2_m2] <= list1[l1_m1]:   # L2下 <= L2上 <= L1下 <= L1上
50             return problem_9_3_8(list1, list2, l1, l1_m1, l2_m2, r2)
51         elif (list1[l1_m1] <= list2[l2_m1]) and (list2[l2_m1] <= list1[l1_m2]) and (list1[l1_m2] <= list2[l2_m2]): # L1下 <= L2下 <= L1上 <= L2上
52             return list2[l2_m1], list1[l1_m2]
53         elif (list2[l2_m1] <= list1[l1_m1]) and (list1[l1_m1] <= list2[l2_m2]) and (list2[l2_m2] <= list1[l1_m2]): # L2下 <= L1下 <= L2上 <= L1上
54             return list1[l1_m1], list2[l2_m2]
55         elif (list2[l2_m1] <= list1[l1_m1]) and (list1[l1_m2] <= list2[l2_m2]): # L2下 <= L1下 <= L1上 <= L2上
56             return list1[l1_m1], list1[l1_m2]
57         else: # (list1[l1_m1] <= list2[l2_m1]) and (list2[l2_m2] <= list1[l1_m2]): # L1下 <= L2下 <= L2上 <= L1上
58             return list2[l2_m1], list2[l2_m2]
59 
60 
61 list1 = [i*11 for i in range(300)]
62 list2 = [i*7 for i in range(300)]
63 
64 list4 = merge(list1, list2)
65 print(list4)
66 print(list4[math.floor((len(list4)-1)/2)], list4[math.ceil((len(list4)-1)/2)])
67 
68 m1,m2 = problem_9_3_8(list1, list2, 0, len(list1)-1, 0, len(list2)-1)
69 print(m1,m2)