max double slice sum

Solution to Max-Double-Slice-Sum by codility

25 JAN

January 25, 2014

Question: http://codility.com/demo/take-sample-test/max_double_slice_sum

Question Name: MaxDoubleSliceSum

A variant of the classic maximum subarray problem. We should travel the array twice. For the first travel, we compute and record the maximum sub-array sum, which ends at each position. At the second reverse travel, we compute and record the maximum sub-array sum, which starts at each position. Finally, we combine two sub-arrays into one double slice, and find out the maximum sum.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

def solution ( A ) :      A_len = len ( A )      # The length of array A        # Get the sum of maximum subarray, which ends this position      # Method: http://en.wikipedia.org/wiki/Maximum_subarray_problem      max_ending_here = [ 0 ] * A_len      max_ending_here_temp = 0      for index in xrange ( 1 , A_len - 1 ) :          max_ending_here_temp = max ( 0 , A [ index ] + max_ending_here_temp )          max_ending_here [ index ] = max_ending_here_temp        # Get the sum of maximum subarray, which begins this position      # The same method. But we travel from the tail to the head      max_beginning_here = [ 0 ] * A_len      max_beginning_here_temp = 0      for index in xrange ( A_len - 2 , 0 , - 1 ) :          max_beginning_here_temp = max ( 0 , A [ index ] + max_beginning_here_temp )          max_beginning_here [ index ] = max_beginning_here_temp        # Connect two subarray for a double_slice. If the first subarray      # ends at position i, the second subarray starts at position i+2.      # Then we compare each double slice to get the one with the      # greatest sum.      max_double_slice = 0      for index in xrange ( 0 , A_len - 2 ) :          max_double_slice = max ( max_double_slice ,                  max_ending_here [ index ] + max_beginning_here [ index + 2 ] )        return max_double_slice