最大子数组问题的不同解法比较

2017/3/24 22:38:54

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《算法导论》第四章 分治策略 练习4.1-3 要求比较三种方法的时间走势，找出递归算法和暴力算法的分界点（前期暴力算法会更快）。

该问题有三个常规解法：暴力、分治法、动态规划

 

 

实践代码：

1. # -*- coding: utf-8 -*-
2. from time import time
3. import numpy as np
4. import matplotlib.pyplot as plt
5. classMaxSubArraySolution:
6. def force( self, A ):
7. l = len(A)
8. if l is0:return0;
9. ts =[ A[0]]+[0]*( l -1)
10. # 以i为结束点，之前所有的元素求和
11. for i , j in enumerate(A[1:],1):
12. ts[i]= ts[i-1]+ j
13. # 设置双指针指向起始位置，依次求和
14. max_sum = ts[0]
15. for i , v1 in enumerate(ts[1:]):
16. for j , v2 in enumerate(ts[i:]):
17. arr_sum = v2 - ts[i]
18. max_sum = max(arr_sum , max_sum)
19. return max_sum
21. def divide(self , A ):
22. return self.divideAndConquerHelper( A ,0, len(A)-1)
24. def divideAndConquerHelper(self , A , low , high):
25. if low == high :return A[low]
26. mid =( low + high )/2
27. left_max = self.divideAndConquerHelper( A , low , mid)
28. right_max = self.divideAndConquerHelper( A , mid+1, high)
29. # 包含mid的情况
30. left_sum , ts = float('-inf'),0
31. for i in reversed(A[low:mid+1]):
32. ts=ts+i
33. left_sum = max( left_sum , ts )
34. right_sum , ts = float('-inf'),0
35. for j in A[mid+1:high+1]:
36. ts=ts+j
37. right_sum = max( right_sum , ts )
38. # print left_sum , right_sum
39. return max( max(left_max , right_max), left_sum+right_sum)
41. def dp( self , A ):
42. max_sum , ts =0,0
43. for i , v in enumerate(A):
44. ts = ts + v if ts + v >0else0
45. max_sum = max( max_sum , ts )
46. return max_sum
48. if __name__ =='__main__':
49. scalar = np.logspace(0,4,100)
50. #scalar = np.linspace(1,2000,20)
51. so =MaxSubArraySolution()
52. time_force , time_divide , time_dp =[],[],[]
53. for sc in scalar:
54. print sc
55. start = time()
56. max_sum = so.force( np.arange(sc))
57. end = time()
58. time_force.append( end - start )
59. #print "force : " , end - start
61. start = time()
62. max_sum = so.divide( np.arange(sc))
63. end = time()
64. time_divide.append( end - start )
65. #print "divide : " , end - start
67. start = time()
68. max_sum = so.dp( np.arange(sc))
69. end = time()
70. time_dp.append( end - start )
71. #print "dp : " , end - start
72. #print '---------------------'
74. plt.plot( scalar , time_force ,'r-', label='force')
75. plt.plot( scalar , time_divide ,'g-', label='divide')
76. plt.plot( scalar , time_dp ,'b-', label='dp')
77. plt.title('Time of Force , Divide , DP')
78. plt.legend()
79. plt.tight_layout()
80. plt.grid()
81. plt.show()