The Divide and Conquer Approach - 归并排序

Posted 2020-10-23 zzYzz

  1 The divide and conquer approach - 归并排序

  2     归并排序所应用的理论思想叫做分治法.
  3     分治法的思想是: 将问题分解为若干个规模较小,并且类似于原问题的子问题,
  4     然后递归(recursive) 求解这些子问题, 最后再合并这些子问题的解以求得
  5     原问题的解.
  6         即, 分解 -> 解决 -> 合并.
  7 
  8     The divide and conquer approach 
  9         分解: 将待排序的含有 n 个元素的的序列分解成两个具有 n/2 的两个子序列.
 10         解决: 使用归并排序递归地排序两个子序列.
 11         合并: 合并两个已排序的子序列得出结果.
 12 
 13     归并排序算法的 ‘时间复杂度‘ 是 nlogn
 14 
 15 import time, random
 16 
 17 def sortDivide(alist):     # 分解 divide
 18     if len(alist) <= 1:
 19         return alist
 20     l1 = sortDivide(alist[:alist.__len__()//2])
 21     l2 = sortDivide(alist[alist.__len__()//2:])
 22     return sortMerge(l1,l2)
 23 
 24 def sortMerge(l1, l2):     # 解决 & 合并  sort & merge
 25     listS = []
 26     print("Left - ", l1)
 27     print("Right - ", l2)
 28     i,j = 0,0
 29     while i < l1.__len__() and j < l2.__len__():
 30         if l1[i] <= l2[j]:
 31             listS.append(l1[i])
 32             i += 1
 33             print("-i", i)
 34         else:
 35             listS.append(l2[j])
 36             j += 1
 37             print("-j", j)
 38         print(listS)
 39     else:
 40         if i == l1.__len__():
 41             listS.extend(l2[j:])
 42         else:
 43             listS.extend(l1[i:])
 44         print(listS)
 45     print("Product -",listS)
 46     return listS
 47 
 48 def randomList(n,r):
 49     F = 0
 50     rlist = []
 51     while F < n:
 52         F += 1
 53         rlist.append(random.randrange(0,r))
 54     return rlist
 55 
 56 if __name__ == "__main__":
 57     alist = randomList(9,100)
 58     print("List-O",alist)
 59     startT =time.time()
 60     print("List-S", sortDivide(alist))
 61     endT = time.time()
 62     print("Time elapsed :", endT - startT)
 63 
 64 output,
 65     List-O [88, 79, 52, 78, 0, 43, 21, 55, 62]
 66     Left -  [88]
 67     Right -  [79]
 68     -j 1
 69     [79]
 70     [79, 88]
 71     Product - [79, 88]
 72     Left -  [52]
 73     Right -  [78]
 74     -i 1
 75     [52]
 76     [52, 78]
 77     Product - [52, 78]
 78     Left -  [79, 88]
 79     Right -  [52, 78]
 80     -j 1
 81     [52]
 82     -j 2
 83     [52, 78]
 84     [52, 78, 79, 88]
 85     Product - [52, 78, 79, 88]
 86     Left -  [0]
 87     Right -  [43]
 88     -i 1
 89     [0]
 90     [0, 43]
 91     Product - [0, 43]
 92     Left -  [55]
 93     Right -  [62]
 94     -i 1
 95     [55]
 96     [55, 62]
 97     Product - [55, 62]
 98     Left -  [21]
 99     Right -  [55, 62]
100     -i 1
101     [21]
102     [21, 55, 62]
103     Product - [21, 55, 62]
104     Left -  [0, 43]
105     Right -  [21, 55, 62]
106     -i 1
107     [0]
108     -j 1
109     [0, 21]
110     -i 2
111     [0, 21, 43]
112     [0, 21, 43, 55, 62]
113     Product - [0, 21, 43, 55, 62]
114     Left -  [52, 78, 79, 88]
115     Right -  [0, 21, 43, 55, 62]
116     -j 1
117     [0]
118     -j 2
119     [0, 21]
120     -j 3
121     [0, 21, 43]
122     -i 1
123     [0, 21, 43, 52]
124     -j 4
125     [0, 21, 43, 52, 55]
126     -j 5
127     [0, 21, 43, 52, 55, 62]
128     [0, 21, 43, 52, 55, 62, 78, 79, 88]
129     Product - [0, 21, 43, 52, 55, 62, 78, 79, 88]
130     List-S [0, 21, 43, 52, 55, 62, 78, 79, 88]
131     Time elapsed : 0.0010027885437011719