Software engineering Third personal job-maximum contiguous subarray and

Maximum contiguous Subarray and (maximum sub-segments and)

Question: A sequence of n integers (possibly negative numbers) a[1],a[2],a[3],..., A[n], and the maximum value of the sub-segments of the sequence, such as A[i]+a[i+1]+...+a[j], is obtained. When the given integer is negative, define the sub-segment and 0, according to this definition, the optimal value is: max{0,a[i]+a[i+1]+...+a[j]},1<=i<=j<=n
For example, when (a[1],a[2],a[3],a[4],a[5],a[6]) = ( -2,11,-4,13,-5,-2), the maximum child segment and is 20.
--Quote from "Baidu Encyclopedia"

Environment

• Language: Python 3.6

• Integrated development environment: Pycharm 2017.3

• Operating system: Arch Linux kernel version 4.15.12

1. Poor Lifting method

Coding

def  enumerate_arrays ( Numbers): Max_sum =  numbers[0 ] Num_len =  
    
     len  (Numbers) 
     for  i 
     in  
     range
       (Num_len): Tmp_sum =  numbers[i] max_sum =  max  (Tmp_sum, max_sum) for  J in  range (i +  1 , Num_len): Tmp_sum +=  number S[J] max_sum =  max  (Tmp_sum, max_sum) return  max  (0 , max_sum) 
     

Enumerates all successive sub-arrays, summing them separately, finding the maximum sum, and the time complexity of \ (O (n^2) \)

2.Kadane algorithm

Coding

def kadane_solve(numbers):    = numbers[0]    =0    forin numbers:        if<0:            = i        else:            += i        =max(tmp_sum, max_sum)    returnmax(0, max_sum)

If the accumulated value is negative, overwrite the accumulated value with the newly read-in value, otherwise continue to accumulate with a time complexity of \ (O (n) \)

Test Cases

Coding

ImportUnitTest fromHomework.a.aImportEnumerate_arrays fromHomework.a.aImportKadane_solveclassTestA (unittest. TestCase):defTestenumerate ( Self): NUM1=[-2, One,-4, -,-5,-2] Num2=[1,2,3] Num3=[-1,-2] Num4=[1] Self. Assertequal (Enumerate_arrays (NUM1), -) Self. Assertequal (Enumerate_arrays (num2),6) Self. Assertequal (Enumerate_arrays (num3),0) Self. Assertequal (Enumerate_arrays (NUM4),1)defTestkadane ( Self): NUM1=[-2, One,-4, -,-5,-2] Num2=[1,2,3] Num3=[-1,-2] Num4=[1] Self. Assertequal (Kadane_solve (NUM1), -) Self. Assertequal (Kadane_solve (num2),6) Self. Assertequal (Kadane_solve (num3),0) Self. Assertequal (Kadane_solve (NUM4),1)if __name__ == ' __main__ ': Unittest.main ()

Use the test cases provided in the topic and all positive numbers, all negative, single number test

Test results

• In the Pycharm:

, the test passes

• In the terminal:

Type the command:

python -m tests.test_a

, the test passes

Software engineering Third personal job-maximum contiguous subarray and